Simulation of compressible flow in high pressure buried gas pipelines

The aim of this work is to analyze the gas flow in high pressure buried pipelines subjected to wall friction and heat transfer. The governing equations for one-dimensional compressible pipe flow are derived and solved numerically. The effects of friction, heat transfer from the wall and inlet temperature on various parameters such as pressure, temperature, Mach number and mass flow rate of the gas are investigated. The numerical scheme and numerical solution was confirmed by some previous numerical studies and available experimental data. The results show that the rate of heat transfer has not a considerable effect on inflow Mach number, but it can reduce the choking length in larger f_DL/D values. The temperature loss will also increase in this case, if smaller pressure drop is desired along the pipe. The results also indicate that for f_DL/D = 150, decreasing the rate of heat transfer from the pipe wall, indicated here by Biot number from 100 to 0.001, will cause an increase of about 7% in the rate of mass flow carried by the pipeline, while for f_DL/D = 50, the change in the rate of mass flow has not a considerable effect. Furthermore, the mass flow rate of choked flow could be increased if the gas flow is cooled before entrance to the pipe.     

Second law optimization of a solar air heater having chamfered rib–groove roughness on absorber plate

Artificially roughened solar air heaters perform better than the plane ones under the same operating conditions. However, artificial roughness leads to even more fluid pressure thereby increasing the pumping power. The entropy generation in the duct of solar air heater having repeated transverse chamfered rib–groove roughness on one broad wall is studied numerically. Roughness parameters, viz., relative roughness pitch P/e, relative roughness height e/D_h relative groove position g/P, chamfer angle φ and flow Reynolds number Re have a combined effect on the heat transfer as well as fluid friction. The entropy generation is minimized and reasonably optimized designs of roughness are found.     

Roughness enhanced mechanism for turbulent convective heat transfer

The mechanism of turbulent convective heat transfer enhancement was experimentally investigated by measuring the heat transfer in two dimensional roughness tubes with different roughness heights at various Reynolds numbers. The results show that there is a maximum Nusselt number ratio (Nu/Nu₀) for a fixed roughness height with increasing Reynolds numbers. For water as working fluid, heat transfer can hardly be increased when the roughness height is lower than the thickness of the viscous sublayer, and both heat transfer and flow friction begin to increase when the roughness height is higher than the viscous sublayer. When the roughness height is more than five times of the viscous sublayer thickness, the flow friction begins to increase sharply but heat transfer is slowly enhanced. So the best heat transfer enhancement for a given pumping power is reached when the roughness height is about three times of the viscous sublayer thickness. The Prandtl number influences to the turbulent heat transfer enhancement by roughness were also analyzed.     

Numerical Investigation on Natural Convection Inside the Side Ventilated Square Enclosure with Vertical Mid-Partition

A finite volume-based computational study of steady laminar natural convection inside the square enclosure with cold partition wall centrally placed on top and bottom is presented. The fluid considered is air with Prandtl number 0.71. Except the partition walls, all other walls were assumed as hot. The heights of inlet and outlet ports are constantly fixed as 20% of height of the enclosure. The height of the opening in the partition walls were 10%, 20%, and 30% of height of enclosure. The buoyancy-driven heat transfer mechanism inside the domain is influenced by the percentage of opening in the partition, Rayleigh number, and geometrical position of inlet and outlet. The cold partition walls attract the flow that subsequently influences the thermal modifications around the partition. The fluid flow and heat transfer were investigated for 81 cases with different positions of inlet and outlet and varying height of openings for Ra = 10³, 10⁴, and 10⁵. The cross flow between the vertical walls through the opening in the central partition wall was considered in this study. The formation of vortices and their sizes depends on the configuration of inlet and outlet ports. The higher temperature gradient occurs near the inlet and outlet port of vertical walls. Local Nusselt number is maximum just below the inlet for all cases. Due to the dominance of buoyancy forces, heat transfer rate increases when Rayleigh number increases for all the cases. The hydrodynamic block effect by the openings on the partition wall has significant effect on the velocity profile than on the heat transfer.     

Cocurrent turbulent mixed convection heat and mass transfer in falling film of water inside a vertical heated tube

A detailed numerical study has been conducted in order to analyse the combined buoyancy effects of thermal and mass diffusion on the turbulent mixed convection tube flows. Numerical results for air-water system are presented under different conditions. A low Reynolds number k-ε turbulent model is used with combined heat and mass transfer analysis in a vertical heated tube. The local heat fluxes, Nusselt and Sherwood numbers are reported to obtain an understanding of the physical phenomena. Predicted results show that a better heat transfer results for a higher gas flow Reynolds number Re, a higher heat flux q_w or a lower inlet water flow Γ₀. Additionally, the results indicate that the convection of heat by the flowing water film becomes the main mechanism for heat removal from the wall.     

Heat transfer coefficient and friction factor correlations for rectangular solar air heater duct having transverse wedge shaped rib roughness on the absorber plate

As is well known, the heat transfer coefficient of a solar air heater duct can be increased by providing artificial roughness on the heated wall (i.e. the absorber plate). Experiments were performed to collect heat transfer and friction data for forced convection flow of air in solar air heater rectangular duct with one broad wall roughened by wedge shaped transverse integral ribs. The experiment encompassed the Reynolds number range from 3000 to 18000; relative roughness height 0.015 to 0.033; the relative roughness pitch 60.17φ^−1.0264<p/e<12.12; and rib wedge angle (φ) of 8, 10, 12 and 15°. The effect of parameters on the heat transfer coefficient and friction factor are compared with the result of smooth duct under similar flow conditions. Statistical correlations for the Nusselt number and friction factor have been developed in terms of geometrical parameters of the roughness elements and the flow Reynolds number.     

Forced convective heat transfer in a microtube including rarefaction,viscous dissipation and axial conduction effects

Subsonic gas convective heat transfer in a microtube with a constant cross-sectional area and uniform wall temperature is investigated both analytically and numerically. First, the effect of rarefaction on heat transfer characteristics, at a distance from the inlet where Nu becomes constant, is analytically investigated for two cases: (i) including and (ii) neglecting the viscous dissipation effect. An exact solution for Nu in fully developed flow is presented for the case without viscous dissipation, while a closed-form solution for the asymptotic Nu is also provided for the case with viscous dissipation. Next, a numerical model is employed to investigate the simultaneous effects of rarefaction, viscous dissipation, and axial conduction for developing hydrodynamic and temperature conditions. The Nusselt number is substantially affected by viscous dissipation, rarefaction and axial conduction.     

Heat transfer and friction factor correlations for a solar air heater duct roughened artificially with multiple v-ribs

The use of artificial roughness on the underside of the absorber plate is an effective and economic way to improve the thermal performance of a solar air heater. Several experimental investigations, involving different types of roughness elements, have been carried out to improve the heat transfer from the absorber plate to air flowing in solar air heaters. This paper presents an experimental investigation carried out to study the effect of multiple v-rib roughness on heat transfer coefficient and friction factor in an artificially roughened solar air heater duct. The experiment encompassed Reynolds number (Re) from 2000 to 20000, relative roughness height (e/D) values of 0.019-0.043, relative roughness pitch (P/e) range of 6-12, angle of attack (α) range of 30-75° and relative roughness width (W/w) range of 1-10. Extensive experimentation has been conducted to collect data on heat transfer and fluid flow characteristics of a rectangular duct roughened with multiple v-ribs. Using these experimental data, correlations for Nusselt number and friction factor in terms of roughness geometry and flow parameters have been developed.     

Thermal protection with liquid film in turbulent mixed convection channel flows

In this numerical study, a channel flow of turbulent mixed convection of heat and mass transfer with film evaporation has been conducted. The turbulent hot air flows downward of the vertical channel and is cooled by the laminar liquid film on both sides of the channel with thermally insulated walls. The effect of gas–liquid phase coupling, variable thermophysical properties and film vaporization are considered in the analysis. In the air stream, the k–ε turbulent model has been utilized to formulate the turbulent flow. Parameters used in this study are the mass flow rate of the liquid film B, Reynolds number Re, and the free stream temperature of the hot air T_o. Results show that the heat flux was dramatically increases due to the evaporation of liquid water film. The heat transfer increases as the mass flow rate of the liquid film decreases, while the Reynolds number and inlet temperature increase, and the influences of the Re and T_o are more significant than that of the liquid flow rate. It is also found that liquid film helps lowering the heat and mass transfer rate from the hot gas in the turbulent channel, especially at the downstream.     

Heat Transfer Characteristics of Gaseous Flows in Micro-Channel with Negative Heat Flux

Two-dimensional compressible momentum and energy equations are solved to obtain the heat transfer characteristics of gaseous flows in micro-channels with constant heat flux for which the value is negative for no-slip flow. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian method. The computations are performed for channels with constant heat flux ranging from ?10⁴ to ?10² W/m². The channel height ranges from 10 to 100 μ m and the aspect ratio of the channel height and length is 200. The stagnation pressure is chosen such that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in micro-channels with negative heat flux are compared with those of positive heat flux cases obtained in our previous work and also those of the incompressible flow in a conventional sized channel. In the case of fast flow, temperatures normalized by heat flux have different trends whether heat flux value is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the micro-channel is proposed. The rarefaction effect is investigated for the cases of channel height of 10 μ m with slip boundary conditions. The magnitudes of viscous dissipation term and compressibility term are also investigated. The effect of each term on heat transfer characteristics is discussed.     

STUDY OF MIXED-CONVECTION HEAT TRANSFER FROM AN IMPINGING JET TO A SOLID WALL USING A FINITE-ELEMENT METHOD—APPLICATION TO COOKTOP MODELING

The mixed-convection flow from a hot vertical impinging jet on a colder horizontal disc has been studied. The geometry is analogous to a conventional burning gas cooktop. A numerical simulation of the system has been carried out using the finite-element method to study the dependence of fluid flow and heat transfer on the geometric, thermal, and fluid flow parameters. Results show that heat transfer efficiency versus several parameters such as inlet velocity magnitude and flue gas temperature has an optimum value, in which heat transfer efficiency is maximum. With thermal conductivity of the solid wall, velocity angle, and solid wall diameter heat transfer efficiency has increasing behavior. Finally, with solid wall height and solid wall thickness, heat transfer efficiency has diminishing behavior.     

Size effect on microscale single-phase flow and heat transfer

The present discussion will focus on the size effect induced by the variation of dominant factors and phenomena in the flow and heat transfer as the device scale decreases. Due to the larger surface to volume ratio for microchannels and microdevices, factors related to surface effects have more impact to microscale flow and heat transfer. For example, surface friction induced flow compressibility makes the fluid velocity profiles flatter and leads to higher friction factors and Nusselt numbers; surface roughness is likely responsible for the early transition from laminar to turbulent flow and the increased friction factor and Nusselt number; the relative importance of viscous force modifies the correlation between Nu and Ra for natural convection in a microenclosure and, other effects, such as channel surface geometry, surface electrostatic charges, axial heat conduction in the channel wall and measurement errors, could lead to different flow and heat transfer behaviors from that at conventional scales.     

Compressibility and rarefaction effect on heat transfer in rough microchannels

High pressure drop and high length to hydraulic diameter ratios yield significant compressibility effects in microchannel flows, which compete with rarefaction phenomena at the smaller scale. In such regimes, flow field and temperature field are no longer decoupled. In presence of significant heat transfer, and combined with the effect of viscous dissipation, this yields to a quite complex thermo-fluid dynamic problem. A finite volume compressible solver, including generalized Maxwell slip flow and temperature jump boundary conditions suitable for arbitrary geometries, is adopted. Roughness geometry is modeled as a series of triangular shaped obstructions, and relative roughness from 0% to 2.65% were considered. The chosen geometry allows for direct comparison with pressure drop computations carried out, in a previous paper, under adiabatic conditions. A wide range of Mach number is considered, from nearly incompressible to chocked flow conditions. Flow conditions with Reynolds number up to around 300 were computed. The outlet Knudsen number corresponding to the chosen range of Mach and Reynolds number ranges from very low value to around 0.05, and the competing effects of rarefaction, compressibility and roughness are investigated in detail. Compressibility is found to be the most dominant effect at high Mach number, yielding even inversion of heat flux, while roughness has a strong effect in the case of rarefied flow. Furthermore, the mutual interaction between heat transfer and pressure drop is highlighted, comparing Poiseuille number values for both cooled and heated flows with previous adiabatic computations.     

Heat transfer and friction in solar air heater duct with W-shaped rib roughness on absorber plate

Artificial roughness in form of ribs is convenient method for enhancement of heat transfer coefficient in solar air heater. This paper presents experimental investigation of heat transfer and friction factor characteristics of rectangular duct roughened with W-shaped ribs on its underside on one broad wall arranged at an inclination with respect to flow direction. Range of parameters for this study has been decided on basis of practical considerations of system and operating conditions. Duct has width to height ratio (W/H) of 8.0, relative roughness pitch (p/e) of 10, relative roughness height (e/D_h) 0.018-0.03375 and angle of attack of flow (α) 30-75°. Air flow rate corresponds to Reynolds number between 2300-14,000. Heat transfer and friction factor results have been compared with those for smooth duct under similar flow and thermal boundary condition to determine thermo-hydraulic performance. Correlations have been developed for heat transfer coefficient and friction factor for roughened duct.     

The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer

The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer rates, as given by the Nusselt number, is numerically evaluated subject to constant wall heat flux (H2) and constant wall temperature (T) thermal boundary conditions. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. For the limiting case of parallel plate channels, analytic solutions for the thermally and hydrodynamically fully developed momentum and energy equations are derived, subject to both first- and second-order slip velocity and temperature jump boundary conditions, from which analytic Nusselt number solutions are then obtained. Excellent agreement between the analytical and numerical results verifies the accuracy of the numerical algorithm, which is then employed to obtain three-dimensional rectangular channel and thermally/hydrodynamically developing Nusselt numbers. Nusselt number data are presented as functions of Knudsen number, Brinkman number, Peclet number, momentum and thermal accommodation coefficients, and aspect ratio. Rarefaction and viscous dissipation effects are shown to significantly affect the convective heat transfer rate in the slip flow regime.     

Numerical study of the radiation effect on the jet array impinging heat transfer in a feeding pipe

The present study deals with the turbine casing radiation effect on the impinging cooling encountered in the blade tip active clearance control (ACC) system of aero-engine turbine. To this end, numerical simulations are carried out for a simplified model, that is, a pipe with a single row of impinging jets. The effects of the nozzle-to-plate distance to the diameter of the impinging hole (H/d?=?2–8), the number of the holes (n?=?17–68), the impinging wall temperature (T_p?=?400–800?K), and the inlet Reynolds number (Re?=?5,000–20,000) on the flow and heat transfer are investigated. Analysis is performed on the radiation heat transfer effects on the corresponding flow fields and surface heat flux distributions. The results indicate that, with the radiation included in the simulations, the mass flow rate of the cooling jet near the end of the pipe decreases significantly under the conditions of high wall temperature and small nozzle-to-plate distance. Radiation heat transfer should be accounted for in the numerical study for the casing cooling as it affects the flow and heat transfer remarkably. When the nozzle-to-plate distance is relatively large, such as H/d is larger than 8, the radiative heating leads to uniform heat flux and the radiative heating can suppress the uneven distributions of the heat flux.     

Study of Convergence Time for Rarefied Gas Simulations Using an Unstructured DSMC Solver

This article studies the required convergence time for direct-simulation Monte Carlo (DSMC) simulations of rarefied gas flows. An arbitrary-geometry DSMC solver (RGS2D) with an efficient particle-tracking algorithm is introduced and employed for macro-/micro-scale flow applications. Convergence time study is performed by tracing different heat and flow parameters such as intermolecular collision rate, number of particles, drag coefficient, inlet/outlet mass flow rate, and distributions over the wall, i.e., pressure coefficient, skin friction coefficient, heat transfer coefficient, and wall collision rate. The results indicate that the required simulation time depends on the capturing parameter.     

Correlations for solar air heater duct with dimpled shape roughness elements on absorber plate

An experimental investigation has been carried out for a range of system and operating parameters in order to analyse the effect of artificial roughness on heat transfer and friction characteristics in solar air heater duct which is having dimple shaped elements arranged in angular fashion (arc) as roughness elements on absorber plate. Duct has an aspect ratio (W/H) of 11, relative roughness pitch (p/e) range of 10–20, relative roughness height (e/D_h) range of 0.021–0.036, arc angle (α) range of 45–75° and Reynolds number (Re) ranges from 3600 to 18,000. A considerable increase in heat transfer and friction loss has been observed. The experimental data have been used to develop Nusselt number and friction factor correlations as a function of roughness parameters and operating parameters.     

Development of correlations for Nusselt number and friction factor for solar air heater with roughened duct having arc-shaped wire as artificial roughness

An experimental study has been carried out for enhancement of heat transfer coefficient of a solar air heater having roughened air duct provided with artificial roughness in the form of arc-shape parallel wire as roughness element. Increment in friction factor by provided with such artificial roughness elements has also been studied. The effect of system parameters such as relative roughness height (e/d) and arc angle (α/90) have been studied on Nusselt number (Nu) and friction factor (f) with Reynolds number (Re) varied from 2000 to 17000. Considerable enhancement in heat transfer coefficient has been achieved with such roughness element. Using experimental data correlations for Nusselt number and friction factor have also been developed for such solar air heaters, which gives a good agreement between predicted values and experimental values of Nusselt number and friction factor.     

Calculation of turbulent flow and heat transfer in a porous-baffled channel

This study presents the numerical predictions on the turbulent fluid flow and heat transfer characteristics for rectangular channel with porous baffles which are arranged on the bottom and top channel walls in a periodically staggered way. The turbulent governing equations are solved by a control volume-based finite difference method with power-law scheme and the k-ε turbulence model associated with wall function to describe the turbulent structure. The velocity and pressure terms of momentum equations are solved by SIMPLE (semi-implicit method for pressure-linked equation) method.The parameters studied include the entrance Reynolds number Re (1×10⁴-5×10⁴), the baffle height (h=10, 20 and 30 mm) and kind of baffles (solid and porous); whereas the baffle spacing S/H are fixed at 1.0 and the working medium is air. The numerical calculations of the flow field indicate that the flow patterns around the porous- and solid-type baffles are entirely different due to different transport phenomena and it significantly influences the local heat transfer coefficient distributions. Relative to the solid-type baffle channel, the porous-type baffle channel has a lower friction factor due to less channel blockage.Concerning the heat transfer effect, both the solid-type and porous-type baffles walls enhanced the heat transfer relative to the smooth channel. It is further found that at the higher baffle height, the level of heat transfer augmentation is nearly the same for the porous-type baffle, the only difference being the Reynolds number dependence. As expected, the centerline-averaged Nusselt number ratio increases with increasing the baffle height because of the flow acceleration.