# Latest papers in fluid mechanics

### Numerical simulation and modeling of the hydrodynamic forces and torque acting on individual oblate spheroids

Physics of Fluids, Volume 32, Issue 7, July 2020.

Computation of a three-dimensional uniform, steady Newtonian flow past oblate spheroidal particles is undertaken. The main objective of the present study is to compute the hydrodynamic forces on oblate spheroidal particles as a function of the particle orientation, for different particle aspect ratios and a large range of particle Reynolds number. The results of the simulations are used to provide a new complete set of correlations for drag, lift, and torque coefficients. These correlations are derived for an aspect ratio ranging from 0.2 to 1, for particle Reynolds number up to 100, and for all orientations. In addition, it is found that the Stokesian evolution of the drag and lift coefficients as a function of the incidence remains still valid at moderate particle Reynolds number; that is, drag coefficient evolves as sine squared and lift coefficient evolves as (sin ϕ cos ϕ).

Computation of a three-dimensional uniform, steady Newtonian flow past oblate spheroidal particles is undertaken. The main objective of the present study is to compute the hydrodynamic forces on oblate spheroidal particles as a function of the particle orientation, for different particle aspect ratios and a large range of particle Reynolds number. The results of the simulations are used to provide a new complete set of correlations for drag, lift, and torque coefficients. These correlations are derived for an aspect ratio ranging from 0.2 to 1, for particle Reynolds number up to 100, and for all orientations. In addition, it is found that the Stokesian evolution of the drag and lift coefficients as a function of the incidence remains still valid at moderate particle Reynolds number; that is, drag coefficient evolves as sine squared and lift coefficient evolves as (sin ϕ cos ϕ).

Categories: Latest papers in fluid mechanics

### On fluid flow and heat transfer of turbulent boundary layer of pseudoplastic fluids on a semi-infinite plate

Physics of Fluids, Volume 32, Issue 7, July 2020.

The boundary layer of a pseudoplastic fluid on a semi-infinite plate for a high generalized Reynolds number is analyzed. Based on the Prandtl mixing length theory, the turbulent region is divided into two regions. The coupled momentum and temperature equations, with a generalized thermal conductivity model, have made the process of finding the analytical solutions much difficult. By using the similarity transformation, the equations are converted to four ordinary differential equations constrained by ten boundary conditions. An interesting technique of scaling and translation of the calculation domain of one region into another is used to make the system of equations easier to solve. It is found that the fluid with a smaller power-law index, associated with a thinner velocity boundary layer thickness, processes a lower friction coefficient. Furthermore, the increase in the Reynolds number causes a thinner velocity boundary layer and a decreasing friction coefficient on the wall. Changes in temperature occur more slowly near the plate surface with a rise in the power-law index and a decrease in the Reynolds number.

The boundary layer of a pseudoplastic fluid on a semi-infinite plate for a high generalized Reynolds number is analyzed. Based on the Prandtl mixing length theory, the turbulent region is divided into two regions. The coupled momentum and temperature equations, with a generalized thermal conductivity model, have made the process of finding the analytical solutions much difficult. By using the similarity transformation, the equations are converted to four ordinary differential equations constrained by ten boundary conditions. An interesting technique of scaling and translation of the calculation domain of one region into another is used to make the system of equations easier to solve. It is found that the fluid with a smaller power-law index, associated with a thinner velocity boundary layer thickness, processes a lower friction coefficient. Furthermore, the increase in the Reynolds number causes a thinner velocity boundary layer and a decreasing friction coefficient on the wall. Changes in temperature occur more slowly near the plate surface with a rise in the power-law index and a decrease in the Reynolds number.

Categories: Latest papers in fluid mechanics

### Short cylindrical nozzles in a jet-driven Helmholtz oscillator

Physics of Fluids, Volume 32, Issue 7, July 2020.

The present paper elaborates on the experimental study of jet-excited pressure fluctuations in a Helmholtz oscillator model with two openings in a cylindrical cavity. The length of the cylindrical nozzle in the front cover ℓN normalized by the nozzle diameter dN was ℓN/dN = 0.125, 0.33, 0.47, and 0.67. The diameter of the outlet opening in the back cover dOUT was in the range dOUT/dN = 1–2.5. The length of the cylindrical cavity LCH determined the jet length LJET in the spacing between the covers, LCH/dN = 0.5–3.5. The amplitude–frequency spectra were studied when the oscillator configuration was changed in the indicated intervals. From the generation amplitude, the best ratio of the sizes of the nozzle, chamber, and outlet was determined. The appearance of the jet tone of the hole and the alternation of acoustic modes were observed with a smooth increase in the Reynolds number to ∼8 · 104. The measurements showed very high amplitude of pressure fluctuations in an oscillator with a short nozzle and a short chamber at a significant jet velocity. A slight increase in the length of the chamber led to a rapid decrease in the generation amplitude. It is determined that the tone frequency is usually much lower than the resonance frequency in the chamber. Moreover, the tone frequency gradually increases with increasing jet velocity, while the resonance frequency remains unchanged, close to the natural frequency of the cavity chamber.

The present paper elaborates on the experimental study of jet-excited pressure fluctuations in a Helmholtz oscillator model with two openings in a cylindrical cavity. The length of the cylindrical nozzle in the front cover ℓN normalized by the nozzle diameter dN was ℓN/dN = 0.125, 0.33, 0.47, and 0.67. The diameter of the outlet opening in the back cover dOUT was in the range dOUT/dN = 1–2.5. The length of the cylindrical cavity LCH determined the jet length LJET in the spacing between the covers, LCH/dN = 0.5–3.5. The amplitude–frequency spectra were studied when the oscillator configuration was changed in the indicated intervals. From the generation amplitude, the best ratio of the sizes of the nozzle, chamber, and outlet was determined. The appearance of the jet tone of the hole and the alternation of acoustic modes were observed with a smooth increase in the Reynolds number to ∼8 · 104. The measurements showed very high amplitude of pressure fluctuations in an oscillator with a short nozzle and a short chamber at a significant jet velocity. A slight increase in the length of the chamber led to a rapid decrease in the generation amplitude. It is determined that the tone frequency is usually much lower than the resonance frequency in the chamber. Moreover, the tone frequency gradually increases with increasing jet velocity, while the resonance frequency remains unchanged, close to the natural frequency of the cavity chamber.

Categories: Latest papers in fluid mechanics

### Persistence analysis of velocity and temperature fluctuations in convective surface layer turbulence

Physics of Fluids, Volume 32, Issue 7, July 2020.

Persistence is defined as the probability that the local value of a fluctuating field remains at a particular state for a certain amount of time, before being switched to another state. The concept of persistence has been found to have many diverse practical applications, ranging from non-equilibrium statistical mechanics to financial dynamics to distribution of time scales in turbulent flows and many more. In this study, we carry out a detailed analysis of the statistical characteristics of the persistence probability density functions (PDFs) of velocity and temperature fluctuations in the surface layer of a convective boundary layer using a field-experimental dataset. Our results demonstrate that for the time scales smaller than the integral scales, the persistence PDFs of turbulent velocity and temperature fluctuations display a clear power-law behavior, associated with a self-similar eddy cascading mechanism. Moreover, we also show that the effects of non-Gaussian temperature fluctuations act only at those scales that are larger than the integral scales, where the persistence PDFs deviate from the power-law and drop exponentially. Furthermore, the mean time scales of the negative temperature fluctuation events persisting longer than the integral scales are found to be approximately equal to twice the integral scale in highly convective conditions. However, with stability, this mean time scale gradually decreases to almost being equal to the integral scale in the near-neutral conditions. Contrarily, for the long positive temperature fluctuation events, the mean time scales remain roughly equal to the integral scales, irrespective of stability.

Persistence is defined as the probability that the local value of a fluctuating field remains at a particular state for a certain amount of time, before being switched to another state. The concept of persistence has been found to have many diverse practical applications, ranging from non-equilibrium statistical mechanics to financial dynamics to distribution of time scales in turbulent flows and many more. In this study, we carry out a detailed analysis of the statistical characteristics of the persistence probability density functions (PDFs) of velocity and temperature fluctuations in the surface layer of a convective boundary layer using a field-experimental dataset. Our results demonstrate that for the time scales smaller than the integral scales, the persistence PDFs of turbulent velocity and temperature fluctuations display a clear power-law behavior, associated with a self-similar eddy cascading mechanism. Moreover, we also show that the effects of non-Gaussian temperature fluctuations act only at those scales that are larger than the integral scales, where the persistence PDFs deviate from the power-law and drop exponentially. Furthermore, the mean time scales of the negative temperature fluctuation events persisting longer than the integral scales are found to be approximately equal to twice the integral scale in highly convective conditions. However, with stability, this mean time scale gradually decreases to almost being equal to the integral scale in the near-neutral conditions. Contrarily, for the long positive temperature fluctuation events, the mean time scales remain roughly equal to the integral scales, irrespective of stability.

Categories: Latest papers in fluid mechanics

### Shock-tube measurements of coupled vibration–dissociation time-histories and rate parameters in oxygen and argon mixtures from 5000 K to 10 000 K

Physics of Fluids, Volume 32, Issue 7, July 2020.

Shock-tube experiments were conducted behind reflected shocks using ultraviolet (UV) laser absorption to measure coupled vibration–dissociation (CVDV) time-histories and rate parameters in dilute mixtures of oxygen (O2) and argon (Ar). Experiments probed 2% and 5% O2 in Ar mixtures for initial post-reflected-shock conditions from 5000 K to 10 000 K and 0.04 atm to 0.45 atm. A tunable, pulsed UV laser absorption diagnostic measured absorbance time-histories from the fourth, fifth, and sixth vibrational levels of the electronic ground state of O2, and experiments were repeated—with closely matched temperature and pressure conditions—to probe absorbance time-histories corresponding to each vibrational level. The absorbance ratio from two vibrational levels, interpreted via an experimentally validated spectroscopic model, determined vibrational temperature time-histories. In contrast, the absorbance involving a single vibrational level determined vibrational-state-specific number density time-histories. These temperature and state-specific number density time-histories agree reasonably well with state-to-state modeling at low temperatures but deviate significantly at high temperatures. Further analysis of the vibrational temperature and number density time-histories isolated coupling parameters from the Marrone and Treanor CVDV model, including vibrational relaxation time (τ), average vibrational energy loss (ε), vibrational coupling factor (Z), and dissociation rate constant (kd). The results for τ and kd are consistent with previous results, exhibit low scatter, and—in the case of vibrational relaxation time—extend measurements to higher temperatures than previous experiments. The results for ε and Z overlap some common models, exhibit relatively low scatter, and provide novel experimental data.

Shock-tube experiments were conducted behind reflected shocks using ultraviolet (UV) laser absorption to measure coupled vibration–dissociation (CVDV) time-histories and rate parameters in dilute mixtures of oxygen (O2) and argon (Ar). Experiments probed 2% and 5% O2 in Ar mixtures for initial post-reflected-shock conditions from 5000 K to 10 000 K and 0.04 atm to 0.45 atm. A tunable, pulsed UV laser absorption diagnostic measured absorbance time-histories from the fourth, fifth, and sixth vibrational levels of the electronic ground state of O2, and experiments were repeated—with closely matched temperature and pressure conditions—to probe absorbance time-histories corresponding to each vibrational level. The absorbance ratio from two vibrational levels, interpreted via an experimentally validated spectroscopic model, determined vibrational temperature time-histories. In contrast, the absorbance involving a single vibrational level determined vibrational-state-specific number density time-histories. These temperature and state-specific number density time-histories agree reasonably well with state-to-state modeling at low temperatures but deviate significantly at high temperatures. Further analysis of the vibrational temperature and number density time-histories isolated coupling parameters from the Marrone and Treanor CVDV model, including vibrational relaxation time (τ), average vibrational energy loss (ε), vibrational coupling factor (Z), and dissociation rate constant (kd). The results for τ and kd are consistent with previous results, exhibit low scatter, and—in the case of vibrational relaxation time—extend measurements to higher temperatures than previous experiments. The results for ε and Z overlap some common models, exhibit relatively low scatter, and provide novel experimental data.

Categories: Latest papers in fluid mechanics

### Kinetic equation for particle transport in turbulent flows

Physics of Fluids, Volume 32, Issue 7, July 2020.

With a new approach based on the ensemble average over particle state transition paths in phase space, a kinetic equation for particles transported in turbulent flows is derived. The probability density function (PDF) for particles is defined as an ensemble average of a special fine-grained PDF, referred to as the local path density operator. The kinetic equation is derived from a Taylor series expansion of the PDF in terms of the cumulants with respect to particle paths in phase space and leads to a closed expression for its diffusion terms. It shows that the random forcing of eddy fluctuations, non-stationarity of turbulence, and inertia of particles are explicitly presented in the diffusion coefficient, which could help us to understand how particles are diffused by these underlying mechanisms. The kinetic equation is applicable to non-Markovian, non-Gaussian, and non-stationary stochastic processes, while for Markovian processes, it recovers the classical Fokker–Planck equation. The macroscopic equations for particle phase are derived based on the kinetic equation and compared with the direct numerical simulation of particles transported in turbulent flows.

With a new approach based on the ensemble average over particle state transition paths in phase space, a kinetic equation for particles transported in turbulent flows is derived. The probability density function (PDF) for particles is defined as an ensemble average of a special fine-grained PDF, referred to as the local path density operator. The kinetic equation is derived from a Taylor series expansion of the PDF in terms of the cumulants with respect to particle paths in phase space and leads to a closed expression for its diffusion terms. It shows that the random forcing of eddy fluctuations, non-stationarity of turbulence, and inertia of particles are explicitly presented in the diffusion coefficient, which could help us to understand how particles are diffused by these underlying mechanisms. The kinetic equation is applicable to non-Markovian, non-Gaussian, and non-stationary stochastic processes, while for Markovian processes, it recovers the classical Fokker–Planck equation. The macroscopic equations for particle phase are derived based on the kinetic equation and compared with the direct numerical simulation of particles transported in turbulent flows.

Categories: Latest papers in fluid mechanics

### Stability of a non-Newtonian falling film due to three-dimensional disturbances

Physics of Fluids, Volume 32, Issue 7, July 2020.

In this paper, we apply the normal modes method to study the linear stability of a liquid film flowing down an inclined plane, taking into account the complex rheology of the media. We consider generalized Newtonian liquids; the conditions of the Squire theorem do not hold for this case. We check if the flow is unstable due to three-dimensional (3D) disturbances that propagate at a certain angle to the flow direction but stable for the two-dimensional (2D) ones. We derived the generalized Orr–Sommerfeld equation, considered a long-wave approximation, and proved that 3D long-wave disturbances are less growing than the 2D ones for any rheological law. We solved the problem for finite wavenumbers numerically and found that for low inclination angles of the plane, instability due to 3D disturbances prevails. In this case, the shear mode of instability dominates, and the surface tension destabilizes the flow. For shear-thickening liquids, the critical Reynolds number decreases down to zero.

In this paper, we apply the normal modes method to study the linear stability of a liquid film flowing down an inclined plane, taking into account the complex rheology of the media. We consider generalized Newtonian liquids; the conditions of the Squire theorem do not hold for this case. We check if the flow is unstable due to three-dimensional (3D) disturbances that propagate at a certain angle to the flow direction but stable for the two-dimensional (2D) ones. We derived the generalized Orr–Sommerfeld equation, considered a long-wave approximation, and proved that 3D long-wave disturbances are less growing than the 2D ones for any rheological law. We solved the problem for finite wavenumbers numerically and found that for low inclination angles of the plane, instability due to 3D disturbances prevails. In this case, the shear mode of instability dominates, and the surface tension destabilizes the flow. For shear-thickening liquids, the critical Reynolds number decreases down to zero.

Categories: Latest papers in fluid mechanics

### Direct numerical simulation of drag reduction by spanwise oscillating dielectric barrier discharge plasma force

Physics of Fluids, Volume 32, Issue 7, July 2020.

DBD (dielectric barrier discharge) plasma actuators have in recent years become increasingly attractive in studies of flow control due to their light structures and easy implementation, but the design of a series of actuators enabling drag reduction depends on many parameters (e.g., the length of the actuator, the space between actuators, and voltage applied) and remains a significant issue to address. In this study, velocities created by the DBD plasma actuators in stagnant flow obtained by the numerical model are compared with experimental results. Then, a DNS study is carried on, and spanwise oscillated DBD plasma actuators are examined to obtain a drag reduction in a fully developed turbulent channel flow. This study connects the conventional spanwise oscillated force in drag reduction studies with DBD plasma actuators. While the former is one of the most successful applications for the drag reduction, the latter is a most promising tool with its light and feasible structure.

DBD (dielectric barrier discharge) plasma actuators have in recent years become increasingly attractive in studies of flow control due to their light structures and easy implementation, but the design of a series of actuators enabling drag reduction depends on many parameters (e.g., the length of the actuator, the space between actuators, and voltage applied) and remains a significant issue to address. In this study, velocities created by the DBD plasma actuators in stagnant flow obtained by the numerical model are compared with experimental results. Then, a DNS study is carried on, and spanwise oscillated DBD plasma actuators are examined to obtain a drag reduction in a fully developed turbulent channel flow. This study connects the conventional spanwise oscillated force in drag reduction studies with DBD plasma actuators. While the former is one of the most successful applications for the drag reduction, the latter is a most promising tool with its light and feasible structure.

Categories: Latest papers in fluid mechanics

### Liquid jet disintegration memory effect on downstream spray fluctuations in a coaxial twin-fluid injector

Physics of Fluids, Volume 32, Issue 7, July 2020.

This paper intends to investigate the influence of unsteadiness in the liquid jet disintegration process on downstream fluctuations of spray characteristics in a coaxial twin-fluid injector. Time-resolved high-speed shadowgraphic imaging of the spray was obtained for different axial locations downstream of the injector exit at z = 0, 8Dl, and 30Dl, where Dl is the central liquid tube diameter. The primary jet breakup unsteadiness close to the injector exit was characterized by measuring both shear-driven Kelvin–Helmholtz (KH) instability and flapping instability in addition to jet breakup length fluctuations. Downstream of the liquid jet core region, the liquid shedding rate ([math]) was measured at z = 8Dl. The power spectrum of time series data of instantaneous volume mean diameter (VMD) measured at z = 30Dl indicated periodic variation of the droplet size. The corresponding frequency (fVMD) was obtained. It was found that for lower range of gas-to-liquid momentum flux ratio (M < 4), both [math] and fVMD are larger than the frequency of KH instability. Also, for such conditions, larger temporal variation of the droplet size is realized, and this leads to higher fluctuations of the local liquid mass flux. Proper orthogonal decomposition analysis of the shadowgraph images for different axial locations identified similar topology of the dominant mode that corresponds to flapping instability. The results suggest that even far downstream of the injector exit, some memory of the upstream unsteady jet breakup process is retained, which strongly influences spatio-temporal evolution of droplet characteristics, thereby contributing to local spray fluctuations.

This paper intends to investigate the influence of unsteadiness in the liquid jet disintegration process on downstream fluctuations of spray characteristics in a coaxial twin-fluid injector. Time-resolved high-speed shadowgraphic imaging of the spray was obtained for different axial locations downstream of the injector exit at z = 0, 8Dl, and 30Dl, where Dl is the central liquid tube diameter. The primary jet breakup unsteadiness close to the injector exit was characterized by measuring both shear-driven Kelvin–Helmholtz (KH) instability and flapping instability in addition to jet breakup length fluctuations. Downstream of the liquid jet core region, the liquid shedding rate ([math]) was measured at z = 8Dl. The power spectrum of time series data of instantaneous volume mean diameter (VMD) measured at z = 30Dl indicated periodic variation of the droplet size. The corresponding frequency (fVMD) was obtained. It was found that for lower range of gas-to-liquid momentum flux ratio (M < 4), both [math] and fVMD are larger than the frequency of KH instability. Also, for such conditions, larger temporal variation of the droplet size is realized, and this leads to higher fluctuations of the local liquid mass flux. Proper orthogonal decomposition analysis of the shadowgraph images for different axial locations identified similar topology of the dominant mode that corresponds to flapping instability. The results suggest that even far downstream of the injector exit, some memory of the upstream unsteady jet breakup process is retained, which strongly influences spatio-temporal evolution of droplet characteristics, thereby contributing to local spray fluctuations.

Categories: Latest papers in fluid mechanics

### Thrust generation by pitching and heaving of an elastic plate at low Reynolds number

Physics of Fluids, Volume 32, Issue 7, July 2020.

We computationally study thrust generation and propulsive characteristics of an elastic plate pitching and/or heaving in free stream laminar flow. The pitching is considered about the leading edge, and the Reynolds number based on the plate length and free stream velocity is 150. An in-house fluid–structure interaction (FSI) solver is employed to simulate the large-scale flow-induced deformation of the structure along with active pitching and heaving in two-dimensional coordinates. The FSI solver utilizes a partitioned approach to strongly couple a sharp-interface immersed boundary method based flow solver with an open-source finite-element structural dynamics solver. We elucidate the mechanism of the thrust generation in the rigid and elastic plate by comparing the time-variation of thrust and work done by the plate, together with the wake signatures in the downstream. The time variation of the thrust is explained using first-order scaling arguments. The computed thrust as a function of pitching frequency for the rigid pitching plate shows a similar trend as compared to the published data of rigid foils, while the elastic plate exhibits a strong influence of the flow-induced deformation of the plate. They both exhibit reverse von Kármán-like vortex shedding in the downstream. We quantify the differences in propulsive characteristics of these two plate types as a function of pitching frequency. We found that there lies an optimum pitching frequency for the elastic plate for efficient propulsion, while the rigid one outperforms the elastic plate at larger pitching frequency. This is due to the fact that the elastic plate locks in to a higher mode of vibration at a larger pitching frequency. Furthermore, the influence of mass ratio, flexural rigidity, pitching amplitude, and Reynolds number on the performance of the elastic plate is also investigated. Finally, we study the combined effect of pitching and heaving on the propulsive performance. The pitching frequency for the maximum efficiency is lesser for the combined heaving and pitching plate as compared to only heaving or only pitching. Our results provide fundamental insights into the propulsive characteristics of the elastic pitching and/or heaving plates, which could help design autonomous underwater vehicles.

We computationally study thrust generation and propulsive characteristics of an elastic plate pitching and/or heaving in free stream laminar flow. The pitching is considered about the leading edge, and the Reynolds number based on the plate length and free stream velocity is 150. An in-house fluid–structure interaction (FSI) solver is employed to simulate the large-scale flow-induced deformation of the structure along with active pitching and heaving in two-dimensional coordinates. The FSI solver utilizes a partitioned approach to strongly couple a sharp-interface immersed boundary method based flow solver with an open-source finite-element structural dynamics solver. We elucidate the mechanism of the thrust generation in the rigid and elastic plate by comparing the time-variation of thrust and work done by the plate, together with the wake signatures in the downstream. The time variation of the thrust is explained using first-order scaling arguments. The computed thrust as a function of pitching frequency for the rigid pitching plate shows a similar trend as compared to the published data of rigid foils, while the elastic plate exhibits a strong influence of the flow-induced deformation of the plate. They both exhibit reverse von Kármán-like vortex shedding in the downstream. We quantify the differences in propulsive characteristics of these two plate types as a function of pitching frequency. We found that there lies an optimum pitching frequency for the elastic plate for efficient propulsion, while the rigid one outperforms the elastic plate at larger pitching frequency. This is due to the fact that the elastic plate locks in to a higher mode of vibration at a larger pitching frequency. Furthermore, the influence of mass ratio, flexural rigidity, pitching amplitude, and Reynolds number on the performance of the elastic plate is also investigated. Finally, we study the combined effect of pitching and heaving on the propulsive performance. The pitching frequency for the maximum efficiency is lesser for the combined heaving and pitching plate as compared to only heaving or only pitching. Our results provide fundamental insights into the propulsive characteristics of the elastic pitching and/or heaving plates, which could help design autonomous underwater vehicles.

Categories: Latest papers in fluid mechanics

### Hydrodynamic forces on a clean spherical bubble translating in a wall-bounded linear shear flow

Author(s): Pengyu Shi, Roland Rzehak, Dirk Lucas, and Jacques Magnaudet

Fully resolved simulations are conducted to determine hydrodynamic forces on clean spherical bubbles translating near a flat rigid wall in a linear shear flow. Flows range from low-but-finite Re to nearly inviscid situations. Based on simulation results, semi-empirical expressions for drag and lift forces at arbitrary Re, relative shear rate, and separation distance are found. These improve over current ‘point-particle’ models which ignore wall effects, and may be used to predict realistic bubble trajectories and distributions in wall-bounded flows.

[Phys. Rev. Fluids 5, 073601] Published Wed Jul 01, 2020

Categories: Latest papers in fluid mechanics

### Modeling the dielectric strength variation of supercritical fluids driven by cluster formation near critical point

Physics of Fluids, Volume 32, Issue 7, July 2020.

Density fluctuation driven by cluster formation causes drastic changes in the dielectric breakdown characteristics of supercritical fluids that cannot be described solely based on the conventional Townsend’s gas discharge theory and Paschen’s law. In this study, we model the dielectric breakdown characteristics of supercritical CO2 as a function of pressure based on the electron scattering cross section data of CO2 clusters that vary in size as a function of temperature and pressure around the critical point. The electron scattering cross section data of CO2 clusters are derived from those of gaseous CO2. We solve the Boltzmann equation based on the electron scattering cross section data to obtain critical electrical fields of various cluster sizes as a function of pressure. To validate our model, we compare the modeled breakdown voltage with the experimental breakdown measurements of supercritical CO2, which show close agreement.

Density fluctuation driven by cluster formation causes drastic changes in the dielectric breakdown characteristics of supercritical fluids that cannot be described solely based on the conventional Townsend’s gas discharge theory and Paschen’s law. In this study, we model the dielectric breakdown characteristics of supercritical CO2 as a function of pressure based on the electron scattering cross section data of CO2 clusters that vary in size as a function of temperature and pressure around the critical point. The electron scattering cross section data of CO2 clusters are derived from those of gaseous CO2. We solve the Boltzmann equation based on the electron scattering cross section data to obtain critical electrical fields of various cluster sizes as a function of pressure. To validate our model, we compare the modeled breakdown voltage with the experimental breakdown measurements of supercritical CO2, which show close agreement.

Categories: Latest papers in fluid mechanics

### An investigation on the disturbance evolution and the transition by resonant-triad interactions with a side-frequency disturbance in a boundary layer

Physics of Fluids, Volume 32, Issue 7, July 2020.

In practical engineering problems, there are always side-frequency components whose frequencies are close to those of the dominant-frequency waves. In this paper, the parabolized stability equations are employed to study the influence of a side-frequency component on the development of a dominant-frequency disturbance and on the transition by resonant-triad interactions. The numerical results are qualitatively consistent with the experimental data and the asymptotic analysis results. It is found that the resonant-triad waves and the mean flow distortion cannot trigger transition by themselves. We identify a new mechanism, which we refer to as the Steady-Spanwise-Waves-Working (SSWW) mechanism, which is necessary to cause transition, in that the steady spanwise waves generated by the nonlinear interaction between the pair of three-dimensional waves play an indispensable role. For the transition caused by resonant-triad interactions with a side-frequency component, the side-frequency wave makes transition occur earlier, and the relative amplitude rather than the absolute amplitude of the side-frequency disturbance plays the essential role in the transition advance. If the relative amplitude reaches the threshold level of 40%, the transition location can be affected substantially. In this kind of transition, the SSWW mechanism still works, and the side-frequency perturbation enhances the effects of the SSWW mechanism such that the transition occurs earlier.

In practical engineering problems, there are always side-frequency components whose frequencies are close to those of the dominant-frequency waves. In this paper, the parabolized stability equations are employed to study the influence of a side-frequency component on the development of a dominant-frequency disturbance and on the transition by resonant-triad interactions. The numerical results are qualitatively consistent with the experimental data and the asymptotic analysis results. It is found that the resonant-triad waves and the mean flow distortion cannot trigger transition by themselves. We identify a new mechanism, which we refer to as the Steady-Spanwise-Waves-Working (SSWW) mechanism, which is necessary to cause transition, in that the steady spanwise waves generated by the nonlinear interaction between the pair of three-dimensional waves play an indispensable role. For the transition caused by resonant-triad interactions with a side-frequency component, the side-frequency wave makes transition occur earlier, and the relative amplitude rather than the absolute amplitude of the side-frequency disturbance plays the essential role in the transition advance. If the relative amplitude reaches the threshold level of 40%, the transition location can be affected substantially. In this kind of transition, the SSWW mechanism still works, and the side-frequency perturbation enhances the effects of the SSWW mechanism such that the transition occurs earlier.

Categories: Latest papers in fluid mechanics

### Wake and thermal characteristics for cross-buoyancy mixed convection around and through a porous cylinder

Physics of Fluids, Volume 32, Issue 7, July 2020.

The influence of cross buoyancy on the steady flow and mixed convective heat transfer around and through a porous cylinder with internal heat generation is investigated numerically. Based on the Darcy–Brinkman–Forchheimer extended porous medium model, the finite volume method is applied to investigate the wake structure and thermal characteristics in terms of the streamlines, asymmetry of recirculating wakes, temperature distribution, and average Nusselt number. The ranges chosen for the Reynolds number (Re), Darcy number (Da), and Richardson number (Ri) are 5 ≤ Re ≤ 40, 10−6 ≤ Da ≤ 10−2, and 0 ≤ Ri ≤ 1, respectively. For certain ranges above, a pair of asymmetric recirculating wakes is observed, with the upper recirculating wake detached from and the lower one partially penetrating or also detached from the cylinder. The asymmetry of the recirculating wake increases with Ri but decreases with Re. Two or three regimes with the distinct asymmetric characteristics are identified over the range of Da investigated, depending on Re. For the heat transfer performance, cross buoyancy is found to have a certain impeditive impact on the average Nusselt number.

The influence of cross buoyancy on the steady flow and mixed convective heat transfer around and through a porous cylinder with internal heat generation is investigated numerically. Based on the Darcy–Brinkman–Forchheimer extended porous medium model, the finite volume method is applied to investigate the wake structure and thermal characteristics in terms of the streamlines, asymmetry of recirculating wakes, temperature distribution, and average Nusselt number. The ranges chosen for the Reynolds number (Re), Darcy number (Da), and Richardson number (Ri) are 5 ≤ Re ≤ 40, 10−6 ≤ Da ≤ 10−2, and 0 ≤ Ri ≤ 1, respectively. For certain ranges above, a pair of asymmetric recirculating wakes is observed, with the upper recirculating wake detached from and the lower one partially penetrating or also detached from the cylinder. The asymmetry of the recirculating wake increases with Ri but decreases with Re. Two or three regimes with the distinct asymmetric characteristics are identified over the range of Da investigated, depending on Re. For the heat transfer performance, cross buoyancy is found to have a certain impeditive impact on the average Nusselt number.

Categories: Latest papers in fluid mechanics