Flow Boundary Research Articles

Using transducerless time-domain thermoreflectance technique to measure in- and cross-plane thermal conductivity of nanofilms

Time-domain thermoreflectance (TDTR) and frequency-domain thermoreflectance techniques have been widely used to measure thermal properties. However, the existence of the metal sensor brings some limitations to the experimental measurement, such as temperature limits, disability to measure low in-plane thermal conductivity, in situ measurement cannot be achieved, etc. This paper proposes a transducerless time-domain thermoreflectance method to measure in- and cross-plane thermal conductivity of nanofilms, in which the optical absorption depth and thermal conductivity tensor are considered to establish a new differential equation that can describe the heat conduction process in multilayer structures. This thermal model can also calculate the effects of spot ellipticity and spot offset distance. Then, the analytical solution and relative deviation of this new model and the surface heat flow boundary model used in conventional TDTR are compared by calculating the phase signals. In terms of experimental measurement, this model is successfully used to derive cross- and in-plane thermal conductivity of PdSi and IrNiTa amorphous alloy nanofilms without a metal sensor.

Analysis of Steady Groundwater Flow in Confined Aquifer Due to Long-Strip Pit Dewatering with Suspended Cut-Off Wall

This study investigates the steady flow resulting from dewatering by a partially penetrating well in a confined aquifer with a cut-off barrier. By considering flow in both horizontal and vertical directions and incorporating the barrier and pumping well as flow boundary conditions, separate mathematical models are established for the inside and outside of the cut-off barrier. The interaction between these zones is ensured through continuous conditions along the opening of the two zones. A semi-analytical solution is derived for the problem using the finite Fourier cosine transform and boundary transformation methods. The effectiveness of the method is verified by comparing it with the finite element numerical results and pumping test data respectively. Based on the proposed solutions, we proceed to analyze the influence of some relevant factors: the extent to which the cut-off wall is embedded within the confined aquifer, the depth of the partially penetrating well, and the distance to the lateral head boundary. Results indicate that a greater depth of the cut-off wall leads to a reduced pumping rate requirement for achieving a desired drawdown of the confined water level within the excavation. According to the presented solution, placing pumping wells near the top of the confined aquifer in excavation dewatering projects can facilitate a faster reduction of the confined water head at the excavation bottom. Additionally, proximity of lateral head boundary could significantly impact dewatering, with closer boundaries reducing dewatering effectiveness due to improved aquifer recharge. Finally, the use of the Fourier method showcases impressive convergence properties in the approach presented in this study. The computed results maintain a high level of approximation quality, even with extremely coarse discretization.

Experimental investigation on long hydrodynamic slugs in offshore pipeline

In the process of liquid-dominated offshore oil and gas transportation, long hydrodynamic slugs are likely to occur in subsea pipelines at high liquid holdup. A large number of long hydrodynamic slug data at high liquid velocity and low gas velocity were obtained by using visual images in a 46 mm ID, 1657 m long pipeline. The flow pattern map close to the industrial parameters is plotted, and slug flow can take place at a lower superficial gas velocity (VSG = 0.045 m/s) in the long pipeline. The maximum slug length is 2.5 times the average slug length, and the longest liquid slug is 969 D near the transition boundary of slug flow. When VSG < 1.00 m/s, slug length increases rapidly and slug frequency decreases significantly with the decrease of superficial gas velocity at the same superficial liquid velocity. The prediction correlations of slug velocity, length, and frequency are developed for long-distance offshore pipelines at high liquid velocity and low gas velocity, and the maximum error is less than 25%.

Developing a New Oxygen Atlas of the World’s Oceans Using Data Interpolating Variational Analysis

Abstract We present a new global oxygen atlas. This atlas uses all of the available full water column profiles of oxygen, salinity, and temperature available as part of the World Ocean Database released in 2018. Instead of optimal interpolation, we use the Data Interpolating Variational Analysis (DIVA) approach to map the available profiles onto 108 depth levels between the surface and 6800 m, covering more than 99% of ocean volume. This 1/2° × 1/2° atlas covers the period 1955–2018 in 1-yr intervals. The DIVA method has significant benefits over traditional optimal interpolation. It allows the explicit inclusion of advection and boundary constraints, thus offering improvements in the representations of oxygen, salinity, and temperature in regions of strong flow and near coastal boundaries. We demonstrate these benefits of this mapping approach with some examples from this atlas. We can explore the regional and temporal variations of oxygen in the global oceans. Preliminary analyses confirm earlier analyses that the oxygen minimum zone in the eastern Pacific Ocean has expanded and intensified. Oxygen inventory changes between 1970 and 2010 are assessed and compared against prior studies. We find that the full ocean oxygen inventory decreased by 0.84% ± 0.42%. For this period, temperature-driven solubility changes explain about 21% of the oxygen decline over the full water column; in the upper 100 m, solubility changes can explain all of the oxygen decrease; for the 100–600 m depth range, it can explain only 29%, 19% between 600 and 1000 m, and just 11% in the deep ocean. Significance Statement The purpose of this study is to create a new oxygen atlas of the world’s oceans using a technique that better represents the effects of ocean currents and topographic boundaries, and to investigate how oxygen in the ocean has changed over recent decades. We find the total quantity of oxygen in the world’s oceans has decreased by 0.84% since 1970, similar to previous studies. We also examine how much of this change can be explained by changes in water temperature; we find that this can explain all the changes in the upper 100 m but only 21% of the oxygen decline over the whole water column.

Lift at low Reynolds number.

Lift forces are widespread in hydrodynamics. These are typically observed for big and fast objects and are often associated with a combination of fluid inertia (i.e. large Reynolds numbers) and specific symmetry-breaking mechanisms. In contrast, the properties of viscosity-dominated (i.e. low Reynolds numbers) flows make it more difficult for such lift forces to emerge. However, the inclusion of boundary effects qualitatively changes this picture. Indeed, in the context of soft and biological matter, recent studies have revealed the emergence of novel lift forces generated by boundary softness, flow gradients and/or surface charges. The aim of the present review is to gather and analyse this corpus of literature, in order to identify and unify the questioning within the associated communities, and pave the way towards future research.

An efficient and accurate DSRFG method via nonuniform energy spectra discretization

An appropriate set-up of inflow boundary conditions is crucial for accurate prediction of wind effects on the target structures using Large Eddy Simulation (LES). The discretizing and synthesizing random flow generation (DSRFG) method is a commonly used method which however requires considerable computational cost. This paper attempts to improve the efficiency and accuracy of the DSRFG method by modifying the way of discretizing the energy spectra. Since the DSRFG method is originated from the Kraichnan’s method, the grid effects on both methods are analyzed theoretically and examined numerically. Research results show that the Kraichnan’s method is sensitive to the grid effects while the improved DSRFG method is slightly affected. Additionally, the improved DSRFG method is applied to simulate the wind effects on a low-rise building by LES and the results agree well with the NIST aerodynamic database.

Large Eddy Simulation of a Low-Pressure Turbine Cascade with Turbulent End Wall Boundary Layers

We present results of implicit large eddy simulation (LES) and different Reynolds-averaged Navier–Stokes (RANS) models of the MTU 161 low pressure turbine at an exit Reynolds number of 90000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$90\\,000$$\\end{document} and exit Mach number of 0.6. The LES results are based on a high-order discontinuous Galerkin method and the RANS is computed using a classical finite-volume approach. The paper discusses the steps taken to create realistic inflow boundary conditions in terms of end wall boundary layer thickness and freestream turbulence intensity. This is achieved by tailoring the input distribution of total pressure and temperature, Reynolds stresses and turbulence length scale to a Fourier series based synthetic turbulence generator. With this procedure, excellent agreement with the experiment can be achieved in terms of blade loading at midspan and wake total pressure losses at midspan and over the channel height. Based on the validated setup, we focus on the discussion of secondary flow structures emerging due to the interaction of the incoming boundary layer and the turbine blade and compare the LES to two commonly used RANS models. Since we are able to create consistent setups for both LES and RANS, all discrepancies can be directly attributed to physical modelling problems. We show that both a linear eddy viscosity model and a differential Reynolds stress model coupled with a state-of-the-art correlation-based transition model fail, in this case, to predict the separation induced transition process around midspan. Moreover, their prediction of secondary flow losses leaves room for improvement as shown by a detailed discussion of turbulence kinetic energy and anisotropy fields.

Convergent evolving finite element approximations of boundary evolution under shape gradient flow

Abstract As a specific type of shape gradient descent algorithm, shape gradient flow is widely used for shape optimization problems constrained by partial differential equations. In this approach, the constraint partial differential equations could be solved by finite element methods on a domain with a solution-driven evolving boundary. Rigorous analysis for the stability and convergence of such finite element approximations is still missing from the literature due to the complex nonlinear dependence of the boundary evolution on the solution. In this article, rigorous analysis of numerical approximations to the evolution of the boundary in a prototypical shape gradient flow is addressed. First-order convergence in time and $k$th order convergence in space for finite elements of degree $k\geqslant 2$ are proved for a linearly semi-implicit evolving finite element algorithm up to a given time. The theoretical analysis is consistent with the numerical experiments, which also illustrate the effectiveness of the proposed method in simulating two- and three-dimensional boundary evolution under shape gradient flow. The extension of the formulation, algorithm and analysis to more general shape density functions and constraint partial differential equations is also discussed.

Numerical Study on the Influence of Aquitard Layer Distribution and Permeability Parameters on Foundation Pit Dewatering

Evaluating the influence of geologic features on dewatering efficiency, particularly within strata of varying permeability, is critical to optimizing dewatering designs for deep excavations. In river valley areas, river sedimentation results in a discontinuous distribution of relatively aquitard layers (clay layers). The evaluation and calculation of the distribution and permeability parameters for foundation pit dewatering are very important when on-site geological data are insufficient. For this purpose, the deep excavation pit on the right bank and floodplain of Chongjiang River is taken as an example in this article. A three-dimensional groundwater flow model was constructed using the Unstructured Grid (MODFLOW-USG) software package version 1. The model was carefully calibrated using hydrogeologic features and observed groundwater levels to ensure its reliability. The simulation results effectively reproduce actual dewatering processes. The study reveals the following findings: (1) Increased aquitard layers (clay layer) enhance the barrier effect, thereby improving dewatering efficiency. (2) Increased clay layer permeability and storage coefficients reduce dewatering efficiency, while the specific yield of the clay layer has less pronounced effects. (3) Due to the discontinuous nature of the clay layer, dewatering rates are higher when the clay layer is below the riverbed than when it is in the flow boundary area (foothills).

On the role of unsteadiness in impulsive-flow-driven shear instabilities: precursors of fragmentation

Shear instabilities at the interface of two fluids, such as classical Kelvin–Helmholtz instability (KHI), is the precursor of interface destabilization, leading to fluid fragmentation critical in a wide range of applications. While many insights into such instabilities are derived for steady background forcing flow, unsteady impulse flows are ubiquitous in environmental and physiological processes. Yet, little is understood on how unsteadiness shapes the initial interface amplification necessary for the onset of its topological change enabling subsequent fragmentation. In this combined theoretical, numerical and experimental study, we focus on an air-on-liquid interface exposed to canonical unsteady shear flow profiles. Evolution of the perturbed interface is formulated theoretically as an impulse-driven initial value problem using both linearized potential flow and nonlinear boundary integral methods. We show that the unsteady airflow forcing can amplify the interface's inherent gravity–capillary wave, up to wave-breaking transition, even if the configuration is classically KH stable. For impulses much shorter than the gravity–capillary wave period, it is the cumulative action, akin to total energy, that determines amplification, independent of the details of the impulse profile. However, for longer impulses, the details of the impulse profile become important. In this limit, akin to a resonance, it is the entangled history of the interaction of the forcing, i.e. the impulse, that changes rapidly in amplitude, and the response of the oscillating interface that matters. The insights gained are discussed and experimentally illustrated in the context of interface distortion and destabilization relevant for upper respiratory mucosalivary fluid fragmentation in violent exhalations.

Uncertainty and Sensitivity Evaluation of the QUENCH-02 Experiment Simulation Using the ASYST Code

Abstract Uncertainty and sensitivity methods are increasingly used in safety analyzes of nuclear power plants to address the unreliability of input data, numerical models, and, in general, the lack of knowledge regarding certain physical phenomena, in determining safety margins and acceptance criteria. The ASYST code, developed as part of an international nuclear technology ASYST Development and Training Program (ADTP) managed by Innovative Systems Software (ISS), is used to perform an uncertainty analysis of the QUENCH-02 experiment conducted at the Karlsruhe Institute of Technology. The code uses a probabilistic methodology based on the propagation of input uncertainties. The QUENCH facility contains electrically heated PWR fuel rod simulators and the aim of the experiment is to examine hydrogen generation and the behavior of the fuel rod cladding during core reflood. For selected input parameters, such as steam/water flow, electrical power, and other relevant boundary conditions, it is necessary to define their probability density functions. Input databases are then prepared for individual calculations based on the selected confidence level and confidence interval. The number of performed calculations is 60, large enough to ensure at least 95% coverage of expected output results and uncertainty limits. The results of the calculations are compared with the experimental measurements. The Pearson correlation coefficient is used to obtain correlation between the input uncertain parameters and the output data. Sensitivity analyses cover the influence of variations in the heater's electrical power and the steam flow rate on the hydrogen production and the maximum cladding temperature.

A high-resolution marine mercury model MITgcm-ECCO2-Hg with online biogeochemistry

Abstract. Mercury (Hg) is a global persistent contaminant. Modeling studies are useful means of synthesizing a current understanding of the Hg cycle. Previous studies mainly use coarse-resolution models, which makes it impossible to analyze the role of turbulence in the Hg cycle and inaccurately describes the transport of kinetic energy. Furthermore, all of them are coupled with offline biogeochemistry, and therefore they cannot respond to short-term variability in oceanic Hg concentration. In our approach, we utilize a high-resolution ocean model (MITgcm-ECCO2, referred to as “high-resolution-MITgcm”) coupled with the concurrent simulation of biogeochemistry processes from the Darwin Project (referred to as “online”). This integration enables us to comprehensively simulate the global biogeochemical cycle of Hg with a horizontal resolution of 1/5∘. The finer portrayal of surface Hg concentrations in estuarine and coastal areas, strong western boundary flow and upwelling areas, and concentration diffusion as vortex shapes demonstrate the effects of turbulence that are neglected in previous models. Ecological events such as algal blooms can cause a sudden enhancement of phytoplankton biomass and chlorophyll concentrations, which can also result in a dramatic change in particle-bound Hg (HgaqP) sinking flux simultaneously in our simulation. In the global estuary region, including riverine Hg input in the high-resolution model allows us to reveal the outward spread of Hg in an eddy shape driven by fine-scale ocean currents. With faster current velocities and diffusion rates, our model captures the transport and mixing of Hg from river discharge in a more accurate and detailed way and improves our understanding of Hg cycle in the ocean.

Modeling study on the geometric optimization of thermoelectric modules

Abstract The performance of thermoelectric power generators (TEG) primarily depends on the properties of the thermoelectric materials employed. For conventional thermoelectric modules (TEM) utilizing the same material, the geometric parameters also play a significant role in determining TEM performance. As such, optimizing the geometry of TEM can lead to improved performance. In this study, TEM were modeled, designed, fabricated, and tested to investigate the effects of different geometric parameters on their performance. Numerical simulations were conducted under both constant temperature and constant flow boundary conditions, and the results were validated through experimental testing. The simulation results under constant flow boundary conditions exhibited good agreement with the experimental results. The effects of thickness, cross-sectional area, and filling ratio of thermoelectric legs on TEM performance were investigated through numerical simulations and compared with findings from previous studies. It was observed that increasing the cross-sectional area of the thermoelectric legs led to a decrease in the power output of TEM. Conversely, increasing the filling ratio effectively enhanced the TEM's performance. Furthermore, an optimal thermoelectric leg thickness was identified through the numerical simulations that could yield the maximum power output of TEM. The underlying mechanism behind this observation was explained, shedding light on why different reports have identified different optimal thicknesses. Optimizing the thermoelectric leg thickness can help maintain a high effective temperature difference and low internal resistance, which can vary based on the specific type of TEM and the thickness and thermal conductivity of the insulating substrates and copper sheets.

Laplace transform solution of the time-dependent annular Couette flow with dynamic wall slip

The annular Couette flow has several industrial applications, particularly for the characterization of the fluid flow and deformation behavior of fluids. The inclusion of the dynamic wall slip into the flow boundary conditions seems to be necessary for an efficient continuum description of motion of nanofluidics as it reflects the importance of fluid–structure interface related phenomena. Dynamic wall slip introduces a dissipative boundary condition and thus increases the difficulties of finding solutions to related problems. In the present work we investigate the behavior of fluid flow between two infinitely long coaxial circular cylinders, when the inner cylinder is axially moving due to sudden constant velocity, while the outer cylinder is held stationary. The boundary condition on the outer cylinder is that of dynamic wall slip, in addition to the usual Navier slip. The medium considered here is a Newtonian viscous fluid. The solution of the governing equations, initial and boundary conditions for this flow is obtained using the Laplace transform technique and inversion by Laguerre polynomials. This method may be useful, when applied in conjunction with perturbation methods, to solve nonlinear Couette flow problems involving temperature changes. Numerical results are presented and discussed.

Impact of Local Terrain Features on Urban Airflow

Past work has shown that coupling can exist between atmospheric air flows at street scale (O(0.1 km)) and city scale (O(10 km)). It is generally impractical at present to develop high-fidelity urban simulations capable of capturing such effects. This limitation imposes a need to develop better parameterisations for meso-scale models but an information gap exists in that past work has generally focused on simplified urban geometries and assumed the buildings to be on flat ground. This study aimed to begin to address this gap in a systematic way by using the large eddy simulation method with synthetic turbulence inflow boundary conditions to simulate atmospheric air flows over the University of Southampton campus. Both flat and realistic terrains were simulated, including significant local terrain features, such as two valleys with a width about 50 m and a depth about average building height, and a step change of urban roughness height. The numerical data were processed to obtain averaged vertical profiles of time-averaged velocities and second order turbulence statistics. The flat terrain simulation was validated against high resolution particle image velocimetry data, and the impact of uncertainty in defining the turbulence intensity in the synthetic inflow method was assessed. The ratio between realistic and flat terrains of time-mean streamwise velocity at the same ground level height over a terrain crest location can be >2, while over a valley trough it can be <0.5. Further data analysis conclusively showed that the realistic terrain can have a considerable effect on global quantities, such as the depth of the spanwise-averaged internal boundary layer and spatially-averaged turbulent kinetic energy. These highlight the potential impact that local terrain features (O(0.1 km)) may have on near-field dispersion and the urban micro-climate.

3D model for inertial cavitation bubble dynamics in binary immiscible fluids

The physics of cavitation bubbles in water has been extensively studied for over a century. However, our understanding of bubble dynamics in binary immiscible fluids, such as a water-oil system, is limited. These systems have recently gained a lot of interest due to their relevance in modern medical treatment, emulsification, and the food industry. In this study, we establish an accurate and inexpensive three-dimensional boundary integral (BI) model for inertial cavitation bubble dynamics in binary immiscible fluid systems. Our novel scheme for solving velocities on the flow boundaries, expressed in a matrix form, can be easily extended to complex situations where multiple bubbles are generated in different phases. Additionally, we employ a density potential method and a weighted moving least-squares method to maintain a high level of mesh regularity. Our results demonstrate that the proposed 3D model is comparable in accuracy to a 3D axisymmetric model by comparing it against analytical solutions and the results obtained from an axisymmetric model. Furthermore, we compare our numerical simulations against a purposely conducted experiment for the bubble-droplet interaction, and excellent agreement is achieved. For the first time, we present simulation results of two-bubble interactions with an initially flat fluid-fluid interface and inside a droplet surrounded by a second fluid. We also reveal the dependences of the two-bubble morphologies, flow patterns, and jet velocities on the density ratio between the two phases. Finally, we find a significant difference in the mechanism of fluid mixing by multiple bubbles compared to that of a single bubble case.

Energetic impact of reconstructed debris flow on the intensity and duration of growth disturbances in tree rings

A rare study on the quantitative relationship between the energetic impact of debris flows on the intensity and duration of growth disturbances of tree rings was carried out, partly due to a lack of feasible approaches and detailed field evidence. In this study, we first used a dendrogeomorphic technique to determine the age of a recent debris flow derived from historic landslide deposits at Qingyang Mountain (QYM) on the northeastern Tibet plateau. We acquired the quantitative data on the annual widths of tree rings in history and confirmed the influence of the debris flow rather than other factors (e.g., climatic events and inset outbreaking) in disturbing the growth of tree rings in a specific year. Using this approach, we determined that the age of the debris flow at QYM occurred in 1982, which was speculated to be triggered by the high monthly precipitation registered during July 1982. Subsequently, based on the boundaries of historic debris flow identified on remote sensing images before and after 1982 and the depth-integrated continuum model, we reconstructed the process of the 1982 debris flow and obtained the kinematic energy of the debris flow impacting the sampled trees. Based on the study, we observed that two growth disturbance patterns of tree rings influenced by the reconstructed 1982 debris flow were revealed, including growth suppression and asymmetric growth. We obtained a raw logarithm relationship between duration (i.e., lasting time for the disturbed tree rings to recover the initial width) and intensity of growth disturbances (i.e., growth suppression ratio of disturbed tree rings). We concluded that there is a negative exponential relationship between the simulated kinematic energy of debris flow impacting the disturbed trees and the time to recover the initial width of corresponding tree rings.

Prediction of urban airflow fields around isolated high-rise buildings using data-driven non-linear correction models

When it comes to predicting urban airflow, steady Reynolds-averaged Navier-Stokes (SRANS) models that rely on Reynolds stress often face a challenge called the closure problem. This problem involves unresolved structural flaws and uncertainties in the closure coefficients used in the models. Previous attempts to recalibrate coefficients for specific urban flows without breaking the linear constitutive relation have resulted in simulation results constrained by the baseline turbulence model. Therefore, this study aims to enhance the performance of SRANS models by addressing these structural flaws. To achieve this, a novel data-driven framework is proposed. It leverages the deterministic symbolic regression algorithm to discover explicit algebraic expressions for a non-linear Reynolds stress correction model. The robustness of the correction model is ensured by maintaining the linear eddy viscosity model for iterative calculations while keeping the non-linear component frozen. The proposed framework is evaluated using three isolated building cases with varying geometric configurations and inflow boundary conditions. Findings demonstrate that computational fluid dynamics (CFD) predictions incorporating the data-driven non-linear correction model consistently align closer to wind tunnel experimental results compared to both standard and non-linear versions of the k-ε turbulence model. This improvement is reflected in reduced reattachment lengths and more accurate mean velocity distributions in the wake of buildings. However, it should be noted that there is a possibility of overpredicting wind velocity in the windward area. This study introduces valuable insights and additional strategies to enhance the prediction accuracy of SRANS models in urban airflow simulations.

Flash-back, blow-off, and symmetry breaking of premixed conical flames

Hydrodynamic and thermal-diffusive effects subject premixed flames to intrinsic instabilities that strongly influence their shape and propagation/stabilization characteristics. However, the interaction and coupling of intrinsic flame dynamics with background flow gradients and boundary conditions remain poorly understood. This paper presents a global nonlinear bifurcation analysis of burner-stabilized laminar premixed conical flames with varying reaction rates and reactant diffusivities, respectively parameterized by the Damköhler number Da and the Lewis number Le. Using a dimensionless formulation of the reacting, weakly-compressible Navier–Stokes equations, the dynamics of flash-back, blow-off, and cellular instability are explored in a fully-coupled framework. Our analysis identifies steady conical flame states over a finite range of Da and Le, limited by saddle–node bifurcations corresponding to spontaneous blow-off of the axisymmetric flame below a Le-dependent lower critical Da value and spontaneous boundary-layer flash-back beyond a higher critical Da value. Furthermore, the analysis reveals that the conical flame loses its axisymmetry via circle–pitchfork bifurcations as Le or Da decrease or increase beyond respective critical values. These bifurcations are shown to correspond to stationary three-dimensional global modes describing steady polyhedral or tilted flame structures, each associated with distinct azimuthal periodicities. Statement of SignificanceThis work presents a bifurcation analysis of laminar premixed conical flames within a fully-coupled flame/flow model. By considering variations in reaction rate and reactant diffusivity, the analysis identifies saddle–node bifurcations corresponding to spontaneous flash-back and blow-off of the axisymmetric flame. It also identifies axisymmetry breaking bifurcations associated with transitions to steady three-dimensional polyhedral and tilted flame states. These global instabilities indicate that hydrodynamic and thermal-diffusive effects strongly influence a flame’s steady structure in the azimuthal dimension even when no instabilities appear in the plane of symmetry. As such, future analyses of flame dynamics should rule out symmetry-breaking behaviors before adopting a two-dimensional computational framework.

Stabilisation of Hydrodynamic Instabilities by Critical Layers in Acoustic Lining Boundary Layers

Acoustics are considered in a straight cylindrical lined duct with an axial mean flow that is uniform apart from a boundary layer near the wall. Within the boundary layer, which may or may not be thin, the flow profile is quadratic and satisfies no-slip at the wall. Time-harmonic modal solutions to the linearized Euler equations are found by solving the Pridmore-Brown equation using Frobenius series. The Briggs–Bers criterion is used to ascertain the spatial stability of the modes, without considering absolute instabilities. The modes usually identified as hydrodynamic instabilities are found to interact with the critical layer branch cut, also known as the continuous spectrum. By varying the boundary-layer thickness, flow speed, frequency, and wall impedance, it is found that these spatial instabilities can be stabilized behind the critical layer branch cut. In particular, spatial instabilities are only found for a boundary layer thinner than a critical boundary-layer thickness . The behaviors observed for the uniform-quadratic sheared flow considered here are further compared to a uniform-linear sheared flow, and a uniform slipping flow under the Ingard–Myers boundary condition, where this process of stabilization is not observed. It is therefore argued that modeling a sufficiently smooth mean flow boundary layer is necessary to predict the correct stability of flow over a lined wall.