Internal Shear Layers Research Articles

Jet noise of a low bypass turbofan with internal mixing and external plug

Jet noise generated by turbofan engines which are designed for supersonic aircraft operation is expected to remain a challenge for the aerospace industry. For civil supersonic transport, low bypass ratio engines with internal mixing and external plugs are currently seen as promising exhaust architecture to meet aircraft mission and certification requirements. Measurements of the noise from a representative low-bypass ratio long duct mixed flow with external plug exhaust configuration were made, along with corresponding steady-RANS and LES analyses. The measured data showed excess high frequency noise across a wide range of operating conditions as compared to an equivalent single stream jet, or an equivalent uniform jet with internal plug. The absolute levels of the excess noise were relatively insensitive to forward flight, and the excess noise was most dominant when the primary and secondary streams had large velocity and temperature mismatch just upstream of the internal mixer. Preliminary indications from the LES analysis also indicated that significant pressure fluctuations, at the same frequencies which are insensitive to forward flight, develop inside the nozzle as the internal shear layer from the mixer grows and gets accelerated by the external plug. Parametric study test measurements on the fan and core operating conditions were performed, providing support for the hypothesis that the excess noise is generated as the internal shear layer, starting inside the nozzle, gets accelerated by the plug and passes through the weak shock at the nozzle exit where the flow accelerates more and turns over the external plug.

Internal shear layers in librating spherical shells: the case of attractors

Following our previous work on periodic ray paths (He et al., J. Fluid Mech., vol. 939, 2022, A3), we study asymptotically and numerically the structure of internal shear layers for very small Ekman numbers in a three-dimensional spherical shell and in a two-dimensional cylindrical annulus when the rays converge towards an attractor. We first show that the asymptotic solution obtained by propagating the self-similar solution generated at the critical latitude on the librating inner core describes the main features of the numerical solution. The internal shear layer structure and the scaling for its width and velocity amplitude in $E^{1/3}$ and $E^{1/12}$ , respectively, are recovered. The amplitude of the asymptotic solution is shown to decrease to $E^{1/6}$ when it reaches the attractor, as is also observed numerically. However, some discrepancies are observed close to the particular attractors along which the phase of the wave beam remains constant. Another asymptotic solution close to those attractors is then constructed using the model of Ogilvie (J. Fluid Mech., vol. 543, 2005, pp. 19–44). The solution obtained for the velocity has an $O(E^{1/6})$ amplitude, but a self-similar structure different from the critical-latitude solution. It also depends on the Ekman pumping at the contact points of the attractor with the boundaries. We demonstrate that it reproduces correctly the numerical solution. Surprisingly, the numerical solution close to an attractor with phase shift (that is, an attractor touching the axis in three or two dimensions with a symmetric forcing) is also found to be $O(E^{1/6})$ , but its amplitude is much weaker. However, its asymptotic structure remains a mystery.

Multiphase flow characteristics and gas loss in the shear layer on a ventilated supercavity wall

The shear flow on the large-scale gas–water wall inside a ventilated supercavity exhibits gas entrainment mode and determines the change law of the supercavity's gas loss, significantly impacting the shape and dynamics of the supercavity. Therefore, to develop an accurate prediction model and a ventilation control method for a supercavity under complex motion conditions, it is required to systematically and quantitatively study the shear flow characteristics and rules. This study calculates and comparatively analyzes the shear layers on either side of the supercavity wall based on numerical simulations of ventilated supercavitating flows in an unbounded field using the gas–vapor–water multi-fluid model. It is shown that the external shear layer with a very irregular outer boundary is considerably thinner than the internal shear layer. We further analyze the flow and distribution characteristics of all the phases in the shear layers with and without the influence of gravity. Our analysis confirms that all the phases exhibit a similar velocity change rule along the supercavity radial direction in the shear layer, whereas gas and water phases exhibit opposite radial phase distribution trends. It was also seen when natural cavitation occurs that the vapor phase is mainly distributed in the head of the supercavity. Moreover, at the same radial position, it was seen that the vapor velocity was higher than the gas velocity and slightly lower than the water velocity. Using the shear flow and phase distribution characteristics, a shear-layer gas loss model is established and validated for ventilated supercavitating flows.

Internal shear layers in librating spherical shells: the case of periodic characteristic paths

Internal shear layers generated by the longitudinal libration of the inner core in a spherical shell rotating at a rate $\varOmega ^*$ are analysed asymptotically and numerically. The forcing frequency is chosen as $\sqrt {2}\varOmega ^*$ such that the layers issued from the inner core at the critical latitude in the form of concentrated conical beams draw a simple rectangular pattern in meridional cross-sections. The asymptotic structure of the internal shear layers is described by extending the self-similar solution known for open domains to closed domains where reflections on the boundaries occur. The periodic ray path ensures that the beams remain localised around it. Asymptotic solutions for both the main beam along the critical line and the weaker secondary beam perpendicular to it are obtained. The asymptotic predictions are compared with direct numerical results obtained for Ekman numbers as low as $E=10^{-10}$ . The agreement between the asymptotic predictions and numerical results improves as the Ekman number decreases. The asymptotic scalings in $E^{1/12}$ and $E^{1/4}$ for the amplitudes of the main and secondary beams, respectively, are recovered numerically. Since the self-similar solution is singular on the axis, a new local asymptotic solution is derived close to the axis and is also validated numerically. This study demonstrates that, in the limit of vanishing Ekman numbers and for particular frequencies, the main features of the flow generated by a librating inner core are obtained by propagating through the spherical shell the self-similar solution generated by the singularity at the critical latitude on the inner core.

Physical and numerical study on the transition of gas leakage regime of ventilated cavitating flow

The objective of this paper is mainly to investigate the ventilated cavitating flow around an axisymmetric body with a focus on the gas leakage mechanisms via combining experimental and numerical methods. A high-speed camera technique is used to record the ventilated cavitating flow patterns. The numerical simulation is performed with a free surface model and Filter-based turbulence model (FBM). Good agreement can be obtained between the experimental and numerical results. In the formation of a ventilated cavity, there are three typical gas leakage types with different Froude numbers Fr and gas entrainment coefficients CQ, including RJ closure mode with gas leakage of toroidal vortex shedding (TVS-RJ), TV closure mode with gas leakage of twin-vortex tube entrainment (TVTE-TV), and the coexistence of toroidal vortex shedding and twin-vortex tube entrainment (TVS-TVTE). The internal flow characteristics revealed three distinct regions with the ventilated cavity, including the ventilation influence region, the internal shear layer and the reverse flow region. With the increase of CQ, the incline angle of the cavity bottom surface α gradually decreases. When the incline angle α decrease to a critical value of ∼17.1°, the flow separation disappears completely and the flow regime migrates completely to TV cavity from RJ cavity.

Outer-layer structure arrangements based on the large-scale zero-crossings at moderate Reynolds number

The structural arrangements in the outer layer of turbulent boundary layer flows were explored with large-field time-resolved particle image velocimetry measurements at moderate Reynolds number. The large- and small-scale structures were reconstructed by the modes of multiscale proper orthogonal decomposition. The association between hairpin packets and uniform momentum zones (UMZs) was examined by the conditional averaging results based on the large-scale positive-to-negative/negative-to-positive (PN/NP) zero-crossings. The scale arrangements provided the spatial evidence that the intense small-scale swirling motions are aligned in the confined internal shear layers along the backside of the large-scale, low-speed region, which was characterized by hairpin vortex packets. The uniform momentum zones (UMZs) conditioned on the large-scale PN/NP zero-crossings were detected from the histograms of the instantaneous streamwise velocity. The attached eddy behavior was consolidated based on the conditional events, by presenting the joint probability of UMZs thickness and wall-normal location. A close agreement of the conditional averaging raw velocity and modal velocity was examined. Moreover, the conditional averaging results of the UMZs interface probability exhibited a similar spatial distribution as the small-scale turbulent kinetic energy and swirling strength, which manifests the coincidence between the hairpin heads and the UMZs interfaces. This result was confirmed by the distribution of the wall-normal locations corresponding to the maximum value of interface probability and small-scale representations, which performs a streamwise inclination angle of 15°. The statistical spatial feature demonstrated the association between hairpin packets and uniform momentum as proposed by Adrian et al. [“Vortex organization in the outer region of the turbulent boundary layer,” J. Fluid Mech. 422, 1–54 (2000)].

Prograde vortices, internal shear layers and the Taylor microscale in high-Reynolds-number turbulent boundary layers

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The uniform-momentum zones and internal shear layers in turbulent pipe flows at Reynolds numbers up to [formula omitted

The statistical characteristics of the internal shear layers (ISL) and the coherent structures around the ISLs in turbulent pipe flows are examined using direct numerical simulation data at four Reynolds numbers Reτ=180, 360, 500 and 1000. The ISLs are defined by the peaks on the velocity gradients with no ad hoc filter applied on the ISL selection. This is different from the previous studies where uniform momentum zones (UMZs) are identified first using a velocity histogram and then the ISL is defined as an UMZ interface. In this study, ISLs are ranked by both their strength and location. The signature behaviours of the ISL including an abrupt streamwise velocity jump and a sharp decrease in velocity fluctuation across the ISL are confirmed. Both the positive and the negative ISLs are stronger towards the wall. The local imbalance between ejections and sweeps are observed around ISLs. Near-wall ISLs have stronger ejections while ISLs in the pipe centre have stronger sweeps. The balance between ejection and sweep is achieved approximately at 0.55-0.6 of the pipe radius for the range of Reynolds numbers studied. The flow structures around an ISL have been identified via 3D conditional sampling. The average positive ISL is located between the high-speed streak above and the low-speed streak below. The low-speed streak is associated with a pair of counter-rotating streamwise vortices which result in a strong ejection around the ISL.

Numerical study of a high-hydrogen micromix model burner using flamelet-generated manifold

The flamelet-generated manifolds (FGM) method was adopted in this study to consider the preferential diffusion in a high-hydrogen micro-mixing model burner. That is, when solving the FGM flamelet, accurate diffusion rate was obtained from two methods: multicomponent formulation and constant detailed Lewis numbers assumption. Then a new method of filling the thermochemical state and the source term in the mixture fraction and the process variable space also was proposed, namely the linear triangular dissection interpolation method, to predict the position of the hydrogen-rich micro-mixing flame front. Compared with the Fluent approach to establish the diffusion FGM flamelet, the results showed that the two FGMs have similar flame predictions in high hydrogen content fuels, and both can accurately capture the location of the internal and external shear layer boundaries of the micro-mixing multi-jet flame in the steady state, while the Fluent approach based on the uniform Lewis number assumption predicts results that deviated significantly from the experimental results. However, for the internal shear layer, both methods have large predicted OH gradients compared to the experimental results due to the lack of effective Lewis number correction for the control variable transport equation. The results using linear triangular dissection interpolation maybe superior to the method with linear interpolation of the process variable quenching boundary toward zero, which leads to flashback due to overestimation of the process variable source term in the region below the diffusion FGM quenching boundary.

Analysis of the Unsteady Flow Field Inside a Fan-Shaped Cooling Hole Predicted by Large Eddy Simulation

Abstract Film cooling is a common technique to manage turbine vane and blade thermal environment. Optimizing its cooling efficiency is furthermore an active research topic which goes in hand with a strong knowledge of the flow associated with a cooling hole. The following paper aims at developing deeper understanding of the flow physics associated with a standard cooling hole and helping guide future cooling optimization strategies. For this purpose, large eddy simulations (LESs) of the 7-7-7 fan-shaped cooling hole are performed and the flow inside the cooling hole is studied and discussed. Use of mathematical techniques such as the fast Fourier transforms (FFTs) and dynamic mode decomposition (DMD) is done to quantitatively access the flow modal structure inside the hole based on the LES unsteady predictions. Using these techniques, distinct vortex features inside the cooling hole are captured. These features mainly coincide with the roll-up of the internal shear layer formed at the interface of the separation region at the hole-inlet. The topology of these vortex features is discussed in detail and it is also shown how the expansion of the cross section in case of shaped holes aids in breaking down these vortices. Indeed upon escaping, these large-scale features are known to not be always beneficial to film cooling effectiveness.

A self-sustaining process theory for uniform momentum zones and internal shear layers in high Reynolds number shear flows

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Internal shear layers and edges of uniform momentum zones in a turbulent pipe flow

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Reflection of oscillating internal shear layers: nonlinear corrections

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The magnetorotational instability prefers three dimensions.

The magnetorotational instability (MRI) occurs when a weak magnetic field destabilizes a rotating, electrically conducting fluid with inwardly increasing angular velocity. The MRI is essential to astrophysical disc theory where the shear is typically Keplerian. Internal shear layers in stars may also be MRI-unstable, and they take a wide range of profiles, including near-critical. We show that the fastest growing modes of an ideal magnetofluid are three-dimensional provided the shear rate, S, is near the two-dimensional onset value, S c . For a Keplerian shear, three-dimensional modes are unstable above S ≈ 0.10S c , and dominate the two-dimensional modes until S ≈ 2.05S c . These three-dimensional modes dominate for shear profiles relevant to stars and at magnetic Prandtl numbers relevant to liquid-metal laboratory experiments. Significant numbers of rapidly growing three-dimensional modes remainy well past 2.05S c . These finding are significant in three ways. First, weakly nonlinear theory suggests that the MRI saturates by pushing the shear rate to its critical value. This can happen for systems, such as stars and laboratory experiments, that can rearrange their angular velocity profiles. Second, the non-normal character and large transient growth of MRI modes should be important whenever three-dimensionality exists. Finally, three-dimensional growth suggests direct dynamo action driven from the linear instability.

How the turbulent/non-turbulent interface is different from internal turbulence

The average patterns of the velocity and scalar fields near turbulent/non-turbulent interfaces (TNTI), obtained from direct numerical simulations (DNS) of planar turbulent jets and shear free turbulence, are assessed in the strain eigenframe. These flow patterns help to clarify many aspects of the flow dynamics, including a passive scalar, near a TNTI layer, that are otherwise not easily and clearly assessed. The averaged flow field near the TNTI layer exhibits a saddle-node flow topology associated with a vortex in one half of the interface, while the other half of the interface consists of a shear layer. This observed flow pattern is thus very different from the shear-layer structure consisting of two aligned vortical motions bounded by two large-scale regions of uniform flow, that typically characterizes the average strain field in the fully developed turbulent regions. Moreover, strain dominates over vorticity near the TNTI layer, in contrast to internal turbulence. Consequently, the most compressive principal straining direction is perpendicular to the TNTI layer, and the characteristic 45-degree angle displayed in internal shear layers is not observed at the TNTI layer. The particular flow pattern observed near the TNTI layer has important consequences for the dynamics of a passive scalar field, and explains why regions of particularly high scalar gradient (magnitude) are typically found at TNTIs separating fluid with different levels of scalar concentration. Finally, it is demonstrated that, within the fully developed internal turbulent region, the scalar gradient exhibits an angle with the most compressive straining direction with a peak probability at around 20$^{\text{o}}$. The scalar gradient and the most compressive strain are not preferentially aligned, as has been considered for many years. The misconception originated from an ambiguous definition of the positive directions of the strain eigenvectors.

Three-dimensional interaction of a shock with a thin non-circular channel of low-density gas

Numerical simulation of three-dimensional interaction of a shock with thin circular or non-circular – elliptic or rectangular – low-density gas channel is presented. Euler’s equations for inviscid gas are solved using 5th-order finite-difference WENO scheme. Large-scaled shock wave precursor structure is described in detail. It is shown that in three-dimensional flow internal shear layer instabilities develop faster than in axisymmetric case. High-pressure jet cumulation effect is found to amplify moderately for elliptic and rectangular cases. An influence of channel cross-section shape on the precursor growth rate is studied. It is found that the duration of linear precursor growth phase is greatly increased for stretched channel cross-section shapes.

Spatial Effects of Interaction of a Shock with a Lateral Low-Density Gas Channel

Three-dimensional interaction of a shock with lateral low-density gas channel of round, elliptic or rectangular cross-section is numerically studied using Euler’s equations. The structure of formed shock wave precursor is described in detail. Internal shear layer instabilities in three-dimensional flow are shown to develop faster than in axisymmetric case. Moderate amplification of high-pressure jet cumulation effect is noted for elliptic and rectangular channel cases. Dependence of precursor growth rate on cross-section shape is studied. It is found that stretching of cross-section shape significantly increases the duration of linear precursor growth phase.

The Rotational Shear Layer inside the Early Red-giant Star KIC 4448777

Abstract We present the asteroseismic study of the early red-giant star KIC 4448777, complementing and integrating a previous work, aimed at characterizing the dynamics of its interior by analyzing the overall set of data collected by the Kepler satellite during the four years of its first nominal mission. We adopted the Bayesian inference code diamonds for the peak bagging analysis and asteroseismic splitting inversion methods to derive the internal rotational profile of the star. The detection of new splittings of mixed modes, which are more concentrated in the very inner part of the helium core, allowed us to reconstruct the angular velocity profile deeper into the interior of the star and to disentangle the details better than in Paper I: the helium core rotates almost rigidly about 6 times faster than the convective envelope, while part of the hydrogen shell seems to rotate at a constant velocity about 1.15 times lower than the He core. In particular, we studied the internal shear layer between the fast-rotating radiative interior and the slow convective zone and we found that it lies partially inside the hydrogen shell above r ≃ 0.05R and extends across the core–envelope boundary. Finally, we theoretically explored the possibility for the future capabilty to sound the convective envelope in the red-giant stars and we concluded that the inversion of a set of splittings with only low-harmonic degree l ≤ 3, even supposing a very large number of modes, will not allow us to resolve the rotational profile of this region in detail.

Magnetohydrodynamic pressure drop and flow balancing of liquid metal flow in a prototypic fusion blanket manifold

Understanding magnetohydrodynamic (MHD) phenomena associated with the flow of electrically conducting fluids in complex geometry ducts subject to a strong magnetic field is required to effectively design liquid metal (LM) blankets for fusion reactors. Particularly, accurately predicting the 3D MHD pressure drop and flow distribution is important. To investigate these topics, we simulate a LM MHD flow through an electrically non-conducting prototypic manifold for a wide range of flow and geometry parameters using a 3D MHD solver, HyPerComp incompressible MHD solver for arbitrary geometry. The reference manifold geometry consists of a rectangular feeding duct which suddenly expands such that the duct thickness in the magnetic field direction abruptly increases by a factor rexp. Downstream of the sudden expansion, the LM is distributed into several parallel channels. As a first step in qualifying the flow, a magnitude of the curl of the induced Lorentz force was used to distinguish between inviscid, irrotational core flows and boundary and internal shear layers where inertia and/or viscous forces are important. Scaling laws have been obtained which characterize the 3D MHD pressure drop and flow balancing as a function of the flow parameters and the manifold geometry. Associated Hartmann and Reynolds numbers in the computations were ∼103 and ∼101-103, respectively, while rexp was varied from 4 to 12. An accurate model for the pressure drop was developed for the first time for inertial-electromagnetic and viscous-electromagnetic regimes based on 96 computed cases. Analysis shows that flow balance can be improved by lengthening the distance between the manifold inlet and the entrances of the parallel channels by utilizing the effect of flow transitioning to a quasi-two-dimensional state in the expansion region of the manifold.

Librational forcing of a rapidly rotating fluid-filled cube

The flow response of a rapidly rotating fluid-filled cube to low-amplitude librational forcing is investigated numerically. Librational forcing is the harmonic modulation of the mean rotation rate. The rotating cube supports inertial waves which may be excited by libration frequencies less than twice the rotation frequency. The response is comprised of two main components: resonant excitation of the inviscid inertial eigenmodes of the cube, and internal shear layers whose orientation is governed by the inviscid dispersion relation. The internal shear layers are driven by the fluxes in the forced boundary layers on walls orthogonal to the rotation axis and originate at the edges where these walls meet the walls parallel to the rotation axis, and are hence called edge beams. The relative contributions to the response from these components is obscured if the mean rotation period is not small enough compared to the viscous dissipation time, i.e. if the Ekman number is too large. We conduct simulations of the Navier–Stokes equations with no-slip boundary conditions using parameter values corresponding to a recent set of laboratory experiments, and reproduce the experimental observations and measurements. Then, we reduce the Ekman number by one and a half orders of magnitude, allowing for a better identification and quantification of the contributions to the response from the eigenmodes and the edge beams.