Laminar Base Flow Research Articles

Influence of bow shape and model scale on the natural transition in boundary layers on underwater axisymmetric bodies with a superhydrophobic surface

This study uses numerical methods to investigate the influence of bow shape and model scale on the natural transition in bow boundary layers on underwater axisymmetric bodies with a superhydrophobic surface. The transition locations for eight bow shapes and four model scales are predicted by using the eN method, which is based on a linear stability theory. The results show that the superhydrophobic surface always stabilizes the boundary layer and delays the transition for different bow shapes and model scales. However, differences are observed in the basic laminar flow, boundary-layer stability, and transition location when different bow shapes are used. These differences are not prominent at the small model scale, but become significant at the medium and large model scales. As the model scale increases, the transition location in the boundary layer on the superhydrophobic surface moves upstream and then downstream, leading to a “dangerous” scale, at which the transition location is closest to the leading edge. Furthermore, this study provides the optimal bow shape with the latest transition location at each model scale, and the optimal bow shape with the longest transition delay distance.

Linear temporal stability of Jeffery–Hamel flow of nanofluids

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 μnf=μf/(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 (Rρ=ρs/ρf). For ϕ∈(0,0.1], flow stabilization occurs with ϕ when Rρ<3.5000, while destabilization is observed when Rρ>4.0135. Notably, nanoparticles exhibit a negligible impact on flow stability when 3.5000≤Rρ≤4.0135.

Influence of distributed hydrogen injection and combustion on supersonic boundary layer stability and transition

This theoretical study recorded the influence of the distributed injection of hydrogen through a permeable surface and its combustion on the stability and transition of a supersonic boundary layer (BL). The laminar base flow for a multicomponent flat-plate BL was computed using the computational fluid dynamics solver with finite-rate chemistry for free-stream Mach number (M) = 2. Linear stability theory (LST) equations for a reactive gas mixture were derived in the local parallel base flow approximation. Stability calculations based on the developed theory revealed the possibility of a decrease in the local spatial amplification rates of unstable perturbations. A double reversal in the maximal amplification rate magnitudes of perturbations was obtained, wherein at first, they increased, then decreased to zero, and then rose again. The influence of the distributed injection and combustion of hydrogen in the supersonic BL on the position of the laminar-turbulent transition was estimated using the LST-based eN-method. Calculated and experimentally obtained dependencies of the relative transition Reynolds number on the relative mass flow rate of injected hydrogen were compared. It was found that depending upon the flow conditions, the hydrogen diffusion flame could accelerate or decelerate the transition in the supersonic M = 2 BL, when compared to absence of hydrogen burning. Two counteracting effects compete: heat supply by combustion exerts stabilizing influence, while low-molecular-weight gas blowing from the surface exerts destabilizing influence. Depending on the interplay of these two factors, it would be possible to obtain acceleration or deceleration of transition.

Global receptivity analysis: physically realizable input–output analysis

In the context of transition analysis, linear input–output analysis determines the worst-case disturbances to a laminar base flow based on a generic right-hand-side volumetric/boundary forcing term. The worst-case forcing is not physically realizable, and, to our knowledge, a generic framework for posing physically realizable worst-case disturbance problems is lacking. In natural receptivity analysis, disturbances are forced by matching (typically local) solutions within the boundary layer to outer solutions consisting of free-stream vortical, entropic and acoustic disturbances. We pose a scattering formalism to restrict the input forcing to a set of realizable disturbances associated with plane-wave solutions of the outer problem. The formulation is validated by comparing with direct numerical simulations of a Mach 4.5 flat-plate boundary layer. We show that the method provides insight into transition mechanisms by identifying those linear combinations of plane-wave disturbances that maximize energy amplification over a range of frequencies. We also discuss how the framework can be extended to accommodate scattering from shocks and in shock layers for supersonic flow.

Instability and Transition of Hypersonic Boundary Layer on a Blunted Delta Wing

The instability and transition of hypersonic boundary layer on a blunted delta wing is performed by numerical simulation of experiments conducted in the quiet wind tunnel. Disturbances are calculated using linear stability theory to obtain the integrated disturbance growth rates and amplification factors from laminar steady base flows. Comparisons are made between the results of the stability analysis and the experimentally measured transition characteristics. The results show that the generalized inflections existing in velocity profiles reveal both the streamwise instability and crossflow instability of the boundary layer on the delta wing. In the parameter spaces of frequency and wave number, there is only one unstable region in which the first-mode and second-mode waves are integrated with each other at angle of attack, whereas the unstable regions of the first-mode and second-mode waves are separately distributed at angle of attack of . The numerically predicted factor distribution is in good agreement with the measured transition front, and the factor is about 3 when boundary-layer transition occurs. The low-frequency unstable waves with about 25–30 kHz play a key role in dominating the boundary-layer transition of the delta wing.

Oblique transition in hypersonic double-wedge flow

We utilize resolvent and weakly nonlinear analyses in combination with direct numerical simulations (DNS) to identify mechanisms for oblique transition in a Mach $5$ hypersonic flow over an adiabatic slender double wedge. Even though the laminar separated flow is globally stable, resolvent analysis demonstrates significant amplification of unsteady external disturbances to the linearized flow equations. These disturbances are introduced upstream of the separation zone and they lead to the appearance of oblique waves further downstream. We demonstrate that the large amplification of oblique waves arises from the growth of fluctuation shear stress due to streamline curvature of the laminar base flow in the separated shear layer. This is in contrast to the attached boundary layers, where no such mechanism exists. We also use a weakly nonlinear analysis to show that the resolvent operator associated with linearization around the laminar base flow governs the evolution of steady reattachment streaks that arise from quadratic interactions of unsteady oblique waves. These quadratic interactions generate vortical excitations in the reattaching shear layer which lead to the formation of streaks in the recirculation zone and their subsequent amplification, breakdown and transition to turbulence downstream. Our analysis of the energy budget shows that deceleration of the base flow near reattachment is primarily responsible for amplification of steady streaks. Finally, we employ DNS to examine latter stages of transition to turbulence and demonstrate the predictive power of a weakly nonlinear input–output framework in uncovering triggering mechanisms for oblique transition in separated high-speed boundary layer flows.

Simulation of turbulent flow over roughness strips

Heterogeneous roughness in the form of streamwise aligned strips is known to generate large scale secondary motions under turbulent flow conditions that can induce the intriguing feature of larger flow rates above rough than smooth surface parts. The hydrodynamical definition of a surface roughness includes a large scale separation between the roughness height and the boundary layer thickness which is directly related to the fact that the drag of a laminar flow is not altered by the presence of roughness. Existing simplified approaches for direct numerical simulation of roughness strips do not fulfil this requirement of an unmodified laminar base flow compared with a smooth wall reference. It is shown that disturbances induced in a modified laminar base flow can trigger large-scale motions with resemblance to turbulent secondary flow. We propose a simple roughness model that allows us to capture the particular features of turbulent secondary flow without impacting the laminar base flow. The roughness model is based on the prescription of a spanwise slip length, a quantity that can directly be translated into the Hama roughness function for a homogeneous rough surface. The heterogeneous application of the slip-length boundary condition results in very good agreement with existing experimental data in terms of the secondary flow topology. In addition, the proposed modelling approach allows us to quantitatively evaluate the drag increasing contribution of the secondary flow. Both the secondary flow itself and the related drag increase reveal a very small dependence on the gradient of the transition between rough and smooth surface parts only. Interestingly, the observed drag increase due to secondary flows above the modelled roughness is significantly smaller than the one previously reported for roughness resolving simulations. We hypothesise that this difference arises from the fact that roughness resolving simulations cannot truly fulfil the requirement of large scale separation.

Linear modal instabilities around post-stall swept finite wings at low Reynolds numbers

Linear modal instabilities of flow over untapered wings with aspect ratios$AR=4$and 8, based on the NACA 0015 profile, have been investigated numerically over a range of angles of attack,$\alpha$, and angles of sweep,$\varLambda$, at chord Reynolds numbers$100\le Re\le 400$. Laminar base flows have been generated using direct numerical simulation and selective frequency damping, as appropriate. Several families of unstable three-dimensional linear global (TriGlobal) eigenmodes have been identified and their dependence on geometric parameters has been examined in detail at$Re=400$. The leading global mode A is associated with the peak recirculation in the three-dimensional laminar separation bubble formed on the wing and becomes unstable when recirculation reaches$\textit {O}(10\,\%)$. On unswept wings, this mode peaks in the midspan region of the wake and moves towards the wing tip with increasing$\varLambda$, following the displacement of peak recirculation; its linear amplification leads to wake unsteadiness. Additional amplified modes exist at nearly the same and higher frequencies compared to mode A. The critical$Re$has been identified and it is shown that amplification increases with increasing sweep, up to$\varLambda \approx 10^\circ$. At higher$\varLambda$, all global modes become less amplified and are ultimately stable at$\varLambda =30^\circ$. An increase in amplification of the leading mode with sweep was not observed over the$AR=4$wing, where tip vortex effects were shown to dominate.

Direct numerical simulation of interaction between a stationary crossflow instability and forward-facing steps

The interaction between forward-facing steps of several heights and a pre-existing critical stationary crossflow instability of a swept-wing boundary layer is analysed. Direct numerical simulations (DNS) are performed of the incompressible three-dimensional laminar base flow and the stationary distorted flow that arise from the interaction between an imposed primary stationary crossflow perturbation and the steps. These DNS are complemented with solutions of the linear and the nonlinear parabolised stability equations, used towards identifying the influence of linearity and non-parallelism near the step. A fully stationary solution of the Navier–Stokes equations is enforced numerically, in order to isolate the mechanisms pertaining to the interaction of the stationary disturbance with the step. Results provide insight into the salient modifications of the base laminar boundary layer due to the step, and the response of the incoming crossflow instability to these changes. The fundamental spanwise Fourier mode of the disturbance field gradually lifts up as it approaches the step and passes over it. The flow environment around the step is characterised by a sudden spanwise modulation of the base-flow streamlines. Additional stationary perturbation structures are induced at the step, which manifest in the form of spanwise-aligned velocity streaks near the wall. Shortly downstream of the step, the fundamental component of the crossflow perturbation maintains a rather constant amplification for the smallest steps studied. For the largest step, however, the fundamental crossflow perturbation is stabilised significantly shortly downstream of the largest step. This surprising result is ascribed to a modulation of the kinetic energy transfer between the base flow and the fundamental perturbation field, which is brought forward as a new step interaction mechanism. Possible non-modal growth effects at the step are discussed. Furthermore, the results from DNS indicate significant amplification of the high-order harmonic crossflow components downstream of the step.

Numerical investigation of the natural transition in flat-plate boundary layers on superhydrophobic surfaces considering the influence of the leading edge region

The natural transition in flat-plate boundary layers on superhydrophobic surfaces is studied while considering the influence of the leading edge region. A method for calculating basic laminar flow on superhydrophobic surfaces while considering the influence of the leading edge region is proposed, which accurately obtains the flow field in the whole computational domain from the leading edge region to the downstream region with acceptable computational load. The results obtained by this method are compared to those ignoring the influence of the leading edge region, such that this influence can be seen. The influence decreases the thickness of the laminar boundary layers on superhydrophobic surfaces and increases the slip velocity on the wall. The linear stability of the boundary layers is also analyzed. The influence of the leading edge region delays the critical location of flow instability on superhydrophobic surfaces and narrows the unstable zone. The eN method is used to predict the transition locations. The influence of the leading edge region further delays the transition location, and the transition delay effect becomes stronger as the slip length or the oncoming flow velocity increases. Furthermore, a method for predicting the spectrum of wall fluctuating pressure in the laminar flow region over underwater vehicles is proposed. At the downstream region, the amplitude of the wall fluctuating pressure increases and the frequency range decreases. Superhydrophobic surfaces suppress the wall fluctuating pressure, and the influence of the leading edge region enhances this suppression effect.

Rapid thermalization by adaptive flow reorientation

Aim of this paper is the enhancement of scalar transport (heat, chemical species) in flow systems with reorientations of a laminar base flow. Conventional heating/mixing protocols comprise of temporal or spatial periodic reorientations of these base flows to promote fluid mixing. However, thermal homogenisation rates of scalar fields are not necessarily accelerated with these approaches due to the substantial effect of diffusion and/or chemical reactions on heat/chemical transport. In the present study we numerically study heat transport with an adaptive approach for an entire parameter space of fluid and flow properties. Key to the approach is real-time control of the fluid flow based on the scalar field due to an efficient numerical model. Results show that the adaptive approach can significantly enhance heat transport over the conventional periodic heating/mixing approach designed for efficient mixing.

Evolution of instability modes in Mach 10 frozen and chemically reacting boundary layers by means of non-linear parabolized stability equations

The physical mechanisms and laminar-to-turbulent transition scenarios characterizing hypersonic flows are not yet completely identified and well described as in low-supersonic and subsonic regimes. Particularly, there is a lack of knowledge about the role chemistry plays and the effects that high temperature has on the transition non-linear stages. In this study, transition in a Mach 10 adiabatic flat-plate boundary layer is investigated by means of non-linear parabolized stability equations, considering both frozen and chemical non-equilibrium (CNE) flow assumptions. A tendency to switch from a H- to a K-type transition scenario at the increment of the primary-mode initial amplitude is found, similar to what occurs in subsonic and low-supersonic regimes. Secondary-waves' initial amplitudes do not affect directly the occurring breakdown type, but they significantly influence the evolution of the higher harmonics, in particular the generation of streamwise steady vortices. Chemical reactions play an indirect role in transition through the determination of the laminar base flow and the linear stability characteristics of the primary instability. Excitation of secondary modes is weaker in CNE than in frozen conditions, but qualitatively similar. Contrary to previous studies, assuming frozen perturbations in a chemically reacting base flow is found to have a significant effect on the higher-harmonics amplitudes, in particular on the relative evolution of the secondary modes.

Stability analysis and transition prediction of streamwise vortices over a yawed cone at Mach 6

An investigation into the linear instability of streamwise vortices over a yawed blunt cone with a half-angle of 7° at 6° angle of attack, a free-stream Mach number of 6, and a Reynolds number of 1.0 × 107/m was performed. The steady laminar base flow obtained using direct numerical simulation (DNS) has a mushroom structure. Three classes of unstable modes (inner mode, outer mode, and Mack mode modified by the streamwise vortices) were identified using a two-dimensional spatial global stability analysis (bi-global). Among them, the inner mode and the modified Mack mode were discovered for the first time for such a configuration. Notably, the inner mode appears only over a short distance upstream of the cone, and its energy is mainly in the vicinity of the symmetry plane of the mushroom structure. By comparing with DNS results, it was shown that multiple instability modes can coexist physically during the transition in the leeward plane. In addition, the eN method based on global stability theory was used to predict the location of the transition along the centerline on the leeward side of the cone. It was found that the inner modes grow rapidly in the upstream region, while the outer mode near the stem of the mushroom structure dominates the transition in the downstream region. Further analysis suggests that the inner modes dominate the transition only in a noisy environment, whereas the traditional centerline modes dominate the transition in quiet free-stream conditions.

From Bypass Transition to Flow Control and Data-Driven Turbulence Modeling: An Input–Output Viewpoint

Transient growth and resolvent analyses are routinely used to assess nonasymptotic properties of fluid flows. In particular, resolvent analysis can be interpreted as a special case of viewing flow dynamics as an open system in which free-stream turbulence, surface roughness, and other irregularities provide sources of input forcing. We offer a comprehensive summary of the tools that can be employed to probe the dynamics of fluctuations around a laminar or turbulent base flow in the presence of such stochastic or deterministic input forcing and describe how input–output techniques enhance resolvent analysis. Specifically, physical insights that may remain hidden in the resolvent analysis are gained by detailed examination of input–output responses between spatially localized body forces and selected linear combinations of state variables. This differentiating feature plays a key role in quantifying the importance of different mechanisms for bypass transition in wall-bounded shear flows and in explaining how turbulent jets generate noise. We highlight the utility of a stochastic framework, with white or colored inputs, in addressing a variety of open challenges including transition in complex fluids, flow control, and physics-aware data-driven turbulence modeling. Applications with temporally or spatially periodic base flows are discussed and future research directions are outlined.

Statistical transition to turbulence in plane channel flow

Intermittent turbulent-laminar patterns characterize the transition to turbulence in pipe, plane Couette and plane channel flows. The time evolution of turbulent-laminar bands in plane channel flow is studied via direct numerical simulations using the parallel pseudospectral code ChannelFlow in a narrow computational domain tilted by $24^{\circ}$ with respect to the streamwise direction. Mutual interactions between bands are studied through their propagation velocities. Energy profiles show that the flow surrounding isolated turbulent bands returns to the laminar base flow over large distances. Depending on the Reynolds number, a turbulent band can either decay to laminar flow or split into two bands. As with past studies of other wall-bounded shear flows, in most cases survival probabilities are found to be consistent with exponential distributions for both decay and splitting, indicating that the processes are memoryless. Statistically estimated mean lifetimes for decay and splitting are plotted as a function of the Reynolds number and lead to the estimation of a critical Reynolds number $Re_{\text{cross}}\simeq 965$, where decay and splitting lifetimes cross at greater than $10^6$ advective time units. The processes of splitting and decay are also examined through analysis of their Fourier spectra. The dynamics of large-scale spectral components seem to statistically follow the same pathway during the splitting of a turbulent band and may be considered as precursors of splitting.

Toward the Highly Ordered Lamellar Hybrid Membrane for Molecular Sieving by One-Pot Self-Assembly of Hybrid Hyperbranched Polymer

Ordered lamellar hybrid membranes are of great interest, due to their application as functional materials, including molecular sieving, biosensors, optical devices, and drug, as well as gene delive...

Transitional Flow Dynamics Behind a Micro-Ramp

Micro-ramps are popular passive flow control devices which can delay flow separation by re-energising the lower portion of the boundary layer. We compute the laminar base flow, the instantaneous transitional flow, and the mean flow around a micro-ramp immersed in a quasi-incompressible boundary layer at supercritical roughness Reynolds number. Results of our Direct Numerical Simulations (DNS) are compared with results of BiLocal stability analysis on the DNS base flow and independent tomographic Particle Image Velocimetry (tomo-PIV) experiments. We analyse relevant flow structures developing in the micro-ramp wake and assess their role in the micro-ramp functionality, i.e., in increasing the near-wall momentum. The main flow feature of the base flow is a pair of streamwise counter-rotating vortices induced by the micro-ramp, the so-called primary vortex pair. In the instantaneous transitional flow, the primary vortex pair breaks up into large-scale hairpin vortices, which arise due to linear varicose instability of the base flow, and unsteady secondary vortices develop. Instantaneous vortical structures obtained by DNS and experiments are in good agreement. Matching linear disturbance growth rates from DNS and linear stability analysis are obtained until eight micro-ramp heights downstream of the micro-ramp. For the setup considered in this article, we show that the working principle of the micro-ramp is different from that of classical vortex generators; we find that transitional perturbations are more efficient in increasing the near-wall momentum in the mean flow than the laminar primary vortices in the base flow.

Acoustic impedance and hydrodynamic instability of the flow through a circular aperture in a thick plate

We study the unsteady flow of a viscous fluid passing through a circular aperture in aplate characterized by a non-zero thickness. We investigate this problem by solving theincompressible Linearized Navier-Stokes Equations (LNSE) around a laminar base flow,in both the forced case (allowing to characterize the coupling of the flow with acousticresonators) and the autonomous regime (allowing to identify the possibility of purelyhydrodynamical instabilities). In the forced case, we calculate the impedances and discussthe stability properties in terms of a Nyquist diagram. We show that such diagramsallow us to predict two kinds of instabilities: (i) a conditional instability linked to theoverreflexion of an acoustic wave but requiring the existence of an conveniently tunedexternal acoustic resonator, and (ii) a purely hydrodynamic instability existing even in astrictly incompressible framework. A parametric study is conducted to predict the rangeof existence of both instabilities in terms of the Reynolds number and the aspect ratio ofthe aperture. Analysing the structure of the linearly forced flow allows to show that theinstability mechanism is closely linked to the existence of a recirculation region withinthe thickness of the plate. We then investigate the autonomous regime using the classicalnormal-mode ansatz. The analysis confirms the existence of the purely hydrodynamicalinstability in accordance with the impedance-based criterion. The spatial structure ofthe unstable eigenmodes are found to be similar to the structure of the correspondingunsteady flows computed using the forced problem. Analysis of the adjoint eigenmodesand of the adjoint-based structural sensitivity confirms that the origin of the unstabilitylies in the recirculation region existing within the thickness of the plate.

Linear instability of Poiseuille flows with highly non-ideal fluids

The objective of this work is to investigate linear modal and algebraic instability in Poiseuille flows with fluids close to their vapour–liquid critical point. Close to this critical point, the ideal gas assumption does not hold and large non-ideal fluid behaviours occur. As a representative non-ideal fluid, we consider supercritical carbon dioxide ($\text{CO}_{2}$) at a pressure of 80 bar, which is above its critical pressure of 73.9 bar. The Poiseuille flow is characterized by the Reynolds number ($Re=\unicode[STIX]{x1D70C}_{w}^{\ast }u_{r}^{\ast }h^{\ast }/\unicode[STIX]{x1D707}_{w}^{\ast }$), the product of the Prandtl ($Pr=\unicode[STIX]{x1D707}_{w}^{\ast }C_{pw}^{\ast }/\unicode[STIX]{x1D705}_{w}^{\ast }$) and Eckert numbers ($Ec=u_{r}^{\ast 2}/C_{pw}^{\ast }T_{w}^{\ast }$) and the wall temperature that in addition to pressure determine the thermodynamic reference condition. For low Eckert numbers, the flow is essentially isothermal and no difference with the well-known stability behaviour of incompressible flows is observed. However, if the Eckert number increases, the viscous heating causes gradients of thermodynamic and transport properties, and non-ideal gas effects become significant. Three regimes of the laminar base flow can be considered: the subcritical (temperature in the channel is entirely below its pseudo-critical value), transcritical and supercritical temperature regimes. If compared to the linear stability of an ideal gas Poiseuille flow, we show that the base flow is modally more unstable in the subcritical regime, inviscid unstable in the transcritical regime and significantly more stable in the supercritical regime. Following the principle of corresponding states, we expect that qualitatively similar results will be obtained for other fluids at equivalent thermodynamic states.

Complexity of the laminar-turbulent boundary in pipe flow

Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of states that separate laminar and turbulent regions of the state space. In addition, some studies determined invariant solutions that reside on this edge. In this paper, we study the unstable manifold of one such solution with the aid of continuous symmetry-reduction, which we formulate here for the first time for the simultaneous quotiening of axial and azimuthal symmetries. Upon our investigation of the unstable manifold, we discover a previously unknown traveling wave solution on the laminar-turbulent boundary with a relatively complex structure. By means of low-dimensional projections, we visualize different dynamical paths that connect these solutions to the turbulence. Our numerical experiments demonstrate that the laminar-turbulent boundary exhibits qualitatively different regions whose properties are influenced by the nearby invariant solutions.