# Latest papers in fluid mechanics

### Ultra-lean dynamics of a holder-stabilized hydrogen enriched flames in a preheated mesoscale combustor

Physics of Fluids, Volume 34, Issue 5, May 2022.

To provide the theoretical basis to suppress the unstable flames under the coupling effect of flow and heat recirculation, the present work experimentally studies the ultra-lean dynamics of a holder stabilized 40%H2–60%CH4–air premixed flame in a preheated mesoscale combustor. The regime diagram of the flame behaviors at various operating conditions is obtained. It is observed that the blow-off limit first increases slightly and then decreases sharply (the anomalous blow-off limit) with the decreased Re value. Three types of the flame behaviors (i.e., the conventional stable flame, the stable residual flame, and the periodic oscillating residual flame) are found before the flame blow-off. In addition, with the decreased Reynolds number, the operating range for the stable residual flame broadens first and then narrows, but that of the periodic oscillating residual flame decreases monotonically, which are observed for the first time. The results show that, with the decreased Reynolds number, the flame root of the conventional stable flame anchors almost at the same location right behind the holder, while the flame tips obviously shift upstream. With the decreased equivalence ratio, the left and right flame tips in the downstream channel shift toward each other and finally merge into a single flame tip, which results in the formation of the stable residual flame. When the equivalence ratio decreases further, the periodic oscillating residual flame occurs. The flame tip periodically oscillates up and down over time. In the end, the blow-off dynamics of the stable residual flame and periodic oscillating residual flame are revealed.

To provide the theoretical basis to suppress the unstable flames under the coupling effect of flow and heat recirculation, the present work experimentally studies the ultra-lean dynamics of a holder stabilized 40%H2–60%CH4–air premixed flame in a preheated mesoscale combustor. The regime diagram of the flame behaviors at various operating conditions is obtained. It is observed that the blow-off limit first increases slightly and then decreases sharply (the anomalous blow-off limit) with the decreased Re value. Three types of the flame behaviors (i.e., the conventional stable flame, the stable residual flame, and the periodic oscillating residual flame) are found before the flame blow-off. In addition, with the decreased Reynolds number, the operating range for the stable residual flame broadens first and then narrows, but that of the periodic oscillating residual flame decreases monotonically, which are observed for the first time. The results show that, with the decreased Reynolds number, the flame root of the conventional stable flame anchors almost at the same location right behind the holder, while the flame tips obviously shift upstream. With the decreased equivalence ratio, the left and right flame tips in the downstream channel shift toward each other and finally merge into a single flame tip, which results in the formation of the stable residual flame. When the equivalence ratio decreases further, the periodic oscillating residual flame occurs. The flame tip periodically oscillates up and down over time. In the end, the blow-off dynamics of the stable residual flame and periodic oscillating residual flame are revealed.

Categories: Latest papers in fluid mechanics

### Publisher's Note: “A novel general modeling of the viscoelastic properties of fluids: Application to mechanical relaxation and low frequency oscillation measurements of liquid water” [Phys. Fluids 34, 043109 (2022)]

Physics of Fluids, Volume 34, Issue 5, May 2022.

Categories: Latest papers in fluid mechanics

### Generation of streamwise helical vortex loops via successive reconnections in early pipe transition

Physics of Fluids, Volume 34, Issue 5, May 2022.

We extend the vortex-surface field (VSF), a Lagrangian-based structure identification method, to investigate the vortex reconnection in temporally evolving transitional pipe flows. In the direct numerical simulation (DNS) of round pipe flows, a radial wave-like velocity disturbance is imposed on the inlet region to trigger the transition. The VSF isosurfaces are vortex surfaces composed of vortex lines, and they are concentric tubes with different wall distances at the initial time. The VSF evolution is calculated by the two-time method based on the DNS velocity field, and it is effective to identify the vortex reconnection. In the early stage of transition, the vortex surfaces are first corrugated with streamwise elongated bulges. The escalation and descent of vortex surfaces characterize the generation of high- and low-speed streaks and streamwise vortex pairs, along with the surge of the wall-friction coefficient. The resultant highly coiled and stretched vortex loops then reconnect with each other under the viscous cancelation mechanism. Subsequently, successive vortex reconnections occur via a “greedy snake” mechanism. The streamwise vortex loops consecutively capture the secondary vortex rings pinched off with self-reconnection, forming long helical vortex loops spanning over ten pipe radii in the streamwise direction. Finally, the Kelvin–Helmholtz instability of the shear layer at the trailing edge breaks down the streamwise helical vortex loops into turbulent spots.

We extend the vortex-surface field (VSF), a Lagrangian-based structure identification method, to investigate the vortex reconnection in temporally evolving transitional pipe flows. In the direct numerical simulation (DNS) of round pipe flows, a radial wave-like velocity disturbance is imposed on the inlet region to trigger the transition. The VSF isosurfaces are vortex surfaces composed of vortex lines, and they are concentric tubes with different wall distances at the initial time. The VSF evolution is calculated by the two-time method based on the DNS velocity field, and it is effective to identify the vortex reconnection. In the early stage of transition, the vortex surfaces are first corrugated with streamwise elongated bulges. The escalation and descent of vortex surfaces characterize the generation of high- and low-speed streaks and streamwise vortex pairs, along with the surge of the wall-friction coefficient. The resultant highly coiled and stretched vortex loops then reconnect with each other under the viscous cancelation mechanism. Subsequently, successive vortex reconnections occur via a “greedy snake” mechanism. The streamwise vortex loops consecutively capture the secondary vortex rings pinched off with self-reconnection, forming long helical vortex loops spanning over ten pipe radii in the streamwise direction. Finally, the Kelvin–Helmholtz instability of the shear layer at the trailing edge breaks down the streamwise helical vortex loops into turbulent spots.

Categories: Latest papers in fluid mechanics

### Equilibrium and non-equilibrium molecular dynamics approaches for the linear viscoelasticity of polymer melts

Physics of Fluids, Volume 34, Issue 5, May 2022.

Viscoelastic properties of polymer melts are particularly challenging to compute due to the intrinsic stress fluctuations in molecular dynamics (MD). We compared equilibrium and non-equilibrium MD approaches for extracting the storage ([math]) and loss moduli ([math]) over a wide frequency range from a bead-spring chain model in both unentangled and entangled regimes. We found that, with properly chosen data processing and noise reduction procedures, different methods render quantitatively equivalent results. In equilibrium MD (EMD), applying the Green−Kubo relation with a multi-tau correlator method for noise filtering generates smooth stress relaxation modulus profiles from which accurate [math] and [math] can be obtained. For unentangled chains, combining the Rouse model with a short-time correction provides a convenient option that circumvents the stress fluctuation challenge altogether. For non-equilibrium MD (NEMD), we found that combining a stress pre-averaging treatment with discrete Fourier transform analysis reliably computes [math] and [math] with a much shorter simulation length than previously reported. Comparing the efficiency and statistical accuracy of these methods, we concluded that EMD is both reliable and efficient, and is suitable when the whole spectrum of linear viscoelastic properties is desired, whereas NEMD offers flexibility only when some frequency ranges are of interest.

Viscoelastic properties of polymer melts are particularly challenging to compute due to the intrinsic stress fluctuations in molecular dynamics (MD). We compared equilibrium and non-equilibrium MD approaches for extracting the storage ([math]) and loss moduli ([math]) over a wide frequency range from a bead-spring chain model in both unentangled and entangled regimes. We found that, with properly chosen data processing and noise reduction procedures, different methods render quantitatively equivalent results. In equilibrium MD (EMD), applying the Green−Kubo relation with a multi-tau correlator method for noise filtering generates smooth stress relaxation modulus profiles from which accurate [math] and [math] can be obtained. For unentangled chains, combining the Rouse model with a short-time correction provides a convenient option that circumvents the stress fluctuation challenge altogether. For non-equilibrium MD (NEMD), we found that combining a stress pre-averaging treatment with discrete Fourier transform analysis reliably computes [math] and [math] with a much shorter simulation length than previously reported. Comparing the efficiency and statistical accuracy of these methods, we concluded that EMD is both reliable and efficient, and is suitable when the whole spectrum of linear viscoelastic properties is desired, whereas NEMD offers flexibility only when some frequency ranges are of interest.

Categories: Latest papers in fluid mechanics

### An AI-based non-intrusive reduced-order model for extended domains applied to multiphase flow in pipes

Physics of Fluids, Volume 34, Issue 5, May 2022.

The modeling of multiphase flow in a pipe presents a significant challenge for high-resolution computational fluid dynamics (CFD) models due to the high aspect ratio (length over diameter) of the domain. In subsea applications, the pipe length can be several hundreds of meters vs a pipe diameter of just a few inches. Approximating CFD models in a low-dimensional space, reduced-order models have been shown to produce accurate results with a speed-up of orders of magnitude. In this paper, we present a new AI-based non-intrusive reduced-order model within a domain decomposition framework (AI-DDNIROM), which is capable of making predictions for domains significantly larger than the domain used in training. This is achieved by (i) using a domain decomposition approach; (ii) using dimensionality reduction to obtain a low-dimensional space in which to approximate the CFD model; (iii) training a neural network to make predictions for a single subdomain; and (iv) using an iteration-by-subdomain technique to converge the solution over the whole domain. To find the low-dimensional space, we compare Proper Orthogonal Decomposition with several types of autoencoder networks, known for their ability to compress information accurately and compactly. The comparison is assessed with two advection-dominated problems: flow past a cylinder and slug flow in a pipe. To make predictions in time, we exploit an adversarial network, which aims to learn the distribution of the training data, in addition to learning the mapping between particular inputs and outputs. This type of network has shown the potential to produce visually realistic outputs. The whole framework is applied to multiphase slug flow in a horizontal pipe for which an AI-DDNIROM is trained on high-fidelity CFD simulations of a pipe of length 10 m with an aspect ratio of 13:1 and tested by simulating the flow for a pipe of length 98 m with an aspect ratio of almost 130:1. Inspection of the predicted liquid volume fractions shows a good match with the high fidelity model as shown in the results. Statistics of the flows obtained from the CFD simulations are compared to those of the AI-DDNIROM predictions to demonstrate the accuracy of our approach.

The modeling of multiphase flow in a pipe presents a significant challenge for high-resolution computational fluid dynamics (CFD) models due to the high aspect ratio (length over diameter) of the domain. In subsea applications, the pipe length can be several hundreds of meters vs a pipe diameter of just a few inches. Approximating CFD models in a low-dimensional space, reduced-order models have been shown to produce accurate results with a speed-up of orders of magnitude. In this paper, we present a new AI-based non-intrusive reduced-order model within a domain decomposition framework (AI-DDNIROM), which is capable of making predictions for domains significantly larger than the domain used in training. This is achieved by (i) using a domain decomposition approach; (ii) using dimensionality reduction to obtain a low-dimensional space in which to approximate the CFD model; (iii) training a neural network to make predictions for a single subdomain; and (iv) using an iteration-by-subdomain technique to converge the solution over the whole domain. To find the low-dimensional space, we compare Proper Orthogonal Decomposition with several types of autoencoder networks, known for their ability to compress information accurately and compactly. The comparison is assessed with two advection-dominated problems: flow past a cylinder and slug flow in a pipe. To make predictions in time, we exploit an adversarial network, which aims to learn the distribution of the training data, in addition to learning the mapping between particular inputs and outputs. This type of network has shown the potential to produce visually realistic outputs. The whole framework is applied to multiphase slug flow in a horizontal pipe for which an AI-DDNIROM is trained on high-fidelity CFD simulations of a pipe of length 10 m with an aspect ratio of 13:1 and tested by simulating the flow for a pipe of length 98 m with an aspect ratio of almost 130:1. Inspection of the predicted liquid volume fractions shows a good match with the high fidelity model as shown in the results. Statistics of the flows obtained from the CFD simulations are compared to those of the AI-DDNIROM predictions to demonstrate the accuracy of our approach.

Categories: Latest papers in fluid mechanics

### Steady flow past elliptic cylinders with blockage effects

Physics of Fluids, Volume 34, Issue 5, May 2022.

In the present work, steady two-dimensional flow past elliptic cylinders with different aspect ratios (Ar) have been investigated for Reynolds number (Re) up to 200. Main characteristics such as the bubble length, bubble width, separation Reynolds number, separation angle, drag coefficient, coefficients of the front and rear stagnation pressure, and the maximum vorticity on the cylinder surface have been obtained. Least squares fit equations for some of these quantities have also been presented. In the special case of a circular cylinder, results computed with the largest domain show that the bubble length, bubble width, maximum vorticity on the cylinder surface, coefficient of pressure drag, coefficient of total drag, and flow separation angle are linear functions of Re, [math], and [math], respectively. As Ar changes, the trends in the growth, with respect to Ren (with the corresponding index), for the bubble length, bubble width, and the maximum surface vorticity deviate from their linear nature. The effect of blockage on the steady flow characteristics has been studied by changing the location of the side boundaries. In certain cases, the flow properties are found to vary in a non-monotonic fashion with the change in the blockage. An explanation based on the dual role of the side boundaries in promoting and suppressing the growth of the corresponding flow property is offered.

In the present work, steady two-dimensional flow past elliptic cylinders with different aspect ratios (Ar) have been investigated for Reynolds number (Re) up to 200. Main characteristics such as the bubble length, bubble width, separation Reynolds number, separation angle, drag coefficient, coefficients of the front and rear stagnation pressure, and the maximum vorticity on the cylinder surface have been obtained. Least squares fit equations for some of these quantities have also been presented. In the special case of a circular cylinder, results computed with the largest domain show that the bubble length, bubble width, maximum vorticity on the cylinder surface, coefficient of pressure drag, coefficient of total drag, and flow separation angle are linear functions of Re, [math], and [math], respectively. As Ar changes, the trends in the growth, with respect to Ren (with the corresponding index), for the bubble length, bubble width, and the maximum surface vorticity deviate from their linear nature. The effect of blockage on the steady flow characteristics has been studied by changing the location of the side boundaries. In certain cases, the flow properties are found to vary in a non-monotonic fashion with the change in the blockage. An explanation based on the dual role of the side boundaries in promoting and suppressing the growth of the corresponding flow property is offered.

Categories: Latest papers in fluid mechanics

### The influence of particle size on the fluid dynamics of a laser-induced plasma

Physics of Fluids, Volume 34, Issue 5, May 2022.

The interaction of a laser-induced shock wave with nanoparticles and microparticles of aluminum oxide is investigated through experiments and modeling. The chemistry and physics of the interaction between the particles and plasma generated from laser ablation shows similarities and discrete differences for the two particle sizes. For both particle sizes, early stage (<10 μs) ionization was dominant and evidenced by higher concentrations of Al II. While both sizes exhibit ionization over the same duration, the intensity of emission was greater for nanoparticles indicating greater concentrations of ionized species. Moreover, the dispersion of species was notably more elongated for microparticles while radial dispersion was more pronounced for nanoparticles with elevated drag forces. At later stages (i.e., >10 μs), oxidation reactions were dominant for both particle sizes, but the same distinctions in flow field were observed and attributed to particle drag. In all stages of interaction, microparticles expand axially with less drag that suppresses their radial expansion. As a result, the dispersion of reactive species was mapped over an up to 80% larger area for nanoparticles relative to microparticles. Results shown here can be applied toward advancing experimental diagnostics and particle-shock wave modeling and simulation efforts for energetic materials.

The interaction of a laser-induced shock wave with nanoparticles and microparticles of aluminum oxide is investigated through experiments and modeling. The chemistry and physics of the interaction between the particles and plasma generated from laser ablation shows similarities and discrete differences for the two particle sizes. For both particle sizes, early stage (<10 μs) ionization was dominant and evidenced by higher concentrations of Al II. While both sizes exhibit ionization over the same duration, the intensity of emission was greater for nanoparticles indicating greater concentrations of ionized species. Moreover, the dispersion of species was notably more elongated for microparticles while radial dispersion was more pronounced for nanoparticles with elevated drag forces. At later stages (i.e., >10 μs), oxidation reactions were dominant for both particle sizes, but the same distinctions in flow field were observed and attributed to particle drag. In all stages of interaction, microparticles expand axially with less drag that suppresses their radial expansion. As a result, the dispersion of reactive species was mapped over an up to 80% larger area for nanoparticles relative to microparticles. Results shown here can be applied toward advancing experimental diagnostics and particle-shock wave modeling and simulation efforts for energetic materials.

Categories: Latest papers in fluid mechanics

### Prediction of acoustic pressure of the annular combustor using stacked long short-term memory network

Physics of Fluids, Volume 34, Issue 5, May 2022.

This paper proposes a data-driven method named stacked long short-term memory (S-LSTM) for predicting the future growth of acoustic pressure signals to detect precursors of combustion instability. The application of S-LSTM is investigated using the acoustic pressure data obtained from an annular combustor. The S-LSTM method is compared with the support vector machine (SVM) in terms of the predictive performance and also provides detailed insights into the influence of input choice by interpreting the results of S-LSTM. It is demonstrated that S-LSTM can effectively predict future pressure signals with a better error control performance compared to the SVM method. Furthermore, the feasibility of the S-LSTM in the thermoacoustic instability problem is verified using acoustic pressure data obtained from industrial combustion tests with a low-emission aero-engine. It is expected that the implementation of S-LSTM provides an early prediction solution to avoid thermoacoustic instability.

This paper proposes a data-driven method named stacked long short-term memory (S-LSTM) for predicting the future growth of acoustic pressure signals to detect precursors of combustion instability. The application of S-LSTM is investigated using the acoustic pressure data obtained from an annular combustor. The S-LSTM method is compared with the support vector machine (SVM) in terms of the predictive performance and also provides detailed insights into the influence of input choice by interpreting the results of S-LSTM. It is demonstrated that S-LSTM can effectively predict future pressure signals with a better error control performance compared to the SVM method. Furthermore, the feasibility of the S-LSTM in the thermoacoustic instability problem is verified using acoustic pressure data obtained from industrial combustion tests with a low-emission aero-engine. It is expected that the implementation of S-LSTM provides an early prediction solution to avoid thermoacoustic instability.

Categories: Latest papers in fluid mechanics

### Study of preferential concentration in turbulent flows using combined graph theory and Voronoï analysis

Physics of Fluids, Volume 34, Issue 5, May 2022.

Collisions between particles in turbulent flows may be enhanced by the formation of clusters due to the preferential concentration effect. However, the internal sub-structure of the clusters remains unclear. This paper describes using the “degree of a node” and the “shortest path length” from graph theory, in combination with Voronoï analysis, to gain further insight into both the structure and internal sub-structure of a cluster. This is demonstrated on experimental measurements obtained from a confined counter-flow/jet system. A minority of the particles, which comprise large clusters, are found to have a significantly large number of neighboring particles for collisions. However, particles which comprise small clusters typically have a random number of neighbors.

Collisions between particles in turbulent flows may be enhanced by the formation of clusters due to the preferential concentration effect. However, the internal sub-structure of the clusters remains unclear. This paper describes using the “degree of a node” and the “shortest path length” from graph theory, in combination with Voronoï analysis, to gain further insight into both the structure and internal sub-structure of a cluster. This is demonstrated on experimental measurements obtained from a confined counter-flow/jet system. A minority of the particles, which comprise large clusters, are found to have a significantly large number of neighboring particles for collisions. However, particles which comprise small clusters typically have a random number of neighbors.

Categories: Latest papers in fluid mechanics

### Physics-informed neural networks for phase-field method in two-phase flow

Physics of Fluids, Volume 34, Issue 5, May 2022.

The complex flow modeling based on machine learning is becoming a promising way to describe multiphase fluid systems. This work demonstrates how a physics-informed neural network promotes the combination of traditional governing equations and advanced interface evolution equations without intricate algorithms. We develop physics-informed neural networks for the phase-field method (PF-PINNs) in two-dimensional immiscible incompressible two-phase flow. The Cahn–Hillard equation and Navier–Stokes equations are encoded directly into the residuals of a fully connected neural network. Compared with the traditional interface-capturing method, the phase-field model has a firm physical basis because it is based on the Ginzburg–Landau theory and conserves mass and energy. It also performs well in two-phase flow at the large density ratio. However, the high-order differential nonlinear term of the Cahn–Hilliard equation poses a great challenge for obtaining numerical solutions. Thus, in this work, we adopt neural networks to tackle the challenge by solving high-order derivate terms and capture the interface adaptively. To enhance the accuracy and efficiency of PF-PINNs, we use the time-marching strategy and the forced constraint of the density and viscosity. The PF-PINNs are tested by two cases for presenting the interface-capturing ability of PINNs and evaluating the accuracy of PF-PINNs at the large density ratio (up to 1000). The shape of the interface in both cases coincides well with the reference results, and the dynamic behavior of the second case is precisely captured. We also quantify the variations in the center of mass and increasing velocity over time for validation purposes. The results show that PF-PINNs exploit the automatic differentiation without sacrificing the high accuracy of the phase-field method.

The complex flow modeling based on machine learning is becoming a promising way to describe multiphase fluid systems. This work demonstrates how a physics-informed neural network promotes the combination of traditional governing equations and advanced interface evolution equations without intricate algorithms. We develop physics-informed neural networks for the phase-field method (PF-PINNs) in two-dimensional immiscible incompressible two-phase flow. The Cahn–Hillard equation and Navier–Stokes equations are encoded directly into the residuals of a fully connected neural network. Compared with the traditional interface-capturing method, the phase-field model has a firm physical basis because it is based on the Ginzburg–Landau theory and conserves mass and energy. It also performs well in two-phase flow at the large density ratio. However, the high-order differential nonlinear term of the Cahn–Hilliard equation poses a great challenge for obtaining numerical solutions. Thus, in this work, we adopt neural networks to tackle the challenge by solving high-order derivate terms and capture the interface adaptively. To enhance the accuracy and efficiency of PF-PINNs, we use the time-marching strategy and the forced constraint of the density and viscosity. The PF-PINNs are tested by two cases for presenting the interface-capturing ability of PINNs and evaluating the accuracy of PF-PINNs at the large density ratio (up to 1000). The shape of the interface in both cases coincides well with the reference results, and the dynamic behavior of the second case is precisely captured. We also quantify the variations in the center of mass and increasing velocity over time for validation purposes. The results show that PF-PINNs exploit the automatic differentiation without sacrificing the high accuracy of the phase-field method.

Categories: Latest papers in fluid mechanics

### Simulation of interacting elastic sheets in shear flow: Insights into buckling, sliding, and reassembly of graphene nanosheets in sheared liquids

Physics of Fluids, Volume 34, Issue 5, May 2022.

In liquid-based material processing, hydrodynamic forces are known to produce severe bending deformations of two-dimensional (2D) materials such as graphene. The non-linear rotational and deformation dynamics of these atomically thin sheets is extremely sensitive to hydrodynamic particle-particle interactions. To investigate this problem, we developed a computational model of the flow dynamics of elastic sheets suspended in a linear shear flow, solving the full fluid-solid coupling problem in the two-dimensional, slender-body, Stokes flow regime. Both single and pairs of sheets in close proximity are analyzed. Despite the model being two-dimensional, the critical non-dimensional shear rate yielding single-particle buckling is comparable in order of magnitude to that reported for fully three-dimensional, disk-like sheets. For pairs of interacting sheets, hydrodynamic interactions lead either to parallel sliding or bending, depending on the value of an elasto-viscous number based on particle length. For sufficiently low bending rigidity or large shear rates, large deformations of initially stacked sheets lead to sheet reattachment after separation, unlike for the rigid case. A peeling-like dynamics where lubrication provides a viscous bonding force is observed for sheet pairs when one of the two sheets is more rigid than the other. Practical implications for graphene processing and exfoliation are discussed.

In liquid-based material processing, hydrodynamic forces are known to produce severe bending deformations of two-dimensional (2D) materials such as graphene. The non-linear rotational and deformation dynamics of these atomically thin sheets is extremely sensitive to hydrodynamic particle-particle interactions. To investigate this problem, we developed a computational model of the flow dynamics of elastic sheets suspended in a linear shear flow, solving the full fluid-solid coupling problem in the two-dimensional, slender-body, Stokes flow regime. Both single and pairs of sheets in close proximity are analyzed. Despite the model being two-dimensional, the critical non-dimensional shear rate yielding single-particle buckling is comparable in order of magnitude to that reported for fully three-dimensional, disk-like sheets. For pairs of interacting sheets, hydrodynamic interactions lead either to parallel sliding or bending, depending on the value of an elasto-viscous number based on particle length. For sufficiently low bending rigidity or large shear rates, large deformations of initially stacked sheets lead to sheet reattachment after separation, unlike for the rigid case. A peeling-like dynamics where lubrication provides a viscous bonding force is observed for sheet pairs when one of the two sheets is more rigid than the other. Practical implications for graphene processing and exfoliation are discussed.

Categories: Latest papers in fluid mechanics

### Long-wave instability of a regularized Bingham flow down an incline

Physics of Fluids, Volume 34, Issue 5, May 2022.

We investigate the linear stability of a flow down an incline when the fluid is modeled as a regularized Bingham-like fluid, i.e., a material whose constitutive equation is smoothed out. We perform a theoretical analysis by using the long-wave approximation method. The results show the existence of a critical condition for the onset of instability, which arises when the Reynolds number is above a critical threshold that depends on the tilt angle and on rheological parameters. The comparison of our findings with experimental studies is rather satisfactory.

We investigate the linear stability of a flow down an incline when the fluid is modeled as a regularized Bingham-like fluid, i.e., a material whose constitutive equation is smoothed out. We perform a theoretical analysis by using the long-wave approximation method. The results show the existence of a critical condition for the onset of instability, which arises when the Reynolds number is above a critical threshold that depends on the tilt angle and on rheological parameters. The comparison of our findings with experimental studies is rather satisfactory.

Categories: Latest papers in fluid mechanics

### Thermocapillary patterning of non-Newtonian thin films

Physics of Fluids, Volume 34, Issue 5, May 2022.

Deformation of thin viscous liquid films exposed to a transverse thermal gradient results in Bénard–Marangoni instability, which would lead to the formation of micro- and nano-sized features. Linear and nonlinear analyses are performed to investigate the thermally induced pattern formation in shear thinning and shear thickening liquid films. The so-called thin film (TF) equation is re-derived to include viscosity variations using the power-law (PL) model. The characteristic wavelength for the growth of instabilities is found using a linear stability analysis of the PL-TF equation. A finite-difference-based discretization scheme and adaptive time step solver are used to solve the PL-TF equation for the nonlinear numerical model. The results show that the rheological property affects the timescale of the process and the size and final shape of the formed features. The fastest growth pillar reaching the top substrate in a shear thickening fluid is shorter than both the shear thinning and the Newtonian fluid cases. Moreover, morphological changes between patterns of shear thinning and shear thickening fluids are correlated with local viscosity variations. The number of formed pillars considerably increases with the increasing flow behavior index. The existing model also predicts the formation of pillars and bicontinuous structures at very low and high filling ratios.

Deformation of thin viscous liquid films exposed to a transverse thermal gradient results in Bénard–Marangoni instability, which would lead to the formation of micro- and nano-sized features. Linear and nonlinear analyses are performed to investigate the thermally induced pattern formation in shear thinning and shear thickening liquid films. The so-called thin film (TF) equation is re-derived to include viscosity variations using the power-law (PL) model. The characteristic wavelength for the growth of instabilities is found using a linear stability analysis of the PL-TF equation. A finite-difference-based discretization scheme and adaptive time step solver are used to solve the PL-TF equation for the nonlinear numerical model. The results show that the rheological property affects the timescale of the process and the size and final shape of the formed features. The fastest growth pillar reaching the top substrate in a shear thickening fluid is shorter than both the shear thinning and the Newtonian fluid cases. Moreover, morphological changes between patterns of shear thinning and shear thickening fluids are correlated with local viscosity variations. The number of formed pillars considerably increases with the increasing flow behavior index. The existing model also predicts the formation of pillars and bicontinuous structures at very low and high filling ratios.

Categories: Latest papers in fluid mechanics

### Leading-edge-vortex tailoring on unsteady airfoils using an inverse aerodynamic approach

Physics of Fluids, Volume 34, Issue 5, May 2022.

In this paper, we present an approach to obtain a desired leading-edge vortex (LEV) shedding pattern from unsteady airfoils through the execution of suitable motion kinematics. Previous research revealed that LEV shedding is associated with the leading-edge suction parameter (LESP) exceeding a maximum threshold. A low-order method called LESP-modulated discrete vortex method (LDVM) was also developed to predict the onset and termination of LEV shedding from an airfoil undergoing prescribed motion kinematics. In the current work, we present an inverse-aerodynamic formulation based on the LDVM to generate the appropriate motion kinematics to achieve a prescribed LESP variation, and thus, the desired LEV shedding characteristics from the airfoil. The algorithm identifies the kinematic state of the airfoil required to attain the target LESP value through an iterative procedure performed inside the LDVM simulation at each time step. Several case studies are presented to demonstrate design scenarios such as tailoring the duration and intensity of LEV shedding, inducing LEV shedding from the chosen surface of the airfoil, promoting or suppressing LEV shedding during an unsteady motion on demand, and achieving similar LEV shedding patterns using different maneuvers. The kinematic profiles generated by the low-order formulation are also simulated using a high-fidelity unsteady Reynolds-averaged Navier–Stokes method to confirm the accuracy of the low-order model.

In this paper, we present an approach to obtain a desired leading-edge vortex (LEV) shedding pattern from unsteady airfoils through the execution of suitable motion kinematics. Previous research revealed that LEV shedding is associated with the leading-edge suction parameter (LESP) exceeding a maximum threshold. A low-order method called LESP-modulated discrete vortex method (LDVM) was also developed to predict the onset and termination of LEV shedding from an airfoil undergoing prescribed motion kinematics. In the current work, we present an inverse-aerodynamic formulation based on the LDVM to generate the appropriate motion kinematics to achieve a prescribed LESP variation, and thus, the desired LEV shedding characteristics from the airfoil. The algorithm identifies the kinematic state of the airfoil required to attain the target LESP value through an iterative procedure performed inside the LDVM simulation at each time step. Several case studies are presented to demonstrate design scenarios such as tailoring the duration and intensity of LEV shedding, inducing LEV shedding from the chosen surface of the airfoil, promoting or suppressing LEV shedding during an unsteady motion on demand, and achieving similar LEV shedding patterns using different maneuvers. The kinematic profiles generated by the low-order formulation are also simulated using a high-fidelity unsteady Reynolds-averaged Navier–Stokes method to confirm the accuracy of the low-order model.

Categories: Latest papers in fluid mechanics

### Investigation of counter-rotating shock wave and wave direction control of hollow rotating detonation engine with Laval nozzle

Physics of Fluids, Volume 34, Issue 5, May 2022.

The counter-rotating shock wave and wave direction control of the hollow rotating detonation combustor with Laval nozzle are studied. The in-house solver BYRFoam, developed on the OpenFOAM platform, is used. The phenomenon and spatial distribution of the counter-rotating shock wave in the combustor are revealed. The result suggests that the closer the location is to the outer wall, the stronger the counter-rotating shock wave is. A method of controlling the wave direction is proposed. It is shown that the intensity of the counter-rotating shock wave is controlled by reducing the total pressure of the inlet, and then the direction of the detonation wave is controlled. The process of detonation wave reversing is divided into four steps, namely, counter-rotating shock waves evolve into detonation waves, several detonation waves are extinguished, detonation waves form again, and detonation waves propagate stably. The mechanism of wave direction control is investigated. The result shows that the fluctuation of the total pressure of the inlet stimulates the positive feedback interaction between the counter-rotating shock wave and the fresh gas, which causes initial detonation waves to be extinguished and the intensity of counter-rotating shock waves to become stronger and stronger, and eventually counter-rotating shock waves evolve into reverse detonation waves.

The counter-rotating shock wave and wave direction control of the hollow rotating detonation combustor with Laval nozzle are studied. The in-house solver BYRFoam, developed on the OpenFOAM platform, is used. The phenomenon and spatial distribution of the counter-rotating shock wave in the combustor are revealed. The result suggests that the closer the location is to the outer wall, the stronger the counter-rotating shock wave is. A method of controlling the wave direction is proposed. It is shown that the intensity of the counter-rotating shock wave is controlled by reducing the total pressure of the inlet, and then the direction of the detonation wave is controlled. The process of detonation wave reversing is divided into four steps, namely, counter-rotating shock waves evolve into detonation waves, several detonation waves are extinguished, detonation waves form again, and detonation waves propagate stably. The mechanism of wave direction control is investigated. The result shows that the fluctuation of the total pressure of the inlet stimulates the positive feedback interaction between the counter-rotating shock wave and the fresh gas, which causes initial detonation waves to be extinguished and the intensity of counter-rotating shock waves to become stronger and stronger, and eventually counter-rotating shock waves evolve into reverse detonation waves.

Categories: Latest papers in fluid mechanics

### Three-dimensional direct numerical simulation of Rayleigh–Taylor instability triggered by acoustic excitation

Physics of Fluids, Volume 34, Issue 5, May 2022.

Rayleigh–Taylor instability (RTI) occurs when the interface between two fluids of different densities is removed, with the heavier (cold) fluid resting on top of the lighter (hot) fluid in the equilibrium state. This arrangement is unstable due to buoyancy, in the absence of any other forces. RTI is noted across a range of length scales from very small in nuclear fusion to supernova explosion at astrophysical scales. RTI is viewed as a baroclinic instability if viscous actions are ignored. An accurate non-overlapping parallel algorithm is used to solve a three-dimensional RTI problem, employing more than 4 × 109 points and a refined time step ([math]) for the direct numerical simulation. Air masses at two different temperatures are initially separated by a non-conducting partition inside a box (with a temperature difference of 200 K). The impermeable partition is removed impulsively at t = 0, and the ensuing instability is triggered by an acoustic mechanism involving infra to ultrasonic pulses that travel to either side of the interface. Present high precision petascale computations enable one to capture acoustic disturbances with unprecedented accuracy without any additional interfacial disturbances. The creation of the vorticity is studied by performing enstrophy budget for the compressible flow for RTI, which shows that the viscous terms are dominant compared to the baroclinic one.

Rayleigh–Taylor instability (RTI) occurs when the interface between two fluids of different densities is removed, with the heavier (cold) fluid resting on top of the lighter (hot) fluid in the equilibrium state. This arrangement is unstable due to buoyancy, in the absence of any other forces. RTI is noted across a range of length scales from very small in nuclear fusion to supernova explosion at astrophysical scales. RTI is viewed as a baroclinic instability if viscous actions are ignored. An accurate non-overlapping parallel algorithm is used to solve a three-dimensional RTI problem, employing more than 4 × 109 points and a refined time step ([math]) for the direct numerical simulation. Air masses at two different temperatures are initially separated by a non-conducting partition inside a box (with a temperature difference of 200 K). The impermeable partition is removed impulsively at t = 0, and the ensuing instability is triggered by an acoustic mechanism involving infra to ultrasonic pulses that travel to either side of the interface. Present high precision petascale computations enable one to capture acoustic disturbances with unprecedented accuracy without any additional interfacial disturbances. The creation of the vorticity is studied by performing enstrophy budget for the compressible flow for RTI, which shows that the viscous terms are dominant compared to the baroclinic one.

Categories: Latest papers in fluid mechanics

### A flight test based deep learning method for transition heat flux prediction in hypersonic flow

Physics of Fluids, Volume 34, Issue 5, May 2022.

Computational fluid dynamics predictions based on machine learning methods have become an important area of turbulence and transition research. However, the otherwise efficient and low-cost transition models based on Reynolds-averaged Navier–Stokes (RANS) methods have limited capability for dealing with hypersonic conditions, owing to the strong compressibility and multimodal features that are then present. This paper develops an augmented method for transition heat flux prediction. A deep neural network (DNN) is trained using flight test data from the China Aerodynamics Research and Development Center. The subject of the flight test is an inclined blunt cone on which temperature sensors are mounted. The training data consist of RANS solutions and flight test data, with the input being the mean strain/rotation rate tensor from RANS and the output the heat flux values from the flight test. The trained DNN model based on the RANS results can give heat flux values with similar accuracy to those from the flight test. For the blunt cone, the trained DNN model can accurately forecast the heat distribution caused by the Mack mode and the cross-flow transition under various inflow conditions, and the errors in the prediction results are all within 15%. Furthermore, the generalizability of the trained DNN model is also verified on an elliptic cone under different inflow conditions. This paper provides a new transition prediction approach with low computational cost and high accuracy. The proposed method solves the problem that the transition model fails in some working conditions and avoids re-modifying empirical criteria in the RANS model. It has both advantages of a transition model and flight tests and maintains the excellent potential for application.

Computational fluid dynamics predictions based on machine learning methods have become an important area of turbulence and transition research. However, the otherwise efficient and low-cost transition models based on Reynolds-averaged Navier–Stokes (RANS) methods have limited capability for dealing with hypersonic conditions, owing to the strong compressibility and multimodal features that are then present. This paper develops an augmented method for transition heat flux prediction. A deep neural network (DNN) is trained using flight test data from the China Aerodynamics Research and Development Center. The subject of the flight test is an inclined blunt cone on which temperature sensors are mounted. The training data consist of RANS solutions and flight test data, with the input being the mean strain/rotation rate tensor from RANS and the output the heat flux values from the flight test. The trained DNN model based on the RANS results can give heat flux values with similar accuracy to those from the flight test. For the blunt cone, the trained DNN model can accurately forecast the heat distribution caused by the Mack mode and the cross-flow transition under various inflow conditions, and the errors in the prediction results are all within 15%. Furthermore, the generalizability of the trained DNN model is also verified on an elliptic cone under different inflow conditions. This paper provides a new transition prediction approach with low computational cost and high accuracy. The proposed method solves the problem that the transition model fails in some working conditions and avoids re-modifying empirical criteria in the RANS model. It has both advantages of a transition model and flight tests and maintains the excellent potential for application.

Categories: Latest papers in fluid mechanics

### Parametric analysis of the effects of blade exit angle on the cavitation characteristics in a hydraulic torque converter

Physics of Fluids, Volume 34, Issue 5, May 2022.

Hydraulic torque converters are prone to cavitation due to their high impeller rotational speeds and their complex three-dimensional flow characteristics. Since the blades are the core components of torque converters, the shapes of the blades are important to the hydraulic performance and cavitation characteristics. Different cavitation computational fluid dynamics (CFD) models for a torque converter were developed to simulate the internal cavitation flow for different pump and turbine blade exit angles, and the influence of the blade angles on the cavitation characteristics and cavitation flow field in the torque converter was investigated. Experimental prototypes were produced and tested for verification. The results indicate that the pump and turbine blade exit angles had significant effects on the cavitation number of the torque converter. Increasing the pump and turbine blade exit angles promotes the generation and intensification of cavitation, resulting in severe changes in the shapes and locations of the cavitation bubbles due to changes in the fluid impact angles. Additionally, cavitation is quickly suppressed and the performance is improved when the blade exit angles are reduced within an appropriate range, in particular, that of the turbine blade. These research results can provide guidance for the design of a high-performance hydraulic torque converter cascade system and the suppression of cavitation for practical engineering applications.

Hydraulic torque converters are prone to cavitation due to their high impeller rotational speeds and their complex three-dimensional flow characteristics. Since the blades are the core components of torque converters, the shapes of the blades are important to the hydraulic performance and cavitation characteristics. Different cavitation computational fluid dynamics (CFD) models for a torque converter were developed to simulate the internal cavitation flow for different pump and turbine blade exit angles, and the influence of the blade angles on the cavitation characteristics and cavitation flow field in the torque converter was investigated. Experimental prototypes were produced and tested for verification. The results indicate that the pump and turbine blade exit angles had significant effects on the cavitation number of the torque converter. Increasing the pump and turbine blade exit angles promotes the generation and intensification of cavitation, resulting in severe changes in the shapes and locations of the cavitation bubbles due to changes in the fluid impact angles. Additionally, cavitation is quickly suppressed and the performance is improved when the blade exit angles are reduced within an appropriate range, in particular, that of the turbine blade. These research results can provide guidance for the design of a high-performance hydraulic torque converter cascade system and the suppression of cavitation for practical engineering applications.

Categories: Latest papers in fluid mechanics

### Dynamic characteristics of droplet impact on vibrating superhydrophobic substrate

Physics of Fluids, Volume 34, Issue 5, May 2022.

The vibration of solids is ubiquitous in nature and in industrial applications and gives rise to alternative droplet dynamics during impact. Using many-body dissipative particle dynamics, we investigate the impact of droplets on superhydrophobic solid surfaces vibrating in the vertical direction at a vibration period similar to the contact time. Specifically, we study the influence of the impact phase and vibration frequency. We evaluate the influence from the aspects of maximum spreading diameter, the solid–liquid contact time and area, and the momentum variation during the impact. To quantitatively evaluate the solid–liquid contact, we introduce the area-time integral, which is the integral of the contact area over the whole contact time. It is meaningful when the heat exchange between solid and liquid is considered. One characteristic phenomenon of droplets impacting vibrating substrate is that multiple contacts may occur before the final rebound. Unlike previous studies defining the contact time as the time span from the first impact to the final detachment, we define the contact time as the summation of each individual contact time. Using this definition, we show that the discontinuity at the critical impact phase disappears. The fact that the area-time integral also changes continually with the impact phase supports the assumption that the effect of impact phase on the solid–liquid contact may be continuous. Moreover, we show that the probability of impact phase is affected by the vibrating frequency and use it to calculate the weighted averaged outcome when the impact phase is not controlled. This study not only offers insights into the physics of droplet impact on vibrating surfaces but also can be used to guide the design of surfaces to achieve manageable wetting using vibration.

The vibration of solids is ubiquitous in nature and in industrial applications and gives rise to alternative droplet dynamics during impact. Using many-body dissipative particle dynamics, we investigate the impact of droplets on superhydrophobic solid surfaces vibrating in the vertical direction at a vibration period similar to the contact time. Specifically, we study the influence of the impact phase and vibration frequency. We evaluate the influence from the aspects of maximum spreading diameter, the solid–liquid contact time and area, and the momentum variation during the impact. To quantitatively evaluate the solid–liquid contact, we introduce the area-time integral, which is the integral of the contact area over the whole contact time. It is meaningful when the heat exchange between solid and liquid is considered. One characteristic phenomenon of droplets impacting vibrating substrate is that multiple contacts may occur before the final rebound. Unlike previous studies defining the contact time as the time span from the first impact to the final detachment, we define the contact time as the summation of each individual contact time. Using this definition, we show that the discontinuity at the critical impact phase disappears. The fact that the area-time integral also changes continually with the impact phase supports the assumption that the effect of impact phase on the solid–liquid contact may be continuous. Moreover, we show that the probability of impact phase is affected by the vibrating frequency and use it to calculate the weighted averaged outcome when the impact phase is not controlled. This study not only offers insights into the physics of droplet impact on vibrating surfaces but also can be used to guide the design of surfaces to achieve manageable wetting using vibration.

Categories: Latest papers in fluid mechanics

### Convection-induced bridging during alloy solidification

Physics of Fluids, Volume 34, Issue 5, May 2022.

In this work, the effect of solute expansion coefficient on the natural convection and freezing front propagation is investigated by performing three-side cooled solidification experiments. Four different aqueous salt solutions, and different compositions thereof, were employed for experimentation. The mixtures were solidified to analyze the effect of solute expansion coefficients on the convection currents and the composition distribution in the bulk. The initial compositions were chosen such that all cases have the same primary solid fraction at eutectic temperature, for obtaining similar compositional changes in the bulk liquid at various stages. Similar cooling conditions were also maintained to ensure that the variation in convection strength is primarily caused by different solute expansion coefficients. A distinct observation of the free surface freezing before the bulk, termed bridging, is reported in certain cases. Further analysis revealed that the bridging could be attributed to a difference in solute convection caused by the solute expansion coefficient. Numerical simulations were performed to further ascertain the plausible initiation mechanisms for bridging. The predicted compositional and solid fraction distribution revealed lesser solute accumulation near the surface, for the lower solute expansion cases, and the resulting increase in the tendency of freezing at the top. An upper limit for the ratio of solutal to thermal Rayleigh numbers in the experimental conditions has been identified for the occurrence of bridging in high Prandtl number fluids.

In this work, the effect of solute expansion coefficient on the natural convection and freezing front propagation is investigated by performing three-side cooled solidification experiments. Four different aqueous salt solutions, and different compositions thereof, were employed for experimentation. The mixtures were solidified to analyze the effect of solute expansion coefficients on the convection currents and the composition distribution in the bulk. The initial compositions were chosen such that all cases have the same primary solid fraction at eutectic temperature, for obtaining similar compositional changes in the bulk liquid at various stages. Similar cooling conditions were also maintained to ensure that the variation in convection strength is primarily caused by different solute expansion coefficients. A distinct observation of the free surface freezing before the bulk, termed bridging, is reported in certain cases. Further analysis revealed that the bridging could be attributed to a difference in solute convection caused by the solute expansion coefficient. Numerical simulations were performed to further ascertain the plausible initiation mechanisms for bridging. The predicted compositional and solid fraction distribution revealed lesser solute accumulation near the surface, for the lower solute expansion cases, and the resulting increase in the tendency of freezing at the top. An upper limit for the ratio of solutal to thermal Rayleigh numbers in the experimental conditions has been identified for the occurrence of bridging in high Prandtl number fluids.

Categories: Latest papers in fluid mechanics