Molecular Heat Conduction Research Articles

Quantum bath augmented stochastic nonequilibrium atomistic simulations for molecular heat conduction.

Classical molecular dynamics (MD) has been shown to be effective in simulating heat conduction in certain molecular junctions since it inherently takes into account some essential methodological components which are lacking in the quantum Landauer-type transport model, such as many-body full force-field interactions, anharmonicity effects and nonlinear responses for large temperature biases. However, the classical MD reaches its limit in the environments where the quantum effects are significant (e.g. with low-temperatures substrates, presence of extremely high frequency molecular modes). Here, we present an atomistic simulation methodology for molecular heat conduction that incorporates the quantum Bose-Einstein statistics into an "effective temperature" in the form of a modified Langevin equation. We show that the results from such a quasi-classical effective temperature MD method deviates drastically when the baths temperature approaches zero from classical MD simulations and the results converge to the classical ones when the bath approaches the high-temperature limit, which makes the method suitable for full temperature range. In addition, we show that our quasi-classical thermal transport method can be used to model the conducting substrate layout and molecular composition (e.g. anharmonicities, high-frequency modes). Anharmonic models are explicitly simulated via the Morse potential and compared to pure harmonic interactions to show the effects of anharmonicities under quantum colored bath setups. Finally, the chain length dependence of heat conduction is examined for one-dimensional polymer chains placed in between quantum augmented baths.

Proposal of a turbulent Prandtl number model for Reynolds-averaged Navier–Stokes approach on the modeling of turbulent heat transfer of low-Prandtl number liquid metal

Because of their high molecular heat conductivity, low-Prandtl number liquid metal is a promising candidate coolant for various designs of advanced nuclear systems such as liquid metal–cooled fast reactors and accelerator-driven sub-critical system (ADS). With the fast-growing computational capacity, more and more attention has been paid to applying computational fluid dynamics (CFD) methods in thermal design and safety assessment of such systems for a detailed analysis of three-dimensional thermal–hydraulic behaviors. However, numerical modeling of turbulent heat transfer for low-Prandtl number liquid metal remains a challenging task. Numerical approaches such as wall-resolved large eddy simulation (LES) or direct numerical simulation (DNS), which can provide detailed insight into the physics of the liquid metal flow and the associated heat transfer, were widely applied to investigate the turbulent heat transfer phenomenon. However, these approaches suffer from the enormous computational consumption and are hence limited only to simple geometrical configurations with low to moderate Reynolds numbers. The Reynolds-averaged Navier–Stokes (RANS) approach associated with a turbulent Prandtl number Prt accounting for the turbulent heat flux based on Reynolds analogy is still, at least in the current state in most of the circumstances, the only feasible approach for practical engineering applications. However, the conventional choice of Prt in the order of 0.9∼unity in many commercial computational fluid dynamics codes is not valid for the low-Prandtl number liquid metal. In this study, LES/DNS simulation results of a simple forced turbulent channel flow up to a friction Reynolds number Reτ of 2000 at Pr of 0.01 and 0.025 were used as references, to which the Reynolds-averaged Navier–Stokes approach with varying Prt was compared. It was found that the appropriate Prt for the RANS approach decreases with bulk Peclet number Peb and approaches a constant value of 1.5 when Peb becomes larger than 2000. Based on this calibrated relation with Peb, a new model for Prt used in the RANS approach was proposed. Validation of the proposed model was carried out with available LES/DNS results on the local temperature profile in the concentric annulus and bare rod bundle, as well as with experimental correlations on the Nusselt number in a circular tube and bare rod bundle.

Isotope effect of rovibrational distribution of hydrogen molecules desorbed from amorphous carbon

When the hydrogen isotope atom is injected into the amorphous carbon with the incident energies E in of 20, 50, and 80 eV, we obtain the following physical quantities of hydrogen isotope atoms/molecules emitted from the amorphous carbon using molecular dynamics and heat conduction hybrid simulation. The physical quantities are the time evolution of the emission rate, the depth distribution of the original location of the hydrogen emitted from the target, the polar angular dependence, and the translational, rotational, and vibrational energy distributions. In addition, the approximate analysis yields the emission distributions at the vibrational (v) and rotational (J) levels. Using these distributions, we evaluate the rotational temperature T rot for v = 0 and small J states. From the above, it is found that molecules with higher rotational levels J tend to be emitted as E in increases or as the mass of hydrogen isotope increases. Moreover, the isotope effect appears in the mass dependence of T rot.

Entropy optimization for Darcy–Forchheimer electro-magneto-hydrodynamic slip flow of ferronanofluid due to stretching/shrinking rotating disk

The flow of ferronanofluid due to a rotating disk finds its significant place in biomedical sciences, pharmaceuticals, electronics, aerodynamics etc. Entropy generation appears in the systems/processes where its minimization is needed because it prohibits the decay of available energy which in turn boosts the efficiency of the associated thermal systems where it matters the most. In view of these added advantages, the flow and heat transfer behavior of ferronanofluid subject to slip, suction, electromagnetic field, Darcy–Forchheimer effect, and viscous dissipation, Ohmic heating and thermal radiation has been explored within this research. In addition, the role of entropy minimization associated with the flow concern has been analyzed. The apposite governing equations are numerically treated via shooting method. The important outcome of the study include infusion of more porous matrix develops controlled rotating flow due to both deformed disks. Rise in slip parameter augments flow velocity for stretched RD while that shows the adverse effect for shrunk RD. Controlled rate of heat transportation due to enhanced convective heating is significant for shrunk RD than that of stretched RD. Further, low Prandtl fluids, low molecular heat conduction and liquid friction yield entropy minimization thereby leading to uplift efficiency of thermal systems.

Waves in gas centrifuges: a review

Waves in gas centrifuges are generated by scoops for withdrawal of the gas. The physics of the waves and their role in the gas dynamics are under discussion. Strong centrifugal and Coriolis forces have dramatic impact on the properties and dispersion relation of the waves. The conventional sound, vertex and entropy waves split into 3 families with different dispersion. The entropy wave has zero velocity of propagation but variation of temperature in this wave is accompanied by toroidal motion. Pressure is not perturbed. The rest two families of the waves have nonzero velocities of propagation. Upper family has frequency above doubled frequency of rotation of the rotor with exceptional case of the wave (named acoustic wave) propagating exactly in the axial direction. This wave propagates with the conventional sound velocity and is polarized only in the axial direction. Unique property of this wave is the weakest damping due to the molecular viscosity and heat conductivity. All other waves are damped on distances compared with their wavelength. At the conventional parameters of the IGUASU centrifuge the acoustic waves are damped predominantly due to the viscous interaction and heat exchange with the wall of the rotor. This wave is able to propagate on the distance of ≤ 1 m. Numerical experiments show that the waves can affect the axial circulation and gas content in the centrifuge and produce phenomena of resonances. Possible impact of the waves on the process of separation of the isotopes is also under discussion.

Thermal-hydraulic analysis of a 7-pin sodium-cooled fast reactor wire-wrapped fuel bundle

The thermal-hydraulic characteristics of 7-pin sodium-cooled fast reactor (SFR) wire-wrapped fuel bundle were numerically investigated by commercial computational fluid dynamics (CFD) code ANSYS Fluent. The sensitivity analyses of mesh size, geometric simplification and Reynolds-Averaged Navier–Stokes (RANS) model were conducted. The turbulent Prandtl number model was adopted. The flow field and heat transfer were analyzed. The results show that the geometric simplification has great influences on friction factor and Nusselt number. The simplification should be taken into consideration seriously. The results of the standard k-ε model, realizable k-ε model and Reynolds stress model (RSM) model are close. The results of the Shear Stress Transport (SST) k-ω model has the maximum error compared with experiment correlation. The strong secondary flows and eddies were observed. The flow velocity near the contact of wire and rod is low and causes high temperature. At the cross section of z=50mm, the difference between the highest and lowest temperatures of the central rod is 13K, and the highest and lowest local Nusselt Numbers are 2.29 and 4.07 respectively, which indicates that the inhomogeneity of heat transfer is considerable. The velocity distribution of the boundary layer agrees well with the law-of-the-wall while the temperature boundary layer is much thicker than that of velocity. At least at y+<100, heat transfer is dominated by molecular heat conduction. At high Peclet number, the default value 0.85 of turbulent Prandtl number overestimates the heat transfer performance and the results of Kays model are closer to the experiment correlation. At very low Peclet number, Kays model has a quite different from experiment correlation. This study provides a reference for SFR design.

Thermal effects of nonlinear acoustic-gravity waves propagating at thermospheric temperatures matching high and low solar activity

Numerical high-resolution modeling of nonlinear acoustic-gravity waves (AGWs) generated at the Earth's surface and propagating to the thermosphere shows that wave characteristics are depending on modifications in the mean density, temperature, molecular dissipation and composition due to variations of solar activity (SA). Amplitudes of temperature wave perturbations are generally larger at high SA at altitudes above 150 km, due to larger mean temperature and smaller molecular heat conductivity. Increasing kinematic coefficients of molecular heat conduction and viscosity result in stronger decreasing AGW amplitudes at altitudes larger 150 km at low SA. Dissipating AGWs generally produce heating at altitudes below 120 km. At larger heights, AGWs generally heat the thermosphere at low SA and cool it at high SA. Wave enthalpy fluxes are mainly upwards below 120 km altitude and downwards above 150 km at high SA, where they may have directions opposite to the upward wave energy fluxes. Downward wave enthalpy fluxes correspond to AGW cooling the upper atmosphere at high SA. Nonlinear dissipating AGWs may produce upward and downward transport of atmospheric mass. These mass flows may produce adiabatic heat influxes in the upper atmosphere. Mainly positive residual wave-induced mass flows at altitudes higher 150 km may contribute to the wave cooling of the upper atmosphere. Wave breaking and interactions between waves and the mean flow in the nonlinear model are stronger at higher amplitudes of AGW excitation at the ground, which lead to bigger energy losses for larger-amplitude waves. At high SA, resulting effects in the thermosphere depend on the balance between, on one hand, increases in wave amplitudes, caused by weaker molecular dissipation and smaller transfer of the wave energy to the wave-induced jet flows, and, on the other hand, decreases in the amplitudes due to higher density and larger AGW reflection. The thermal effects of waves in the upper atmosphere may depend on competitions between heating due to dissipation of the upward wave energy flux and cooling due to divergence of the downward wave entropy (or potential enthalpy) flux. At high SA, larger mean temperatures and larger temperature perturbations might increase magnitudes of downward wave entropy fluxes, which may result in more frequent downward wave enthalpy fluxes and wave cooling of the upper atmosphere.

Temperature field in gas-cooled reactor core in transient conditions under different approaches to mass flow profiling

Positive effect of profiling the gas-cooled reactor core within the framework of the GT-MHR project was investigated in (Podgorny and Kuzevanov 2017, Kuzevanov and Podgorny 2017, 2018). The necessity arises to supplement already implemented analysis of equilibrium conditions of core operation with investigation of effects of profiling on the temperature field in transient modes of reactor core operation. The present paper is dedicated to the investigation of development of transients in gas-cooled nuclear reactor core subject to the implementation of different principles of core profiling. Investigation of transients in reactor core represents complex problem, solution of which by conducting direct measurements is beyond the resources available to the authors. Besides the above, numerical simulation based on advanced CFD software complexes (ANSYS 2016, 2016a, 2016b, Shaw 1992, Anderson et al. 2009, Petrila and Trif 2005, Mohammadi and Pironneau 1994) is also fairly demanding in terms of required computer resources. The algorithm for calculating temperature fields using the model where the reactor core is represented as the solid medium with gas voids was developed by the authors and the assumption was made that heat transfer due to molecular heat conductivity can be described by thermal conductivity equation written for continuous medium with thermal physics parameters equivalent to respective parameters of porous object in order to get the possibility of obtaining prompt solutions of this type of problems. Computer code for calculating temperature field in gas-cooled reactor in transient operation modes was developed based on the suggested algorithm. Proprietary computation code was verified by comparing the results of numerous calculations with results of CFD-modeling of respective transients in the object imitating the core of gas-cooled nuclear reactor. The advantage of the developed computer code is the possibility of real-time calculation of evolution of conditions in complex configurations of gas-cooled reactor cores with different channel diameters. This allows using the computer code in the calculations of transients in loops of reactor facility as a whole, in particular for developing reactor simulators. Results are provided of calculations of transients for reactor core imitating the core of gas-cooled nuclear reactor within the framework of GT-MHR project performed for different approaches to profiling coolant mass flow. Results of calculations unambiguously indicate the significant difference of temperature regimes during transients in the reactor core with and without profiling and undeniable enhancement of reliability of nuclear reactor (Design of the Reactor Core 2005, International Safeguards 2014, Safety of Nuclear Power Plants 2014) with profiling of coolant mass flow in the reactor core as a whole.

Optofluidics: the interaction between light and flowing liquids in integrated devices

Optofluidics is a rising technology that combines microfluidics and optics. Its goal is to manipulate light and flowing liquids on the micro/nanoscale and exploiting their interaction in optofluidic chips. The fluid flow in the on-chip devices is reconfigurable, non-uniform and usually transports substances being analyzed, offering a new idea in the accurate manipulation of lights and biochemical samples. In this paper, we summarized the light modulation in heterogeneous media by unique fluid dynamic properties such as molecular diffusion, heat conduction, centrifugation effect, light-matter interaction and others. By understanding the novel phenomena due to the interaction of light and flowing liquids, quantities of tunable and reconfigurable optofluidic devices such as waveguides, lenses, and lasers are introduced. Those novel applications bring us firm conviction that optofluidics would provide better solutions to high-efficient and high-quality lab-on-chip systems in terms of biochemical analysis and environment monitoring.

Waves in strong centrifugal field: dissipative gas

In the fast rotating gas (with the velocity typical for Iguassu gas centrifuge), three families of linear waves exist with different polarizations and law of dispersion. The energy of the waves is basically concentrated at the axis of rotation in the rarefied region. Therefore, these waves decay on the distance comparable with the wavelength. There is only one type of waves propagating strictly along the axis of rotation with the law of dispersion similar to ordinary acoustic waves. These waves are interested for the physics of gas centrifuges. The energy density of these waves concentrates at the wall of the rotor. These waves have weak damping due to the molecular viscosity and heat conductivity. The damping coefficient is determined for this type of waves by numerical calculations. Analytical approximations for the damping coefficient are defined as well. At the parameters typical for the Iguassu centrifuge, the damping is defined by interaction of the waves with the rotor wall.

Dynamic One-Sided Thermal Scanning of Aircraft Composite Fairings

A theoretical and experimental analysis of the dynamic one-sided thermal scanning of aircraft composite fairings during short-time convective heating is carried out. The model of thermal contrast based on the concept of the mechanism of molecular heat conductivity with rationalization of reducing statement from 2D to 1D format is given and an “effective” heat transfer coefficient from the heated convective source to the fairing surface is introduced. The calculation results show the qualitative sufficiency of this approach, and the full-scale experiments for the nose fairing of the MIG-29 aircraft confirm its correctness quantitatively. The conclusions are drawn on the feasibility of the thermal scanning method of aircraft fairings for identifying delamination cavities.

Propagation of non-stationary acoustic-gravity waves at thermospheric temperatures corresponding to different solar activity

Numerical simulation of non-stationary nonlinear acoustic-gravity waves (AGWs) propagating from the surface wave source to the thermosphere reveals that their propagation conditions and parameters depend on changes in background temperature, density, composition, molecular viscosity and heat conduction caused by changes in solar activity (SA). At small wave source amplitudes, AGW amplitudes, momentum fluxes and wave accelerations of the mean flow are slightly larger at altitudes about 150 km at low SA because of smaller mean density and ρ0−1/2dependence of wave amplitudes at low dissipation. Larger kinematic coefficients of molecular viscosity and heat conduction lead to stronger decrease of wave amplitudes and momentum fluxes at altitudes above 150 km at low SA. At large amplitudes of surface wave excitation, AGW breaking and smaller-scale inhomogeneities appear at altitudes 100–150 km, which are stronger at low SA. Increased dissipation of breaking AGWs may produce wave-induced jet streams with velocities close to the wave horizontal phase speed and near-critical layers at altitudes 110–150 km, which dramatically decrease amplitudes and momentum fluxes of the primary AGW mode propagating from the surface wave source. The wave-induced horizontal wind becomes smaller above altitude of 150 km and allows growing amplitudes of the primary wave mode partially penetrating through the near-critical layer and of secondary AGW modes, possibly generating in the wave induced jet stream. The wave amplitude grows at altitudes higher than 150 km is larger at high SA due to smaller velocities of wave-induced mean wind and smaller molecular viscosity and heat conduction. Accelerations of the mean flow by dissipating AGWs are generally larger at low SA. This determines faster grows of wave-induced jet streams in time at low SA. In almost all simulated cases, velocities of the wave-induced mean flows are higher at low SA compared to high SA. Resulting SA impact at a given thermospheric altitude depends on competition between AGW amplitude increase due to smaller molecular dissipation and smaller energy transfer to the wind-induced mean flow and amplitude decrease caused by larger density and stronger reflection at higher SA.

Evaporation of a sessile water drop and a drop of aqueous salt solution

The influence of various factors on the evaporation of drops of water and aqueous salt solution has been experimentally studied. Typically, in the studies of drop evaporation, only the diffusive vapor transfer, radiation and the molecular heat conduction are taken into account. However, vapor-gas convection plays an important role at droplet evaporation. In the absence of droplet boiling, the influence of gas convection turns out to be the prevailing factor. At nucleate boiling, a prevailing role is played by bubbles generation and vapor jet discharge at a bubble collapse. The gas convection behavior for water and aqueous salt solution is substantially different. With a growth of salt concentration over time, the influence of the convective component first increases, reaches an extremum and then significantly decreases. At nucleate boiling in a salt solution it is incorrect to simulate the droplet evaporation and the heat transfer in quasi-stationary approximation. The evaporation at nucleate boiling in a liquid drop is divided into several characteristic time intervals. Each of these intervals is characterized by a noticeable change in both the evaporation rate and the convection role.

Evaporation and heat and mass transfer of a sessile drop of aqueous salt solution on heated wall

The droplets evaporation of water and aqueous salt solution were experimentally studied. The impact of various key factors on the evaporation has been estimated. Typically when considering evaporation of droplets, only the diffusive vapor-gas transfer and the molecular heat conduction are taken into account. However, vapor-gas convection plays an important role at droplets evaporation. The qualitative behavior of gas convection for water and aqueous salt solution is substantially different. The neglect of gas convection in the prediction leads to manifold underestimation of the evaporation rate compared with the experimental data. With a growth of salt concentration with time, the influence of the convective component first increases, reaches an extremum and then significantly decreases. The evaporation at nucleate boiling in the liquid drop is divided into several characteristic time intervals.

Free convection and vapor diffusion of droplet aqueous solutions

Evaporation of drops of water and aqueous solutions of salts LiBr and CaCl2 have been studied experimentally. The impact of various key factors on the evaporation has been estimated. The behavior of convection significantly differs in drops of water and salt solution. The contribution of gas convection changes with an increase in salt concentration. With increasing salt concentration in a drop, the role of the convective component first increases, reaches an extremum and then decreases with time. Usually when modeling droplet evaporation, the only considered are the diffusive vapor transport and the molecular heat conduction in liquid. The neglect of gas convection in the simulation leads to essential (manifold) underestimation of the evaporation rate compared with the experimental data. Gas convection may be neglected at intensive bubble boiling in a water drop. The process of drop boiling is divided into 4–5 characteristic time stages with a significant change of both the rate of evaporation and the role of convection.

Arbitrary-Lagrangian–Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space–time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity.The connection of the old mesh configuration at time tn with the new one at time tn+1 provides the space–time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian–Eulerian (ALE) schemes, where a space–time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total Lagrangian formulations that are based on a fixed computational grid and which instead evolve the mapping of the reference configuration to the current one.Our new Lagrangian-type DG scheme adopts the novel a posteriori sub-cell finite volume limiter method recently developed in [62] for fixed unstructured grids. In this approach, the validity of the candidate solution produced in each cell by an unlimited ADER-DG scheme is verified against a set of physical and numerical detection criteria, such as the positivity of pressure and density, the absence of floating point errors (NaN) and the satisfaction of a relaxed discrete maximum principle (DMP) in the sense of polynomials. Those cells which do not satisfy all of the above criteria are flagged as troubled cells and are recomputed at the aid of a more robust second order TVD finite volume scheme. To preserve the subcell resolution capability of the original DG scheme, the FV limiter is run on a sub-grid that is 2N+1 times finer compared to the mesh of the original unlimited DG scheme. The new subcell averages are then gathered back into a high order DG polynomial by a usual conservative finite volume reconstruction operator.The numerical convergence rates of the new ALE ADER-DG schemes are studied up to fourth order in space and time and several test problems are simulated in order to check the accuracy and the robustness of the proposed numerical method in the context of the Euler and Navier–Stokes equations for compressible gas dynamics, considering both inviscid and viscous fluids. Finally, an application inspired by Inertial Confinement Fusion (ICF) type flows is considered by solving the Euler equations and the PDE of viscous and resistive magnetohydrodynamics (VRMHD).

Influence of radiation absorption by microparticles on the flame velocity and combustion regimes

Thermal radiation of the hot combustion products usually does not influence noticeably the flame propagating through gaseous mixture. the situation is changed drastically in the presence even small concentration of particles, which absorb radiation, transfer the heat to the surrounding unburned gaseous mixture by means of heat conduction, so that the gas phase temperature in front of the advancing flame lags that of the particles. It is shown that radiative preheating of unreacted mixture ahead of the flame results in a modest increase of the advancing flame velocity for a highly reactive gaseous fuel, or to considerable increase of the flame velocity in the case of a slow reactive mixture. The effects of radiation preheating as stronger as smaller the normal flame velocity. The radiation heat transfer can become a dominant mechanism compared with molecular heat conduction, determining the structure and the speed of combustion wave in the case of a small enough velocity of the advancing flame. It is shown that in the case of non-uniform distribution of the particles, such that time of the radiation heating is longer so that the maximum temperature in the region of denser particles cloud ahead of the advancing flame is sufficient for ignition, the thermal radiation may trigger additional independent source of ignition. Depending on the steepness of the temperature gradient formed in the unburned mixture, either deflagration or detonation can be initiated via the Zeldovich's gradient mechanism. Ignition of different combustion regimes, depending on the radiation absorption length, is illustrated for the particle-laden hydrogen-oxygen flame.

Structure of the Contact Region and its Application to the Reflexion of a Plane Shock Wave from a Heat Conducting Wall

A study of the structure of the contact region has been made taking into account the effects of viscosity, heat conduction and radiative heat transfer. Analytical solutions for the temperature, velocity and pressure distributions in a uniformly moving contact region have been obtained under the optically thick-gas approximation when the thermal conductivity and absorption coefficients are given by power laws. Applying the analysis of the contact region to the situation when a plane shock is reflected from a plane heat-conducting wall it has been shown that the reflected shock is attenuated due to the combined effects of molecular heat conduction and radiative heat conduction.

Numerical modeling of the propagation of nonlinear acoustic-gravity waves in the middle and upper atmosphere

A numerical algorithm for modeling the vertical propagation and breaking of nonlinear acoustic-gravity waves (AGWs) from the Earth’s surface to the upper atmosphere is described in brief. Monochromatic variations in the vertical velocity at the Earth’s surface are used as an AGW source in the model. The algorithm for solving atmospheric hydrodynamic equations is based on three-dimensional finite-difference analogues of fundamental conservation laws. This approach selects physically correct generalized solutions to hydrodynamic equations. A numerical simulation is carried out in an altitude region from the Earth’s surface to 500 km. Vertical profiles of the background temperature, density, and coefficients of molecular viscosity and heat conduction are taken from the standard atmosphere models. Calculations are made for different amplitudes of lower-boundary wave forcing. The AGW amplitudes increase with altitude, and waves may break in the middle and upper atmosphere.

Computational-Experimental Determination of Wall Temperature Variation in the Forced Motion of Air Inside a Circular Pipe

We suggest an approach to calculating the change in pipe wall temperature allowing one to evaluate the duration of preheating polyethylene pipes in a coil by a heated air for carrying out installation and placement works in the construction of gas pipes under low-temperature conditions. An example of the computational-experimental determination of the duration of preheating a polyethylene pipe in the range of the ambient air temperatures is given. In the present work, we consider preheating of a long-length polyethylene pipe by a heated air in a coil having the temperature of the ambient air and covered with an airtight material (polyethylene fi lm). Under the cover, a temperature higher than the ambient air temperature is maintained, with a heated air being fed into the pipe. The temperature of the heated air supplied under the cover does not exceed 60 o C. Naturally, the duration of pipe heating will vary greatly depending on the pipe length, wall thickness, environmental temperature, fl ow velocity of the air fed, and its temperature. In practice, the quantity of the standard sizes of heated pipes is very limited and the air fl ow velocities are constant. In connection with this, in the present work we consider a computational-experimental problem consisting in the determination of the duration of heating a pipe of given diameter by a heated air fl ow at a prescribed rate. Mathematical Model. In studying the preheating of a long-length polyethylene pipe we assume that the length of the entry hydrodynamic section is small. Thus, along the entire pipe there is a hydrodynamically and thermally stabilized turbulent fl ow. We also assume that the heat carrier is incompressible and its physical parameters are constant, so that we may neglect the friction heat and energy dissipation. In the case of heat pipes, the heat transfer coeffi cient is usually obtained by introducing a correction factor into the heat transfer coeffi cient for a straight pipe. Therefore, to simplify the conjugate heat transfer problem, we will assume that the pipe is straight. Nevertheless, in the mathematical model we will use the parameters obtained in an experiment with heating a pipe in a coil. It is known that a laminar layer is formed near the wall of a pipe with a turbulent fl ow. Heat is transferred through this layer by means of molecular heat conduction. The remaining part of the pipe section is fi lled with a turbulent air fl ow (turbulent core). In a turbulent fl ow, heat is transferred not only by heat