Viscous Work Research Articles

Effects of pressure work, viscous dissipation, shear work and axial conduction on convective heat transfer in a microtube

This paper investigates the effects of viscous dissipation, pressure work, shear work, rarefaction and axial heat diffusion on convective heat transfer in a microtube gaseous flow. The problem is investigated numerically for the whole flow region using a finite difference scheme and the line Gauss-Seidel iterative technique. Exact solutions of the problem in terms of temperature distribution and Nusselt number variations are also derived under fully developed flow conditions. The microtube is assumed to be sufficiently long, so that fully developed conditions are established. The analysis presented demonstrate that the effect of the boundary shear work is significant and its contribution to heat transfer can be as high as that due to heat conduction close to the upper limit of the slip flow regime. As the shear work is a result of the combined effects of viscous dissipation and pressure work at the boundary, including these effects in the analysis leads to better predictions of heat transfer phenomena. Axial heat diffusion effect on Nusselt number and the thermal entrance length are also quantified.

Analysis of an irregular boundary layer behavior for the steady state flow of a Boussinesq fluid

Using a singular perturbation based approach, we make rigorous the formal boundary layer asymptotic analysis of Turcotte, Spence and Bau from the early eighties for the vertical flow of an internally heated Boussinesq fluid in a vertical channel with viscous dissipation and pressure work. A key point in our proof is to establish the non-degeneracy of a special solution of the Painleve-Ⅰ transcendent. To this end, we relate this problem to recent studies for the ground states of the focusing nonlinear Schrodinger equation in an annulus. We also relate our result to a particular case of the well known Lazer-McKenna conjecture from nonlinear analysis.

Viscoelasticity effects on resonant response of a shear deformable extensible microbeam

In the framework of the third-order shear deformation theory, the coupled size-dependent nonlinear dynamics of a viscoelastic extensible microbeam is investigated on the basis of the modified couple stress theory. Taking into account both the transverse and axial displacements as well as inertia together with the rotation and rotary inertia, the viscous parts of the classical and nonclassical stress tensors are calculated and the corresponding work terms are obtained. These viscous work terms are balanced by the kinetic energy of the system, the size-dependent potential energy, and the work of an external excitation force. This operation leads to coupled expressions for the transverse, rotational, and longitudinal motions. Retaining the rotation, rotary inertia as well as translational displacements and inertia (for the transverse and longitudinal motions), three high-dimensional reduced-order models are obtained for the transverse, longitudinal, and rotational motions employing a weighted-residual method. These three size-dependent viscoelastically coupled models are solved via use of the pseudo-arclength continuation method in conjunction with the backward differentiation formula (BDF). It is shown that the viscoelastic model is an amplitude-dependent energy dissipation mechanism which gives more accurate results compared to an elastic model. More specifically, as the forcing amplitude is increased, the response of the elastic system deviates from that of the viscoelastic system.

A lattice Boltzmann model for thermal flows through porous media

In a three-distribution-function framework, a lattice Boltzmann model was proposed for thermal flows through porous media under local thermal non-equilibrium conditions, in which both viscous dissipation and compression work were considered. In this model, a density distribution function was used to simulate the flow field and two total energy distribution functions were employed to simulate temperature fields for both fluid and solid. Discrete equilibrium density and total energy distribution functions were obtained from Hermite expansions of the corresponding moment equations. Through Chapman-Enskog procedure, macroscopic governing equations could be recovered expediently from the present thermal lattice Boltzmann model. The proposed model was validated by numerical simulations of thermal Poiseuille flow in a planar porous channel and natural convection in a square porous cavity.

Study of Local Turbulence Profiles Relative to the Particle Surface in Particle-Laden Turbulent Flows

As particle-resolved simulations (PRSs) of turbulent flows laden with finite-size solid particles become feasible, methods are needed to analyze the simulated flows in order to convert the simulation data to a form useful for model development. In this paper, the focus is on turbulence statistics at the moving fluid–solid interfaces. An averaged governing equation is developed to quantify the radial transport of turbulent kinetic energy when viewed in a frame moving with a solid particle. Using an interface-resolved flow field solved by the lattice Boltzmann method (LBM), we computed each term in the transport equation for a forced, particle-laden, homogeneous isotropic turbulence. The results illustrate the distributions and relative importance of volumetric source and sink terms, as well as pressure work, viscous stress work, and turbulence transport. In a decaying particle-laden flow, the dissipation rate and kinetic energy profiles are found to be self-similar.

Simulation of Two-Phase Rayleigh-Benard Problem Using Lattice Boltzmann Method

1,2 Abstract: In the present work, two-phase Rayleigh-Benard problem is simulated by lattice Boltzmann method. Two horizontal layers of immiscible fluid are confined in a rectangular cavity. The vertical walls of the cavity are insulated while the horizontal walls are maintained at different constant temperatures. Two-phase lattice Boltzmann method is used to model hydrodynamic field and a passive scalar approach is implemented to model the thermal field. The viscous heat dissipation and compression work done by pressure are neglected. The present model is validated with the single-phase Rayleigh-Benard problem and good agreement is observed. The applicability of this new lattice Boltzmann model for simulating thermal two-phase problems is the main objective of this study. Furthermore, a comprehensive parametric study of the problem is carried out for wide range of different non-dimensional parameters. It is found that with increase of Rayleigh number, the fluid motion becomes stronger and the isotherms are more distorted. Also with decrease of the ratio of Prandtl number of upper fluid to lower fluid, conduction dominates in the upper layer. It is concluded that this new thermal lattice Boltzmann model has a great capability to model thermal two- phase problems.

Variational Integrators for Thermo‐Viscoelastic Discrete Systems

AbstractVariational integrators are modern time‐integration schemes based on a discretization of the underlying variational principle. In this paper, Hamilton's principle is approximated by an action sum, whose vanishing variation results in discrete Euler‐Lagrange equations or, equivalently, in discrete evolution equations for the position and momentum. In order to include the viscous and thermal virtual work (mechanical and thermal virtual dissipation), Hamilton's principle is extended by D'Alembert terms, which account for the time evolution equation of the internal variable and Fourier's law.From this variational formulation, variational integrators using different orders of approximation of the state variables as well as of the quadrature of the action integral are constructed and compared. A thermo‐viscoelastic double pendulum comprised of two discrete masses connected by generalized Maxwell elements, and subject to heat conduction between them serves as a discrete model problem. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Energy separation mechanism in unconfined laminar compressible vortex

A theoretical investigation from the view point of gas-dynamics and thermodynamics was carried out, in order to clarify the energy separation mechanism in an unconfined laminar compressible vortex, as a primary flow element of a vortex tube. The mathematical solutions of density and temperature in a viscous compressible vortical flow, with tangential velocity, were examined using an evaluation equation of total temperature. It is found from the results that a hotter gas in the peripheral region of the vortex is mainly generated by heat caused by viscous dissipation. A colder gas in the vortex center is mainly generated by viscous shear work done by the fluid element onto the surface of the surrounding gas. In addition, it is also found that the larger the representative Mach number of a vortex is, the lower the total temperature at the center of the vortex is, and at the same time, the higher the maximum total temperature in the peripheral region is. The increase in specific heat ratio of the working gas has the same effect, as increasing the representative Mach number of the vortex, on the total temperature in the vortex.

Coupling double-distribution-function thermal lattice Boltzmann method based on the total energy type

Micro-scale flow is a very important and prominent problem in the design and application of micro-electromechanical systems. With the decrease of the scale, effects, such as viscous dissipation, compression work and boundary slip etc., which are ignored in a large-scale flow, play important roles in a microfluidic system. #br#With its certain advantages such as high numerical efficiency, easy implement, parallel algorithms etc., the lattice Boltzmann method is a powerful numerical technique for simulating fluid flows and modeling the physics in fluids. The double-distribution-function lattice Boltzmann method has been widely used in a micro-scale thermal flow system, since it utilizes two different distribution functions to take account of the viscous dissipation and compression work. However, most of the existing double-distribution-function lattice Boltzmann methods are “decoupling” models, and decoupling will cause the models to be limited to Boussinesq flows in which temperature variation is small. In order to overcome the above problem, based on the low-order Hermite expansion of the continuous equilibrium distribution function, we propose a coupling double-distribution-function thermal lattice Boltzmann method. This method introduces temperature changes into the lattice Boltzmann momentum equation in the form of the momentum source, which can affect the distribution of flow velocity and density, so as to realize the coupling between the momentum field and the energy field. In the process of fluid flow, the temperature change of the energy field includes two parts: one is for different times at the same lattice which can cause the change of the fluid characteristic parameters, such as the viscosity coefficient and the thermal diffusivity; the other is for the same time at different lattices which mainly affects the distribution of the velocity. In the collision and the migration processes, temperature change is introduced into the fluid flow to achieve the effect of temperature changes on the flow field and the coupling between the energy field and the momentum field. This method can break up the limitation of the Boussinesq flows and expand the application scope of the lattice Boltzmann method. #br#Two natural convection models (one takes into consideration the viscous dissipation and compression work, and the other does not) are studied in this paper to verify the effectiveness and accuracy of the coupling double-distribution-function thermal lattice Boltzmann method. Flow field and the changing trend in temperature, velocity and the averaged Nusselt number are analyzed emphatically at different Rayleigh number and Prandtl number. Results of this paper are excellently consistent with those in papers published, confirming the validity and accuracy of this method. Results also show that the convective heat transfer gradually enhances with increasing Rayleigh number and Prandtl number in the cavity, and the boundary layer is obviously formed in the regions very close to the walls; the heat transfer is greatly enhanced if viscous dissipation and compression work are considered; and these effects should not be neglected in the micro-scale flow system.

On the interfacial roughness scale in turbulent stratified two-phase flow: 3D lattice Boltzmann numerical simulations with forced turbulence and surfactant

Numerical 3D simulations of turbulent, stratified two-phase shear flow with a surfactant laden interface were used to test and develop a phenomenological interfacial roughness scale model where the energy required to deform the interface (buoyancy, interfacial tension, and viscous work) is proportional to the turbulent kinetic energy adjacent to the interface.The turbulence was forced in the upper and lower liquids in the simulations, to emulate the interfacial dynamics without requiring (prohibitively) large simulation domains and Reynolds numbers. The addition of surfactant lead to an increased roughness scale (for the same turbulent kinetic energy) due to the introduction of interfacial dilatational elasticity that suppressed horizontal motion parallel to the interface, and enhanced the vertical motion.The phenomenological roughness scale model was not fully developed for dilatational elasticity in this work, but we proposed a source term that represents surfactant induced pressure fluctuations near the interface. This source term should be developed further to account for the relation between surfactant density fluctuations and turbulence adjacent to the interface. We foresee that the roughness scale model can be used as a basis for more general interfacial closure relations in Reynolds averaged turbulence models, where also mobile surfactant is accounted for.

항공기용 가스터빈 엔진의 고압터빈에서 열유동 특성해석을 위한 전산해석기법 연구

In this study, a numerical analysis methodology is studied to predict thermal and flow characteristics of C3X vane with internal cooling. Effects of turbulence models, transition models and viscous work term on temperature and pressure distributions on the vane surface are investigated. These optional terms have few effects on the pressure distributions over the vane surface. However, they have great influence on prediction of the temperature distributions on the vane surface. The combination of k-ω based SST turbulence model, γ transition model and viscous work term are better than RSM turbulence model on prediction of the surface temperature. The average temperature difference between CFD results and experimental results is calculated 2 % at the pressure side and 1 % at the suction side. Furthermore computing time of this combination is half of the RSM turbulence model. When k-ω based SST turbulence model and γ transition model with viscous work term are applied, more accurate predictions of thermal and internal flow characteristics of high pressure turbine are expected.

Oxygen cost of exercise hyperpnea is greater in women compared to men (882.3)

We tested the hypothesis that the O2 cost of exercise hyperpnea is greater in women compared to men. Healthy subjects (8M, 7F) first performed a maximal step cycle exercise test with esophageal and gastric balloon instrumentation followed by a hyperpnea familiarization trial on a separate day. Cardiorespiratory parameters were measured and flow‐ and pressure‐volume loops were constructed from the same breaths (~n=10) for each exercise stage. Days 3 and 4 involved exercise hyperpnea mimicking over 5 ventilatory levels while in the cycling position. Mimicking trials were repeated (n=4) for each ventilatory level. End‐tidal CO2 was controlled to a level corresponding to each exercise stage. Respiratory muscle O2 uptake (VO2rm) was linearly related to work of breathing (WOB) in men (r=0.94, P<0.001) and women (r=0.88, P<0.001). The VO2rm to VE relationship was assessed by fitting a regression accounting for viscous and resistive work. There was no difference in viscous work (P=0.45); however, the resistive component was ~13x greater in women (P<0.05). At maximal ventilation the absolute VO2rm was similar between sexes (0.39 vs. 0.42 l min‐1, P=0.52) despite men having a greater VE (108 vs. 169 l min‐1); but the VO2rm represented a greater fraction of whole‐body VO2 in women (14.6 vs. 9.8%, P<0.05). In conclusion, the O2 cost of exercise hyperpnea is greater in women owing to a greater resistive WOB.Grant Funding Source: Natural Sciences and Engineering Research Council of Canada

A Molecular Dynamics Approach to Ligand-Receptor Interaction in the Aspirin-Human Serum Albumin Complex

In this work, we present a study of the interaction between human serum albumin (HSA) and acetylsalicylic acid (ASA, C9H8O4) by molecular dynamics simulations (MD). Starting from an experimentally resolved structure of the complex, we performed the extraction of the ligand by means of the application of an external force. After stabilization of the system, we quantified the force used to remove the ASA from its specific site of binding to HSA and calculated the mechanical nonequilibrium external work done during this process. We obtain a reasonable value for the upper boundary of the Gibbs free energy difference (an equilibrium thermodynamic potential) between the complexed and noncomplexed states. To achieve this goal, we used the finite sampling estimator of the average work, calculated from the Jarzynski Equality. To evaluate the effect of the solvent, we calculated the so-called “viscous work,” that is, the work done to move the aspirin in the same trajectory through the solvent in absence of the protein, so as to assess the relevance of its contribution to the total work. The results are in good agreement with the available experimental data for the albumin affinity constant for aspirin, obtained through quenching fluorescence methods.

Numerical and Experimental Study of a 1-kW Hydrazine Engineering Design Model Arcjet Thruster

AbstractNumerical and experimental study of a 1-kW hydrazine engineering design model arcjet thruster with simulated hydrazine reaction products as propellant was performed. A two-dimensional numerical model incorporating the effects of viscous dissipation, Lorentz force, ohmic heating, heat conduction, radiation loss, and pressure work was developed to model the plasma processes inside the arcjet nozzle. The flow field and heat-transfer characteristics inside the arcjet nozzle obtained from the numerical study are discussed. The effects of the electrical conductivity and the anode wall temperature on arcjet performance prediction are also discussed. Experimental tests of the engineering design model arcjet thruster with simulated hydrazine reaction products as propellant were carried out with a mass flow rate range of 20–32 mg/s and an arc current range of 8–10 A. Over the mass flow rate and arc current ranges tested in the experiment, the specific impulse of the arcjet was in the range 479–528 s, and th...

Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices

In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard two-dimensional nine-velocity (D2Q9) lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and compression work are considered. In the model, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are obtained from the Hermite expansions of the corresponding continuous equilibrium distribution functions. The pressure given by the equation of state of perfect gases is recovered in the macroscopic momentum and energy equations. The coupling between the momentum and energy transports makes the model applicable for general thermal flows such as non-Boussinesq flows, while the existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which the temperature variation is small. Meanwhile, the simple structure and general features of the DDF LB approach are retained. The model is tested by numerical simulations of thermal Couette flow, attenuation-driven acoustic streaming, and natural convection in a square cavity with small and large temperature differences. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.

Shear-thinning film on a porous substrate: Stability analysis of a one-sided model

The temporal stability of a Carreau fluid flowing down an inclined porous substrate is considered. A reduced model is derived under the assumption of small permeability which decouples the flow in the liquid layer from the filtration flow in the porous medium and incorporates the effect of the porous medium by means of an effective slip condition at the liquid–solid interface. The slip coefficient in the effective slip condition is a function of the structure, permeability of the porous medium and the rheology of the fluid saturating the porous medium. The effects of shear-thinning rheology and permeability of the substrate on the stability of the film flow system are investigated. This problem gives rise to a generalized eigenvalue formulation which is solved through two approaches. The problem is solved analytically for long waves in the limiting cases of weakly and strongly non-Newtonian behaviors (power-law limit). A numerical investigation is carried out in the general case. The results are shown to agree well for the weakly non-Newtonian limit. Further, the power-law model and the Carreau model agree on a wide range of shear-thinning parameter values for a thin film over a rigid substrate. However, when considering a porous medium, this trend is not observed. The Carreau model gives valid results for the entire range of shear-thinning parameter values for a film over a rigid/porous substrate. The novelty of the present investigation lies in the inclusion of both the effects of bottom permeability and shear-thinning rheology. Both permeability and shear-thinning rheology have a destabilizing effect on the film flow system. The numerical results indicate the correlation between the effects due to shear-thinning properties and permeability. An energy balance analysis performed on the perturbation fields shows that destabilization induced by both shear-thinning and permeability is linked to the viscous shear work rate on the free surface.

Kinetic theory based lattice Boltzmann equation with viscous dissipation and pressure work for axisymmetric thermal flows

A lattice Boltzmann equation (LBE) for axisymmetric thermal flows is proposed. The model is derived from the kinetic theory which exhibits several features that distinguish it from other previous LBE models. First, the present thermal LBE model is derived from the continuous Boltzmann equation, which has a solid foundation and clear physical significance; Second, the model can recover the energy equation with the viscous dissipation term and work of pressure which are usually ignored by traditional methods and the existing thermal LBE models; Finally, unlike the existing thermal LBE models, no velocity and temperature gradients appear in the force terms which are easy to realize in the present model. The model is validated by thermal flow in a pipe, thermal buoyancy-driven flow, and swirling flow in vertical cylinder by rotating the top and bottom walls. It is found that the numerical results agreed excellently with analytical solution or other numerical results.

Bioenergetics and biomechanics of cycling: the role of ‘internal work’

The 'dissection' of energy expenditure of cycling into the metabolic equivalent of the different forms of mechanical work done, inaugurated 30 years ago by di Prampero and collaborators, has been much debated in the last few decades. The mechanical internal work, particularly, which is currently associated to the movement of the lower limbs, has been approached, estimated and discussed in several different ways and there is no agreed consensus on its role in cycling. This paper, through re-processing previously published data of oxygen consumption during pedalling at different frequency, external load and limb mass, proposes a model equation and a multiple non-linear regression as the method to assess the internal work of cycling. With that tool a very consistent metabolic equivalent of the internal work is obtained. However, a software simulation of pedalling limbs showed, as suggested in the literature, that the link with the chain ring allows the system to passively revolve forever, after an initial push. This result challenges the very existence of the 'kinematic internal work' of cycling. We conclude and suggest that the 'viscous internal work', an often neglected and almost unmeasurable portion of the internal work that could be proportional to the 'kinematic' form, is responsible for the extra metabolic expenditure as measured when the pedalling frequency of cycling increases.

Extended Oberbeck–Boussinesq approximation study of convective instabilities in a porous layer with horizontal flow and bottom heating

A study of the onset of convective instabilities in a porous layer with a horizontal basic flow is performed by including the effects of viscous dissipation and pressure work in the energy balance. Firstly, the so-called extended Oberbeck–Boussinesq approximation, i.e. the model based on the enthalpy formulation of the energy balance, is adopted. Then, the results for the marginal stability condition are compared with those obtained by the so-called Chandrasekhar approximation, i.e. the model based on the internal-energy formulation of the energy balance. It is shown that a marked discrepancy occurs between the two approaches, that becomes specially evident for high values of the Gebhart number. According to the extended Oberbeck–Boussinesq approximation, the effects of the viscous dissipation and of the pressure work result in a stabilization of the basic flow. On the contrary, the Chandrasekhar approximation predicts a destabilization of the basic flow induced by the viscous dissipation. The destabilization can be so intense that the onset of convective rolls may occur even in the absence of a boundary temperature difference, i.e. with a vanishing Darcy–Rayleigh number.

Investigations on the Discharge and Total Temperature Increase Characteristics of the Labyrinth Seals With Honeycomb and Smooth Lands

Abstract The viscous work generated by the rotating components of a seal not only represents a direct loss of power but also causes an increase in the total temperature of fluid (windage effect). In order to study the discharge and total temperature increase characteristics of the stepped labyrinth seals with smooth and honeycomb lands, 3D Reynolds-averaged Navier–Stokes solutions from CFX is used in this work. At first, the influences of the inlet preswirl, leakage flow rate, and rotational speed on the total temperature increase in the convergent and divergent stepped labyrinth seals with smooth and honeycomb lands are conducted. The obtained 3D numerical results are well in agreement with the referenced experimental data. It shows that the utilized numerical approach has sufficient precision to predict the total temperature increase in seals. Then, a range of pressure ratios and four sizes of sealing clearance are performed to investigate the effects of sealing clearances and pressure ratio impact on the discharge and total temperature increase of the stepped labyrinth seals with honeycomb and smooth liners.