Total Energy Dissipation Rate Research Articles

Backscatter in energetically-constrained Leith parameterizations

This paper combines two strains in the literature on subgrid-scale parameterizations for eddying ocean models to develop six new parameterizations and test them in an idealized quasigeostrophic model. The first strain develops nonlinear, Smagorinsky-like Leith scalings for the viscous coefficient based on reasoning about the turbulent forward enstrophy cascade of geophysical turbulence. The second introduces backscatter whose amplitude is scaled to re-inject a portion of the energy dissipated by other parameterizations. In the new parameterizations developed here the backscatter and viscous coefficients depend on each other and are set to simultaneously absorb the forward enstrophy (or potential enstrophy) cascade and backscatter a portion of the dissipated energy. The addition of backscatter to Leith-scaled nonlinear viscosity improves the simulations at resolutions from 4 km to 24 km by increasing the total kinetic energy and by reducing the fraction of the total energy dissipation rate associated with the net effect of viscosity and backscatter. Versions that use biharmonic viscosity to absorb the enstrophy cascade perform better than versions using a harmonic viscosity, and purely viscous closures perform better than closures that dissipate both kinetic and potential energy. Stochastic and deterministic backscatter schemes are developed, and though similar, the deterministic schemes perform slightly better.

Geometric parameters optimization of low resistance T-junction with guide vanes in HVAC system

In recent years, with the increasing energy consumption and carbon emissions, people are paying more and more attention to related measures for energy conservation and emission reduction. As an important conveying component of the HVAC system, the pipe network system plays the function of distributing the fluid medium. However, a large part of the resistance loss is often generated during this transportation process, and the local pressure loss caused by local resistance components (e.g., T-junction) accounts for a large part of the total pressure drop. In this work, the influence of different guide vane positions on the resistance of the T-junction is analyzed. The internal flow field distribution and resistance characteristics of the T-junction are explored by numerical calculation method. The total energy dissipation and resistance reduction rate of the traditional T-junction and the novel T-junction with a guide vane are compared under different flow ratios. The resistance reduction rate of the optimized T-junction with a guide vane is 21.5%. The insertion of guide vanes can reduce the flow resistance and total energy loss of T-junction.

Mesh-free peridynamic coupled simulation of impacting collapse of a granular column with various heights

In this study, a coupled model of Peridynamics into the mesh-free method is extended to simulate the impacting collapse of a granular column with various suspended heights. Experiments on the impacting collapse were conducted to validate the numerical model. It is found that the simulated free surface profiles have a good agreement with the experimental measurements. The numerical model is also validated by simulating the granular column collapse. The simulated kinetic energy and potential energy agree well with the discrete element method (DEM) simulation results in the literature. In the validations, different numerical particle distances are implemented to discrete the fluid and a good numerical convergence is achieved for the numerical method. After model validation, the energy variations in the impacting collapse of the granular column with different suspended heights are analyzed, which include evolutions of the potential energy, horizontal kinetic energy, and vertical kinetic energy. In the analysis, the relative total energy dissipation rate for the flow with various suspended heights is calculated. The analysis shows that the suspended height in the impacting collapse of the granular column can affect the energy dissipation significantly.

Numerical Simulation of Stepped Spillways with Front Step Deformation

In order to solve the flood discharge problem of both small- and medium-sized warping dams in the Loess Plateau, a stepped spillway scheme, based on an ecological bag, to achieve full-section water flow and energy dissipation has been proposed in this paper. The hydraulic and energy dissipation characteristics of a stepped spillway layout scheme were studied using 3D numerical simulation. As the height of the dams is low and the spillways are short, the research has shown that the traditional single-step layout scheme leads to a low overall energy dissipation rate due to the small amount of energy dissipated in the initial steps. As a result of this, this paper has put forward two kinds of step layout schemes such as the shunt type and the staggered type for the initial steps. Through analysis of the flow state, the pressure distribution, and the total energy dissipation rate, the results have shown that shunt type and staggered type with front step deformation produced an obvious mixing of the water flow, fewer negative pressure areas, and a higher energy dissipation rate. The optimal energy dissipation rate of the staggered type reached 87.75%, and the maximum energy dissipation rate was increased by 27.97%.

CFD based mass transfer modeling of a single use bioreactor for production of monoclonal antibody biotherapeutics

In this study, Euler-Euler coupled computational fluid dynamics (CFD), species transport and population balance model (PBM) simulations have been used to model multiphase hydrodynamics and mass (O2) transfer in a single use bioreactor (SUB) for mAb production. In simulations, drag was estimated by Schiller-Neuman equations. O2(g) local volume fraction was estimated via species transport model (STM). The PBM equations were solved using quadrature method of moments (QMOM) to get bubble size distribution (BSD) and thereby the Sauter mean diameter,d32. Also, the mean diameter over surface (d21) and De Brouckere mean (d43) were estimated for calculation of the BSD. The mass transfer coefficient (kLa) was predicted using species transport model (STM) and Higbie’s penetration theory. The experimental estimation of kLa was performed via simplified dynamic pressure method. Total stress (τ) and energy dissipation rate (ε) were estimated as 34.17 Pa and 1.352 m2.s−3, respectively. Calculations of the d32, d21 and d43 indicate that the BSD becomes more dispersed with increase in agitation speed at all aeration rates. Further, the kLa values of STM were within 0.47% to 4.21% of experimental data. In summary, with error between 4 and 10%, the proposed approach offers better visualization of O2 transport mechanism across gas–liquid interface than conventional approaches.

Estimating Energy Dissipation Rate from Breaking Waves Using Polarimetric SAR Images.

The total energy dissipation rate on the ocean surface, (W m), provides a first-order estimation of the kinetic energy input rate at the ocean–atmosphere interface. Studies on the spatial and temporal distribution of the energy dissipation rate are important for the improvement of climate and wave models. Traditional oceanographic research normally uses remote measurements (airborne and platforms sensors) and in situ data acquisition to estimate ; however, those methods cover small areas over time and are difficult to reproduce especially in the open oceans. Satellite remote sensing has proven the potential to estimate some parameters related to breaking waves on a synoptic scale, including the energy dissipation rate. In this paper, we use polarimetric Synthetic Aperture Radar (SAR) data to estimate under different wind and sea conditions. The used methodology consisted of decomposing the backscatter SAR return in terms of two contributions: a polarized contribution, associated with the fast response of the local wind (Bragg backscattering), and a non-polarized (NP) contribution, associated with wave breaking (Non-Bragg backscattering). Wind and wave parameters were estimated from the NP contribution and used to calculate from a parametric model dependent of these parameters. The results were analyzed using wave model outputs (WAVEWATCH III) and previous measurements documented in the literature. For the prevailing wind seas conditions, the estimated from pol-SAR data showed good agreement with dissipation associated with breaking waves when compared to numerical simulations. Under prevailing swell conditions, the total energy dissipation rate was higher than expected. The methodology adopted proved to be satisfactory to estimate the total energy dissipation rate for light to moderate wind conditions (winds below 10 m s), an environmental condition for which the current SAR polarimetric methods do not estimate properly.

Particle-resolved direct numerical simulation of collisions of bidisperse inertial particles in a homogeneous isotropic turbulence

A particle-resolved study of a collision system composed of heavy particles and light particles in a homogeneous isotropic turbulence has been performed. Direct numerical simulations (DNS) of this system were conducted using lattice Boltzmann method (LBM). The effects of hydrodynamics on the collision particles were accounted by directly resolving the flow around finite-size particles with an interpolated bounce-back scheme. A large-scale stochastic forcing scheme was implemented within the mesoscopic multiple-relaxation-time LBM approach to maintain turbulence intensity at targeted levels. Both kinematic and dynamic collision kernels were evaluated to study the correlation of total collision events and turbulent kinetic energy (TKE) dissipation rate. The results show that collisions between particles increase with the increase of TKE dissipation rate as radial relative velocities between particles increase with it. It is found that the dynamic collision kernels do not match with the kinematic collision kernels which is derived from point-particle method. Quantitatively, they were approximately 4 to 10 times smaller than the corresponding dynamic collision kernels. Therefore, it is not reasonable to estimate the kinematic collision kernel in particle-resolved simulations as its rationales are not valid. However, the collision behavior can still be accounted for by means of the dynamic collision kernel since it is obtained from the direct statistical analysis of the collision events.

Comparative numerical and experimental investigation of process viscometry for flows in an agitator with a flat blade turbine impeller

This paper presents a method for measuring the viscosity of generalized Newtonian fluid directly in flows generated by flat-blade turbine impellers, which are commonly used for moderate mixing and dispersion. A flat-blade turbine with four blades is defined as a model system and analyzed through numerical simulations with experimental verification. Carbopol 940 solution, a high viscosity non-Newtonian fluid with a yield stress, and a bentonite based drilling mud solution were selected as test fluids. Numerical simulation techniques for flow in agitators with a yield stress was established using the rotating coordinate system and flow solutions were validated with experiments by comparing the torque on the impeller shaft. The Metzner-Otto constant and the energy dissipation rate constant were predicted by numerical simulations using the Metzner-Otto correlation and validated via experiments. The effective viscosity that reproduces total energy dissipation rate identical to that of a Newtonian fluid was obtained from both numerical and experimental methods at different impeller speeds, from which the material viscosity curve was established as a function of the shear rate. The accuracy of viscosity prediction was compared with a rheological measurement and the average relative error was below 12% and 7% in the experiment and simulation, respectively. This method has the advantage of being able to measure the in-situ viscosity, where a drilling mud needs to transport more and heavier cuttings and careful preparation of the mud is key issue to a successful drilling process.

Disruption of turbulence due to particle loading in a dilute gas–particle suspension

The modification of fluid turbulence due to suspended particles is analysed using direct numerical simulations for the fluid turbulence and discrete particle simulations where the point-particle approximation is used for the particle force on the fluid. Two values of the Reynolds number based on the channel width $h$ and the average gas velocity $\bar{u}$ , $(\unicode[STIX]{x1D70C}_{f}\bar{u}h/\unicode[STIX]{x1D702}_{f})=3300$ and 5600 are considered, where $\unicode[STIX]{x1D70C}_{f}$ and $\unicode[STIX]{x1D702}_{f}$ are the gas density and viscosity. The particle Reynolds number based on the root mean square of the difference in the particle and fluid velocities is in the range 4–15. The particle volume fraction is small, in the range $0{-}3.5\times 10^{-3}$ , the mass loading is varied in the range 0–13.5 and the particle Stokes number (ratio of particle relaxation time and fluid integral time) is varied in the range 1–420. Multiple models for the force on the particles are examined, the Stokes drag law, the Schiller–Naumann correlation, a correction to determine the ‘undisturbed’ fluid velocity at the particle centre, the lift force and wall corrections. In all cases, as the particle volume fraction is systematically increased, there is a discontinuous decrease in the turbulence intensities at a critical volume fraction. The mean square velocities and the rate of production of turbulent energy decrease by 1–2 orders of magnitude when the volume fraction is increased by $10^{-4}$ at the critical volume fraction. There is no compensatory increase in the particle fluctuating velocities or the energy dissipation rate due to the drag force on the particles, and there is a significant decrease in the total fluid energy dissipation rate at the critical volume fraction. This shows that the turbulence collapse is due to a catastrophic reduction in the turbulent energy production rate. This is contrary to the current understanding that turbulence attenuation is caused by the enhanced dissipation due to particle drag.

Viscosity measurement of non-Newtonian fluids in pressure-driven flows of general geometries based on energy dissipation rate

A novel viscosity measurement method is presented, which can be applied to the pressure-driven flow of an inelastic non-Newtonian fluid in an arbitrary geometry. The method is established on the balance of the energy dissipation rate such that the external power is dissipated within the system as viscous dissipation in a laminar regime in the absence of a body force. The effective viscosity can be expressed algebraically in terms of the pressure drop and flow rate and the corresponding effective shear rate is readily determined by flow rate; the relationship between effective viscosity and effective shear rate is found identical to the true material viscosity behavior. The two flow numbers, which depend on flow geometry only and are almost independent of fluid rheology, are involved: the coefficient of energy dissipation rate that associates the total energy dissipation rate to the Reynolds number; and the coefficient of effective shear rate, which relates flow rate to effective shear rate. After analytically validating the method for pressure-driven flow of a power-law fluid in a circular pipe, three different flows with complicated geometries were tested: numerical validations for axisymmetric expansion-contraction flows and flows in a Kenics mixer, and experimental validation for flows in a complex microfluidic array with Xanthan gum solutions. Errors in viscosity were less than 2.9% and 16% in simulations and in experiments, respectively. The method is well-suited for on-line monitoring of in-situ viscosity for non-Newtonian fluid flow in industrial processes.

Global energy fluxes in turbulent channels with flow control

This paper addresses the integral energy fluxes in natural and controlled turbulent channel flows, where active skin-friction drag reduction techniques allow a more efficient use of the available power. We study whether the increased efficiency shows any general trend in how energy is dissipated by the mean velocity field (mean dissipation) and by the fluctuating velocity field (turbulent dissipation). Direct numerical simulations (DNS) of different control strategies are performed at constant power input (CPI), so that at statistical equilibrium, each flow (either uncontrolled or controlled by different means) has the same power input, hence the same global energy flux and, by definition, the same total energy dissipation rate. The simulations reveal that changes in mean and turbulent energy dissipation rates can be of either sign in a successfully controlled flow. A quantitative description of these changes is made possible by a new decomposition of the total dissipation, stemming from an extended Reynolds decomposition, where the mean velocity is split into a laminar component and a deviation from it. Thanks to the analytical expressions of the laminar quantities, exact relationships are derived that link the achieved flow rate increase and all energy fluxes in the flow system with two wall-normal integrals of the Reynolds shear stress and the Reynolds number. The dependence of the energy fluxes on the Reynolds number is elucidated with a simple model in which the control-dependent changes of the Reynolds shear stress are accounted for via a modification of the mean velocity profile. The physical meaning of the energy fluxes stemming from the new decomposition unveils their inter-relations and connection to flow control, so that a clear target for flow control can be identified.

Investigation of the effect of small bubbles on energy dissipation in a vertical Couette–Taylor system

The effect of small bubbles on reduction of energy dissipation has been numerically investigated in a vertical Couette–Taylor system. Flow is in the annular space between two concentric cylinders as the internal cylinder is rotating while the outer cylinder is stationary. Main fluid between cylinders is silicone, while air bubbles are constantly injected into the main flow at the bottom of cylinders’ gap. The air bubbles rise through the flow when they are injected into the silicone flow. The flow is fully turbulence and Taylor vortices have appeared in the annulus gap. The rotational Reynolds number (Reω) varies from 700 to 3000. The fully two-phase turbulent flow has been studied using a discrete phase model and Euler–Lagrange approach. Air bubbles distribution or bubbles pattern through the main flow, which is acquired using numerical method, shows a good agreement to those acquired via experimental data in all Reynolds numbers. To investigate the changes of skin friction drag, the rate of energy dissipation in the system is calculated. The effect of injected air with constant flow rate on the total energy dissipation rate and the drag coefficient is also investigated. The results confirmed reduction of energy dissipation and about 25% of drag reduction when small bubbles were injected in the system. This reduction was the effect of the bubbles on the density of fluid and transformed momentum. Moreover, the acquired numerical results were in good agreement with those found in the previous experimental works, in which maximum Reω is up to 3000.

Investigation of Numerical Dissipation in Classical and Implicit Large Eddy Simulations

The quantitative measure of dissipative properties of different numerical schemes is crucial to computational methods in the field of aerospace applications. Therefore, the objective of the present study is to examine the resolving power of Monotonic Upwind Scheme for Conservation Laws (MUSCL) scheme with three different slope limiters: one second-order and two third-order used within the framework of Implicit Large Eddy Simulations (ILES). The performance of the dynamic Smagorinsky subgrid-scale model used in the classical Large Eddy Simulation (LES) approach is examined. The assessment of these schemes is of significant importance to understand the numerical dissipation that could affect the accuracy of the numerical solution. A modified equation analysis has been employed to the convective term of the fully-compressible Navier–Stokes equations to formulate an analytical expression of truncation error for the second-order upwind scheme. The contribution of second-order partial derivatives in the expression of truncation error showed that the effect of this numerical error could not be neglected compared to the total kinetic energy dissipation rate. Transitions from laminar to turbulent flow are visualized considering the inviscid Taylor–Green Vortex (TGV) test-case. The evolution in time of volumetrically-averaged kinetic energy and kinetic energy dissipation rate have been monitored for all numerical schemes and all grid levels. The dissipation mechanism has been compared to Direct Numerical Simulation (DNS) data found in the literature at different Reynolds numbers. We found that the resolving power and the symmetry breaking property are enhanced with finer grid resolutions. The production of vorticity has been observed in terms of enstrophy and effective viscosity. The instantaneous kinetic energy spectrum has been computed using a three-dimensional Fast Fourier Transform (FFT). All combinations of numerical methods produce a k − 4 spectrum at t * = 4 , and near the dissipation peak, all methods were capable of predicting the k − 5 / 3 slope accurately when refining the mesh.

Kinematic analysis of seismic slope stability with a discretisation technique and pseudo-dynamic approach: a new perspective

Slopes are more vulnerable to instability when subjected to earthquake ground shaking. In order to account for the dynamic forces induced by ground shaking, a novel procedure is introduced in this paper to estimate slope stability under the ultimate limit state with a combination of pseudo-dynamic approach and discretisation technique. A pseudo-dynamic approach is adopted which allows the introduction of an arbitrary time history of seismic accelerations. In order to consider non-uniformity of soil properties of the slope, the discretisation technique is proposed with the aim of generating a potential failure mechanism with discretised points by forward difference ‘point-to-point’ method. Infinitesimal trapezoidal elements composed of successive discretised points and sloping surface are selected for kinematic analysis. In this way, the problem is decomposed into separate components, which aids computational effort. The upper-bound solutions of limiting surcharge loading and yield seismic acceleration are thereafter obtained with the equilibrium of total external work rate and internal energy dissipation rate through the summation from all infinitesimal elements. The methodology is validated through comparison with its degraded approach and conventional upper-bound analysis. Further parametric study is also carried out to highlight the influence of the various soil and loading parameters on the critical seismic acceleration.

Formation of collective conformational degrees of freedom during macromolecular chain folding dynamics in a viscous medium

Computational methods were used to study the dynamics of the formation of the collective conformational degrees of freedom in the relaxation folding of a model biopolymer chain of 50 nodes in a viscous medium; the model has been described previously. Collective conformational motions of the nodes were shown to arise due to friction forces in a viscous medium. The collective motions have several typical forms, including a wave of differently directed motions of chain nodes that propagates from one end of the chain to another (like a soliton) in response to a pertubation in terminal group position. Individual nodes located at the middle of the chain make approximately equal contributions to the total energy dissipation rate. The end nodes contribute approximately 2–4 times more than internal nodes to the total energy dissipation. The results of numerical experiments are consistent with the theoretical concept developed earlier to describe the dynamics of linear macromolecular chains in a viscous medium in the limit of a very large number of nodes.

Reynolds-number dependence of the dimensionless dissipation rate in homogeneous magnetohydrodynamic turbulence.

This paper examines the behavior of the dimensionless dissipation rate C_{ɛ} for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in the presence of external forces. By combining with previous studies for freely decaying MHD turbulence, we obtain here both the most general model equation for C_{ɛ} applicable to homogeneous MHD turbulence and a comprehensive numerical study of the Reynolds number dependence of the dimensionless total energy dissipation rate at unity magnetic Prandtl number. We carry out a series of medium to high resolution direct numerical simulations of mechanically forced stationary MHD turbulence in order to verify the predictions of the model equation for the stationary case. Furthermore, questions of nonuniversality are discussed in terms of the effect of external forces as well as the level of cross- and magnetic helicity. The measured values of the asymptote C_{ɛ,∞} lie between 0.193≤C_{ɛ,∞}≤0.268 for free decay, where the value depends on the initial level of cross- and magnetic helicities. In the stationary case we measure C_{ɛ,∞}=0.223.

Turbulent flow field and air entrainment in laboratory plunging breaking waves

AbstractThis paper presents laboratory measurements of turbulent flow fields and void fraction in deep‐water plunging breaking waves using imaging and optical fiber techniques. Bubble‐size distributions are also determined based on combined measurements of velocity and bubble residence time. The most excited mode of the local intermittency measure of the turbulent flow and its corresponding length scale are obtained using a wavelet‐based method and found to correlate with the swirling strength and vorticity. Concentrated vortical structures with high intermittency are observed near the lower boundaries of the aerated rollers where the velocity shear is high; the length scale of the deduced eddies ranges from 0.05 to 0.15 times the wave height. The number of bubbles with a chord length less than 2 mm demonstrates good correlation with the swirling strength. The power‐law scaling and the Hinze scale of the bubbles determined from the bubble chord length distribution compare favorably with existing measurements. The turbulent dissipation rate, accounting for void fraction, is estimated using mixture theory. When void fraction is not considered, the turbulent dissipation rate is underestimated by more than 70% in the initial impinging and the first splash‐up roller. A significant discrepancy of approximately 67% between the total energy dissipation rate and the turbulence dissipation rate is found. Of this uncounted dissipation, 23% is caused by bubble‐induced dissipation.

Head-on collisions of dense granular jets.

We study head-on impacts of equal-speed but unequal-width incompressible jets in two dimensions with a focus on dense granular jets. We use discrete particle simulations to show that head-on impact of granular jets produces a quasi-steady-state where a fraction of the excess incident momentum from the larger jet is captured by an impact center that drifts steadily over time. By varying the dissipation in our discrete particle simulations and through additional analogous continuum jet impacts of different rheologies, we show that this central drift speed is remarkably dependent primarily on the total dissipation rate to the power 1.5, and largely independent of the dissipation mechanism. We finish by presenting a simple control volume analysis that qualitatively captures the emergence of the drift speed but not the scaling.

Decaying capillary wave turbulence under broad-scale dissipation

We study the freely decaying weak turbulence of capillary waves by direct numerical solution of the primitive Euler equations. By introducing a small amount of wave dissipation, measured by the viscosity magnitude${\it\gamma}_{0}$, we are able to recover phenomena observed in experiments that are not described by weak-turbulence theory (WTT), including the exponential modal decay and time variation of the width and power-law spectral slope${\it\alpha}$of the inertial range. In contrast to WTT, this problem also involves non-constant inter-modal energy transfer across the inertial range, which imposes a difficulty in quantifying and measuring the energy flux$P$associated with a certain power-law spectrum. We propose an effective and novel way to evaluate$P$in such cases by physically considering the unsteady effects of the spectrum and variation of the inter-modal energy transfer. Our results show the fundamental difference between the energy flux$P$and the total energy dissipation rate${\it\Gamma}$, which is due to significant energy dissipation within the inertial range. This settles the previous debate on the measurement of$P$which assumes the equivalence of the two. Based on our numerical data, we obtain a general form of the time-evolving inertial-range spectrum, where the parameters involved are functions of${\it\gamma}_{0}$only. The value of the spectral slope${\it\alpha}$at each time moment in the decay, however, is found to be uniquely related to the spectral magnitude at that time and irrespective of${\it\gamma}_{0}$, in the range we consider. This physically reveals the dominant effect of nonlinear wave interaction in forming the power-law spectrum within the inertial range. The evolutions of the inertial-range energy are shown to be predicted by analytical integration of the evolving spectra for different values of${\it\gamma}_{0}$.

Internal tides and turbulent mixing observed in the Bussol Strait

Repeated observations with a period of about 24h of hydrography, current velocity, and microstructures were performed at three stations surrounding a seamount in the middle of the Bussol Strait, the deepest and widest one of the Kuril Straits, to reveal spatial and temporal variability of internal tides and associated turbulent mixing. It is found that isopycnal displacements are dominated by diurnal tidal components, which show phase differences (namely, time lags) between the three stations that can be explained by a first mode topographically trapped wave (TTW) propagating clockwise around the seamount. Furthermore, at the station located near the center of the strait where energy dissipation rates are largest, diurnal variations of isopycnals and velocities are amplified toward the ocean bottom, consistent with the vertical structure of the first mode TTW. At that station, vigorous turbulent mixing with the energy dissipation rate exceeding 10-6m2s-3 and diapycnal diffusivity exceeding 10-1m2s-1 was observed in deep layers when the diurnal tidal current consisting of the first mode TTW flows from the Okhotsk Sea to the North Pacific, enhancing the mean current. These spatial and temporal variation patterns are confirmed to be reproduced by a previous numerical model successfully for the isopycnals and velocities, and partially for the turbulent mixing. The total energy dissipation rate is, however, by up to a factor of 3–10 smaller than predicted by the numerical model although the observations were performed during spring tides, suggesting that the actual diapycnal mixing is overall weaker than the previous model estimate and/or that extremely strong mixing occurs within highly localized areas.