Viscous Dissipation Rate Research Articles

Non-Newtonian and non-isothermal numerical modelling of a twin screw hydrogen extruder with slip imposed boundary condition on the screw surface

Abstract Fueling a plasma reactor by pellet injection is the most efficient method. Production of a solid hydrogen filament using a Twin screw extruder (TSE) is reported to be most stable among various extrusion techniques. The non-Newtonian behavior of solid hydrogen and non-linearities arising due to temperature dependent thermophysical properties in addition to rotation of two intermeshing screws make the flow modelling challenging. In the present study, a non-isothermal and non-Newtonian model has been developed taking into account the temperature and shear rate dependent Herschel Bulkley viscosity model. The ‘slip’ boundary condition has been imposed on the screw surface to account for the localized melting at the screw surface. The highly nonlinear viscous heating term in the energy equation is handled by using evolution scheme. It is important to accurately estimate the viscous dissipation rate which determines the cooling load required and input power. The viscous dissipation rate and developed torque predicted using the CFD model is in close agreement with the experimental available in the literature. The temperature rise due to viscous heating at the clearance gaps and the intermeshing region is found to be 0.6 K higher than that developed in the non-intermeshing region at 4 rpm screw speed for the given extruder dimensions.

Direct numerical simulations of turbulent viscoelastic jets

Direct numerical simulations (DNS) of spatially evolving turbulent planar jets of viscoelastic fluids described by the FENE-P model, such as those consisting of a Newtonian fluid solvent carrying long chain polymer molecules, are carried out in order to develop a theory for the far field of turbulent jets of viscoelastic fluids. New evolution relations for the jet shear-layer thickness , centreline velocity and maximum polymer stresses are derived and validated by the new DNS data, yielding , , and , respectively, where is the coordinate in the streamwise direction. It is shown that, compared with a classical (Newtonian) turbulent jet, the effect of the polymers is to reduce the spreading rate, centreline velocity decay, Reynolds stresses and viscous dissipation rate. The self-preserving character of the flow is analysed and it is shown that profiles of mean velocity, Reynolds stresses and polymer stresses are self-similar provided the proper scales are used in the normalisation of these quantities. A fundamental difference from the Newtonian jet in this regard is the necessity for two, instead of only one, different velocity and length scales to properly characterise the evolution of the turbulent flow. These extra velocity and length scales are directly related to a time scale associated with the characteristic fading memory property of viscoelastic fluids.

Mixing in forced stratified turbulence and its dependence on large-scale forcing

We study direct numerical simulations of turbulence arising from the interaction of an initial background shear, a linear background stratification and an external body force. In each simulation the turbulence produced is spatially intermittent, with dissipation rates varying over orders of magnitude in the vertical. We focus analysis on the statistically quasi-steady states achieved by applying large-scale body forcing to the domain, and compare flows forced by internal gravity waves with those forced by vertically uniform vortical modes. By considering the turbulent energy budgets for each simulation, we find that the injection of potential energy from the wave forcing permits a reversal in the sign of the mean buoyancy flux. This change in the sign of the buoyancy flux is associated with large, convective density overturnings, which in turn lead to more efficient mixing in the wave-forced simulations. The inhomogeneous dissipation in each simulation allows us to investigate localised correlations between the kinetic and potential energy dissipation rates. These correlations lead us to the conclusion that an appropriate definition of an instantaneous mixing efficiency, (where and are the volume-averaged turbulent viscous dissipation rate and fluctuation density variance destruction rate respectively) in the wave-forced cases is independent of an appropriately defined local turbulent Froude number, consistent with scalings proposed for low Froude number stratified turbulence.

Modelling the cleaning of viscoplastic layers by impinging coherent turbulent water jets

Impinging liquid jets are widely used to clean unwanted soil layers from the walls of structures and vessels. When the soil is a thin layer of an immiscible viscoplastic material, removal involves the growth of a cleared area (which is circular for a jet impinging normally) bounded by a berm of displaced material. Glover et al. [1] presented a semi-empirical model relating the rate of removal to the momentum flow rate in the liquid film. We present a first-order model for cleaning thin layers of these materials based on the rate of viscous dissipation in a shallow wedge of material at the cleaning front. This yields a result of the form of the model in [1], with expressions linking the kinetic parameters to measurable quantities including the rheology of the soil. The fully coupled problem is not solved: the wedge angle and residual layer thickness need to be specified and were obtained here by fitting to the data. The model is compared with experimental results obtained for three soft solids – two petroleum jellies and a soft paraffin – which exhibited Bingham plastic behaviour and creep, for jet Reynolds numbers between 10,000-37,000, and 0.1<h¯/δo<1.5, where h¯ is the average film depth and δo the layer thickness. The data show reasonable agreement with the model.

Englacial Warming Indicates Deep Crevassing in Bowdoin Glacier, Greenland

All around the margins of the Greenland Ice Sheet, marine-terminating glaciers have recently thinned and accelerated. The reduced basal friction has yielded increased flow velocity, while the rate of longitudinal stretching has been limited by ice viscosity, which itself critically depends on temperature. However, ice temperature has rarely been measured on such fast-flowing and heavily crevassed glaciers. Here, we present a three-year record of englacial temperatures obtained 2 (in 2014) to 1 km (in 2017) from the calving front of Bowdoin Glacier (Kangerluarsuup Sermia), a tidewater glacier in northwestern Greenland. Two boreholes separated by 165 (2014) to 197 m (2017) show significant temperature differences averaging 2.07 ∘C on their entire depth. Englacial warming of up to 0.39∘C a−1, an order of magnitude above the theoretical rate of heat diffusion and viscous dissipation, indicates a deep and local heat source within the tidewater glacier. We interpret the heat source as latent heat from meltwater refreezing in crevasses reaching to, or near to, the bed of the glacier, whose localisation may be controlled by preferential meltwater infiltration in topographic dips between ogives.

Vortex-dynamical implications of nonmonotonic viscous dissipation of off-center droplet bouncing

In this paper, vortex-dynamical perspectives were adopted to interpret the recently reported observation that the total viscous dissipation of off-center droplet bouncing varies nonmonotonically with the impact parameter [C. He, X. Xia, and P. Zhang, “Non-monotonic viscous dissipation of bouncing droplets undergoing off-center collision,” Phys. Fluids 31, 052004 (2019)]. The particular interest of this study is on analyzing the velocity and vorticity vector fields and their correlations, such as helicity and enstrophy. The helicity analysis identifies a strong interaction between the “ring-shaped” vortices and the “line-shaped” shear layers in the non-axisymmetric droplet internal flow. A general relation between the total enstrophy and the total viscous dissipation rate for an unsteady free-surface flow was theoretically derived and numerically verified. It shows that the equality between the total enstrophy and the total viscous dissipation rate holds for a single-phase flow confined by stationary boundaries but is not satisfied for a gas–liquid two-phase flow due to the interfacial movement. Both the total enstrophy and a defined “half-domain” helicity show the nonmonotonic variation with the impact parameter, implying their interrelation with the nonmonotonic viscous dissipation.

Numerical Investigation of Forced Convective Heat Transfer and Performance Evaluation Criterion of Al2O3/Water Nanofluid Flow inside an Axisymmetric Microchannel

Al2O3/water nanofluid conjugate heat transfer inside a microchannel is studied numerically. The fluid flow is laminar and a constant heat flux is applied to the axisymmetric microchannel’s outer wall, and the two ends of the microchannel’s wall are considered adiabatic. The problem is inherently three-dimensional, however, in order to reduce the computational cost of the solution, it is rational to consider only a half portion of the axisymmetric microchannel and the domain is revolved through its axis. Hence. the problem is reduced to a two-dimensional domain, leading to less computational grid. At the centerline (r = 0), as the flow is axisymmetric, there is no radial gradient (∂u/∂r = 0, v = 0, ∂T/∂r = 0). The effects of four Reynolds numbers of 500, 1000, 1500, and 2000; particle volume fractions of 0% (pure water), 2%, 4%, and 6%; and nanoparticles diameters in the range of 10 nm, 30 nm, 50 nm, and 70 nm on forced convective heat transfer as well as performance evaluation criterion are studied. The parameter of performance evaluation criterion provides valuable information related to heat transfer augmentation together with pressure losses and pumping power needed in a system. One goal of the study is to address the expense of increased pressure loss for the increment of the heat transfer coefficient. Furthermore, it is shown that, despite the macro-scale problem, in microchannels, the viscous dissipation effect cannot be ignored and is like an energy source in the fluid, affecting temperature distribution as well as the heat transfer coefficient. In fact, it is explained that, in the micro-scale, an increase in inlet velocity leads to more viscous dissipation rates and, as the friction between the wall and fluid is considerable, the temperature of the wall grows more intensely compared with the bulk temperature of the fluid. Consequently, in microchannels, the thermal behavior of the fluid would be totally different from that of the macro-scale.

Numerical Characterization of Viscous Heat Dissipation Rate in Oscillatory Air Flow

Abstract The effect of viscous heat dissipation (VHD) in raising the temperature field of incompressible oscillatory air flow is studied numerically. A threshold is established for when the viscous heat dissipation term in the thermal energy equation changes or does not change the temperature field for the case of oscillatory air flow in a tube connecting two reservoirs. This new criterion has not been specified clearly in earlier oscillatory flow research. According to the defined threshold and when VHD is important, the effect of dissipative bulk heating can be described by a proposed correlation in terms of Womersley number (Wo) and axial tidal displacement (ΔZ) of the oscillatory fluid. These results are determined using two-dimensional (2D) numerical simulations of laminar oscillatory air flow (Pr = 0.7) for different adiabatic unconductive tube-reservoirs' systems configurations over a wide range of oscillatory frequencies and tidal displacements. It is found that the low amount of fluid kinetic energy, which is converted into internal energy, is not sufficient to significantly heat up the fluid at a low rate of the viscous work. Therefore, the effect of viscous heat dissipation in oscillatory air flow can be ignored only below a specific limit of unsteadiness depending on Womersley number and axial tidal displacement. Also, the results showed that the VHD becomes more significant with increasing (Wo) and (ΔZ).

Similarities between the structure functions of thermal convection and hydrodynamic turbulence

In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with the predictions of She and Leveque [“Universal scaling laws in fully developed turbulence,” Phys. Rev. Lett. 72, 336–339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate. This is unlike in hydrodynamic turbulence where the energy flux and the dissipation rate are equal.

Magnetohydrodynamic waves in braided magnetic fields

Aims. We investigate the propagation of transverse magnetohydrodynamic (MHD) wave fronts through a coronal plasma containing a braided magnetic field. Methods. We performed a series of three dimensional MHD simulations in which a small amplitude, transverse velocity perturbation is introduced into a complex magnetic field. We analysed the deformation of the wave fronts as the perturbation propagates through the braided magnetic structures and explore the nature of Alfvénic wave phase mixing in this regime. We considered the effects of viscous dissipation in a weakly non-ideal plasma and evaluate the effects of field complexity on wave energy dissipation. Results. Spatial gradients in the local Alfvén speed and variations in the length of magnetic field lines ensure that small scales form throughout the propagating wave front due to phase mixing. Additionally, the presence of complex, intricate current sheets associated with the background field locally modifies the polarisation of the wave front. The combination of these two effects enhances the rate of viscous dissipation, particularly in more complex field configurations. Unlike in classical phase mixing configurations, the greater spatial extent of Alfvén speed gradients ensures that wave energy is deposited over a larger cross-section of the magnetic structure. Further, the complexity of the background magnetic field ensures that small gradients in a wave driver can map to large gradients within the coronal plasma. Conclusions. The phase mixing of transverse MHD waves in a complex magnetic field will progress throughout the braided volume. As a result, in a non-ideal regime wave energy will be dissipated over a greater cross-section than in classical phase mixing models. The formation rate of small spatial scales in a propagating wave front is a function of the complexity of the background magnetic field. As such, if the coronal field is sufficiently complex it remains plausible that phase mixing induced wave heating can contribute to maintaining the observed temperatures. Furthermore, the weak compressibility of the transverse wave and the observed phase mixing pattern may provide seismological information about the nature of the background plasma.

Improved upper bounds on the energy dissipation rate for shear flow with injection and suction

Improved upper bounds on viscous energy dissipation rates of wall-driven shear flow subject to uniform injection and suction rates are computationally determined. The so-called “background” variational formulation is implemented via a time-stepping numerical scheme to determine optimal estimates. Shear flow Reynolds numbers range from 50 to 40 000 with injection angles up to 2°. The computed upper bounds for preselected angles of injection at high Reynolds numbers significantly improve the rigorously estimated ones. Our results suggest that the steady laminar flow is nonlinearly stable for angles of injection greater than 2°.

Non-dimensional energy dissipation rate near the turbulent/non-turbulent interfacial layer in free shear flows and shear free turbulence

The non-dimensional dissipation rate $C_{\unicode[STIX]{x1D700}}=\unicode[STIX]{x1D700}L/u^{\prime 3}$, where $\unicode[STIX]{x1D700}$, $L$ and $u^{\prime }$ are the viscous energy dissipation rate, integral length scale of turbulence and root-mean-square of the velocity fluctuations, respectively, is computed and analysed within the turbulent/non-turbulent interfacial (TNTI) layer using direct numerical simulations of a planar jet, mixing layer and shear free turbulence. The TNTI layer that separates the turbulent and non-turbulent regions exists at the edge of free shear turbulent flows and turbulent boundary layers, and comprises both the viscous superlayer and turbulent sublayer regions. The computation of $C_{\unicode[STIX]{x1D700}}$ is made possible by the introduction of an original procedure, based on local volume averages within spheres of radius $r$, combined with conditional sampling as a function of the location with respect to the TNTI layer. The new procedure allows for a detailed investigation of the scale dependence of several turbulent quantities near the TNTI layer. An important achievement of this procedure consists in permitting the computation of the turbulent integral scale within the TNTI layer, which is shown to be approximately constant. Both the non-dimensional dissipation rate and turbulent Reynolds number $Re_{\unicode[STIX]{x1D706}}$ vary in space within the TNTI layer, where two relations are observed: $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-1}$ and $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-2}$. Specifically, whereas the viscous superlayer and part of the turbulent sublayer display $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-2}$, the remaining of the turbulent sublayer exhibits $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-1}$, which is consistent with non-equilibrium turbulence (Vassilicos, Annu. Rev. Fluid Mech. vol. 47, 2015, pp. 95–114).

Analysis of Inlet Velocity Profiles in Numerical Assessment of Fontan Hemodynamics.

Computational fluid dynamic (CFD) simulations are widely utilized to assess Fontan hemodynamics that are related to long-term complications. No previous studies have systemically investigated the effects of using different inlet velocity profiles in Fontan simulations. This study implements real, patient-specific velocity profiles for numerical assessment of Fontan hemodynamics using CFD simulations. Four additional, artificial velocity profiles were used for comparison: (1) flat, (2) parabolic, (3) Womersley, and (4) parabolic with inlet extensions [to develop flow before entering the total cavopulmonary connection (TCPC)]. The differences arising from the five velocity profiles, as well as discrepancies between the real and each of the artificial velocity profiles, were quantified by examining clinically important metrics in TCPC hemodynamics: power loss (PL), viscous dissipation rate (VDR), hepatic flow distribution, and regions of low wall shear stress. Statistically significant differences were observed in PL and VDR between simulations using real and flat velocity profiles, but differences between those using real velocity profiles and the other three artificial profiles did not reach statistical significance. These conclusions suggest that the artificial velocity profiles (2)-(4) are acceptable surrogates for real velocity profiles in Fontan simulations, but parabolic profiles are recommended because of their low computational demands and prevalent applicability.

Drag enhancement and turbulence attenuation by small solid particles in an unstably stratified turbulent boundary layer

Point-particle direct numerical simulations of particle-laden flows have been conducted to investigate the complex coupling between inertial particles, buoyancy force, and strong shear flows in an unstably stratified turbulent boundary layer over a flat plate. Two-way coupling and particle-particle collisions, i.e., four-way coupling, are considered in the dilute gas-solid flows. The simulation results indicate that the presence of inertial particles with diameter smaller than the Kolmogorov length scale tends to reduce the thermal displacement thickness and enthalpy thickness, while increasing the mean skin-friction coefficient and Nusselt number. The feedback force exerted by the particles on the fluid is found to contribute largely to the drag enhancement. The turbulence intensities and temperature fluctuations are significantly attenuated in the particle-laden flows with respect to the unladen flow. The budgets of the turbulent kinetic energy show that the particles have direct and indirect effects on the modulation of turbulence. On the one hand, the production and the viscous dissipation rate are suppressed by the particles in most regions of the boundary layer. On the other hand, the particle-turbulence interactions produce an extra energy source in the inner layer, while causing an additional energy sink in the outer layer of the boundary layer. These combined effects lead to the pronounced turbulence attenuation observed in this study.

Layered semi-convection and tides in giant planet interiors

Context. Recent Juno observations have suggested that the heavy elements in Jupiter could be diluted throughout a large fraction of its gaseous envelope, providing a stabilising compositional gradient over an extended region of the planet. This could trigger layered semi-convection, which, in the context of giant planets more generally, may explain Saturn’s luminosity excess and play a role in causing the abnormally large radii of some hot Jupiters. In giant planet interiors, it could take the form of density staircases, which are convective layers separated by thin stably stratified interfaces. In addition, the efficiency of tidal dissipation is known to depend strongly on the planetary internal structure. Aims. We aim to study the resulting tidal dissipation when internal waves are excited in a region of layered semi-convection by tidal gravitational forcing due to other bodies (such as moons in giant planet systems, or stars in hot Jupiter systems). Methods. We adopt a local Cartesian model with a background layered density profile subjected to an imposed tidal forcing, and we compute the viscous and thermal dissipation rates numerically. We consider two sets of boundary conditions in the vertical direction: periodic boundaries and impenetrable, stress-free boundaries, with periodic conditions in the horizontal directions in each case. These models are appropriate for studying the forcing of short-wavelength tidal waves in part of a region of layered semi-convection, and in an extended envelope containing layered semi-convection, respectively. Results. We find that the rates of tidal dissipation can be enhanced in a region of layered semi-convection compared to a uniformly convective medium, where the latter corresponds with the usual assumption adopted in giant planet interior models. In particular, a region of layered semi-convection possesses a richer set of resonances, allowing enhanced dissipation for a wider range of tidal frequencies. The details of these results significantly depend on the structural properties of the layered semi-convective regions. Conclusions. Layered semi-convection could contribute towards explaining the high tidal dissipation rates observed in Jupiter and Saturn, which have not yet been fully explained by theory. Further work is required to explore the efficiency of this mechanism in global models.

Non-monotonic viscous dissipation of bouncing droplets undergoing off-center collision

The off-center collision of binary bouncing droplets of equal size was studied numerically by a volume-of-fluid method with two marker functions, which has been justified and validated by comparing with available experimental results. A nonmonotonic kinetic energy (KE) recovery with varying impact parameters was discovered. This can be explained by the prolonged entanglement time and the enhanced internal-flow-induced viscous dissipation for bouncing droplets at intermediate impact parameters, compared with those at smaller or larger impact parameters. The distribution of the local viscous dissipation rate (VDR) in the droplet interior shows two major concentration areas, and the competition between these two concentration areas accounts for the nonmonotonic viscous dissipation with varying impact parameters. The nonmonotonic KE recovery with varying impact parameters can also be attributed to the competition between the VDR induced by normal strains and shear strains. The nonmonotonicity was further numerically verified for wider ranges of parameters, and a practically useful formula was proposed to correlate the KE dissipation factor with the impact parameter for various Weber numbers and Ohnesorge numbers.

Numerical study of binary droplets collision in the main collision regimes

Direct numerical simulation of binary droplets collision is done using a conservative level-set method. The Navier-Stokes and level-set equations are solved using a finite-volume method on collocated grids. A novel lamella stabilization approach is introduced to numerically resolve the thin lamella film appeared during a broad range of collision regimes. This direction-independent method proves to be numerically efficient and accurate compared with experimental data. When the droplets collide, the fluid between them is pushed outward, leaving a thin gas layer bounded by the surface of two droplets. This layer progressively gets thinner and depending on the collision regime, may rupture resulting in coalescence of the droplets or may linger resulting in bouncing-off the droplets. Embedded ghost-nodes layer makes it possible to mimic both bouncing and coalescence phenomena of the droplets collision. The numerical tools introduced are validated and verified against different experimental results for a wide range of collision regimes. A very good agreement is observed between the results of this paper and experimental data available in the literature. A detailed study of the energy budget for different shares of kinetic and dissipation energies inside of the droplet and matrix, in addition to the surface tension energy for studied cases, is provided. Supplementary quantitative values of viscous dissipation rate inside of the matrix and droplet, and also the radial expansion of the droplet are presented as well.

CFD modelling and performance analysis of a twin screw hydrogen extruder

An intermeshing counter-rotating twin-screw extruder is reported to be more reliable and stable among various methods of extrusion techniques in pellet production systems for the plasma reactors. In the present study, CFD modelling has been successfully carried out using POLYFLOW module of ANSYS, which employs the Mesh Superposition Technique. The shear rate dependent shear stress of solid hydrogen modelled using Herschel-Bulkley equation has been used in the present analysis. A three-dimensional computation neglecting inertia and gravity effects has been carried out to simulate the flow through the extruder which involves leakage flows through the calendar, tetrahedron, flight and side gaps. The flow characteristics of the die was simulated independently and superimposed with the extruder pumping characteristics to arrive at the operating point. The CFD results have been compared with those obtained from an analytical model adopted from the literature on polymer extrusion research. It has been found that the deviation between them becomes narrow when the mechanical clearances of the extruder are made smaller. A systematic parametric analysis was carried out to arrive at an optimum design to produce a 3 mm diameter filament at about 400 mm3/s with a minimum viscous dissipation rate. The analysis revealed that an increase of pitch length or decrease of mechanical clearance gaps in association with either decrease of the number of ‘C’ chambers or the speed will result in smaller viscous dissipation rate.

Can libration maintain Enceladus's ocean?

The process by which the subsurface ocean on Enceladus is heated remains a puzzle. Tidal interaction with Saturn and Dione is the leading candidate but whether the dominant heating occurs in the solid core, ice crust or in the ocean itself is an outstanding question. Here we consider the driving effect of the longitudinal libration of the ice crust on the subsurface ocean and argue that the flow response should be turbulent even in the most benign situation of a smooth spherical ice shell when the motion of the boundary is only transmitted viscously. A rigorous upper bound on the turbulent viscous dissipation rate is then derived and used to argue that libration should be potent enough to explain the observed heat flux emanating out of Enceladus when the effects of tidal distortion and roughness of the ice crust are included.

Heuristic analysis of viscous dissipation in single‐screw extrusion

Modeling the non‐Newtonian flow of polymer melts in single‐screw extrusion generally requires numerical methods. This study analyzes the viscous dissipation of the melt‐conveying zone, which is mainly responsible for the axial melt temperature increase, in single‐screw extruders for both one‐ and two‐dimensional stationary, fully developed flows of a power‐law fluid. Rewriting the flow equations and applying the theory of similarity revealed three independent parameters that influence the physics of the fluid flow: the dimensionless pressure gradient , the power‐law exponent , and the screw‐pitch ratio . Based on these parameters, we carried out a comprehensive numerical parametric study evaluating viscous dissipation and flow rate. Here, we present four heuristic models that predict the viscous dissipation of a power‐law fluid in the melt‐conveying zone of single‐screw extruders. For one‐dimensional and two‐dimensional flows, we developed models for both a given pressure gradient and a given throughput. The approximation equations obtained allow fast and stable prediction without the need for numerical simulations of viscous dissipation. The accuracy of the heuristic models developed was validated in an error analysis, which showed that our approaches provide excellent approximations of the numerical results. POLYM. ENG. SCI., 58:2055–2070, 2018. © 2018 The Authors Polymer Engineering &amp; Science published by Wiley Periodicals, Inc. on behalf of Society of Plastics Engineers