Radiation Effects on Turbulent Mixed Convection in an Asymmetrically Heated Vertical Channel

The purpose of present study is to numerically investigate the radiation effects on turbulent mixed convection flow between two differentially heated vertical parallel plates. Two flow situations known as aiding and opposing flow are considered. Frictional Reynolds number and Grashof number are assumed to be 150 and 1.6 × 10⁶, respectively. Both hydrodynamically and thermally developing and fully developed regions in the channel are investigated. Three Reynolds-averaged Navier–Stokes-based low Reynolds turbulence models are evaluated and the model with better overall performance is applied to the simulations. The radiative transfer equation for the gray and participating fluid is solved using the discrete-ordinates method, adopting its eighth-order quadrature scheme. The effects of two radiative parameters, namely, wall emissivity and optical thickness, on the flow and thermal fields, Nusselt number, and friction factor are addressed. Present results indicate that the presence of thermal radiation has a significant influence on flow and thermal fields. With an increase in wall emissivity and optical thickness, influence of radiation on the mean velocity, mean temperature, and turbulence kinetic energy profiles grows in both aiding and opposing regions. This results in an increase in bulk temperature, centerline velocity, and Nusselt number and a decrease in friction factor on both sides.     

NUMERICAL STUDY ON TURBULENT FLOW AND HEAT TRANSFER IN CIRCULAR COUETTE FLOWS

Abstract

A numerical study is performed to investigate heat transfer and fluid flow in the entrance and fully developed regions of an annulus, consisting of a rotating, insulated inner cylinder and a stationary, heated outer cylinder. Several different k-ε turbulence models are employed to determine the turbulent kinetic energy, its dissipation rate, and the heat transfer performance. The governing boundary layer equations are discretized by means of a control volume finite difference technique and numerically solved using the marching procedure. In the entrance region the axial rotation of the inner cylinder induces a thermal development and causes an increase in both the Nusselt number and the turbulent kinetic energy in the inner cylinder wall region. In the fully developed region, an increase in the Taylor number causes an amplification of the turbulent kinetic energy over the whole cross section, resulting in a substantial enhancement in the Nusselt number. These transport phenomena are also affected by the radius ratio and Reynolds number.     

Two-dimensional simulation of turbulent flow and transfer through stacked spheres

We propose a one-equation model for two-dimensional turbulent flow through porous media. The momentum equation is derived from the space averaging of Navier-Stokes equations, leading to the so-called Darcy-Forchheimer equations. In the turbulent kinetic energy transport equation, the production term is assumed to be proportional to the cube of velocity. The dissipation term is not estimated with a transport equation, it is explicitly given by a law involving turbulent kinetic energy and velocity. The model requires only four experimentally determined parameters. The local Nusselt number was correlated to local Reynolds number, and to local turbulence intensity. Good agreement between the simulated and the experimental local Nusselt number is obtained.     

Thermal performance of dimpled surfaces in laminar flows

The present study provides data which illustrate the effects of an array of dimples on local and spatially-averaged surface Nusselt number distributions, as well as on friction factors in channels with laminar flow. Trends of spatially-averaged Nusselt numbers and friction factors are provided as they vary with dimple depth, channel height, Reynolds number from 260 to 1030, and the use of protrusions on the opposite channel wall. When compared with turbulent flow results, the present laminar data illustrate changes due to the absence of turbulence transport. For example, in contrast to turbulent flows, the present laminar flow data show that there is no overall benefit from the use of a top wall with protrusions. In addition, spatially-averaged Nusselt number ratios and friction factor ratios measured on a deep dimpled surface with a smooth top wall show trends which are opposite from ones observed in turbulent flows, since lower laminar heat transfer augmentations are present for smaller channel heights when compared at the same Reynolds number.     

Numerical investigation of developing turbulent flow in a helical square duct with large curvature

IntroductionCurved pipes, such as bends, belieal coils, spiralcoils etc., are extensively used in piping systemS.Although a large amount Of work have been Publishedregarding Pressure loss, heat transfer and detailed flowmechhasms of curved Pipe flowl"'], more experimentaland numerical stUdy are shll deserved, especially for thecase of develOPing flow, turbulent flow and non-circularcross sechon.Numerical simulation of tUrbulent curved pipe flowis a challenging task for its inherent featUre…     

New scaling of turbulence statistics for incompressible thermal channel flow with different total heat flux gradients

The scaling of turbulence statistics for wall-bounded thermal turbulent flow with different total heat flux gradients was investigated using direct numerical simulation (DNS) of an incompressible turbulent channel flow with passive scalar transport at the friction Reynolds number of 300 and the Prandtl number of 0.72. DNSs for four cases were performed, where the non-dimensional total heat flux gradients were −1, −0.5, 0 and +0.5. It was revealed that temperature variance and turbulent heat flux were well scaled by the local friction temperature. In addition, using the linear stress-heat flux model, it was shown that the appearance of the logarithmic temperature profile was attributed to the distribution of the turbulent Prandtl number.     

Numerical computation of macroscopic turbulence quantities in representative elementary volumes of the porous medium

In this study, fully developed macroscopic turbulence quantities—based on their definitions in some existing turbulence models for porous media as well as those based on definitions introduced in a recently developed model [F.E. Teruel, Rizwan-uddin, A new turbulence model for porous media flows. Part I: Constitutive equations and model closure, Int. J. Heat Mass Transfer (2009)]—are computed and analyzed for different Reynolds numbers as well as for different porosity levels. When computed based on the definition introduced in the new model, these numerically computed, pore-level turbulent quantities provide closure to the formulation. A large set of microscopic turbulent flow simulations of the REV of a porous medium, formed by staggered square cylinders, is carried out to achieve these tasks. For each Reynolds number selected, ten different porosities are simulated in the 5–95% range. The Reynolds number is varied from Re = 10³ to Re = 10⁵, covering four different cases of the turbulence flow regime. Numerical results obtained for the macroscopic turbulent kinetic energy based on the new definition show that the spatial dispersion of the mean flow is the main contributor to this quantity at low porosities. Additionally, it is found that for high porosities, the spatial average of the turbulent kinetic energy is the main contributor but the spatial dispersion of the mean flow cannot be neglected. The new definition of the macroscopic dissipation rate is found to asymptotically approach the volume average of this quantity at high Reynolds numbers. It is confirmed that microscopic numerical simulations are consistent with the macroscopic law that states that the macroscopic dissipation rate is determined by the pressure-drop through the REV.     

Investigation of dimpled fins for heat transfer enhancement in compact heat exchangers

Direct and Large-Eddy simulations are conducted in a fin bank with dimples and protrusions over a Reynolds number range of Re_H = 200 to 15,000, encompassing laminar, transitional and fully turbulent regimes. Two dimple-protrusion geometries are studied in which the same imprint pattern is investigated for two different channel heights or fin pitches, Case 1 with twice the fin pitch of Case 2. The smaller fin pitch configuration (Case 2) develops flow instabilities at Re_H = 450, whereas Case 1 undergoes transition at Re_H = 900. Case 2, exhibits higher Nusselt numbers and friction coefficients in the low Reynolds number regime before Case 1 transitions to turbulence, after which, the differences between the two decreases considerably in the fully turbulent regime. Vorticity generated within the dimple cavity and at the dimple rim contribute substantially to heat transfer augmentation on the dimple side, whereas flow impingement and acceleration between protrusions contribute substantially on the protrusion side. While friction drag dominates losses in Case 1 at low Reynolds numbers, both form and friction drag contributed equally in Case 2. As the Reynolds number increases to fully turbulent flow, form drag dominates in both cases, contributing about 80% to the total losses. While both geometries are viable and competitive with other augmentation surfaces in the turbulent regime, Case 2 with larger feature sizes with respect to the fin pitch is more appropriate in the low Reynolds number regime Re_H < 2000, which makes up most of the operating range of typical compact heat exchangers.     

Laminarization and Turbulentization in a Pulsatile Pipe Flow

A fluid-flow model which automatically determines the flow regime was used to analyze a timewise-periodic pipe flow. Numerical simulation was employed to implement the model. The range of the instantaneous Reynolds number gave rise to four distinct flow regimes: laminarizing, fully laminar, turbulentizing, and fully turbulent. The period of the imposed harmonic oscillations was varied over a very wide range, and the magnitude of the oscillations was of the same order as that of the steady flow on which the oscillations were superimposed. A large-period limit at which the flow is quasi-steady was identified. The predicted quasi-steady fully developed friction factor for each regime was found to be in excellent agreement with steady-state results applied instantaneously. A metric in the form of the ratio of the turbulence production to turbulence destruction was used to exhibit the turbulence characteristics of each of the four flow regimes. The value of this metric was somewhat different in the laminarization and turbulentization regimes at the same instantaneous Reynolds number. This outcome suggests that the flow has memory.     

Prediction of turbulent channel flow with superhydrophobic walls consisting of micro-ribs and cavities oriented parallel to the flow direction

Turbulent flow in a parallel-plate micro-channel with superhydrophobic walls has been explored numerically. The k-ω turbulence model is used for closure to the turbulent Reynolds-averaged Navier-Stokes equations and the Reynolds number was varied from 4 × 10³ to 10⁴. Results show that as the shear-free region increases the apparent velocity slip increases, and the Darcy friction factor decreases. The observed reduction in fraction factor was found to be significantly greater for turbulent flow conditions than for laminar flow scenarios under the same geometric channel conditions. Expressions that correlate the friction factor and apparent slip velocity as functions of the relevant parameters are also presented.     

Numerical simulation of laminar breakdown and subsequent intermittent and turbulent flow in parallel-plate channels: Effects of inlet velocity profile and turbulence intensity

The nature of flow development in a parallel plate channel has been investigated by making use of a newly developed model of intermittency. That model, taken together with the RANS equations of momentum conservation, the continuity equation, and the SST turbulence model, was employed to provide a complete chronology of the development processes and the derived practical results. A major focus of the work is the effect of inlet conditions on the downstream behavior of the developing flow. It was observed that the flow development process depends critically on the specifics of the inlet conditions characterized here by the shape of the velocity profile and the magnitude of the turbulence intensity. Two velocity profile shapes (flat and parabolic), are regarded as limiting cases. Similarly, two turbulence intensities, Tu = 1% and 5%, are employed. From the standpoint of practice, the relationship between the friction factor and the Reynolds number is most significant. It was found that this relationship reflects that of standard practice for only one of the investigated cases (flat velocity profile, Tu = 5%). For the other cases (flat profile, Tu = 1% and parabolic profile, Tu = 1% and 5%), the breakdown of laminar flow is delayed and the onset of full turbulence occurs rather abruptly at Re ～10,000. Three unique fully developed flow regimes are existent, depending on the inlet conditions and on the value of the Reynolds number. In addition to the standard laminar and fully turbulent regimes, another regime, fully developed intermittent, can occur. Specifically, in the latter regime, laminar and turbulent flows occur intermittently.     

An Investigation of Compressible Turbulent Forced Convection by an Implicit Turbulence Model for Large Eddy Simulation

An investigation of compressible turbulent forced convection in a three-dimensional channel flow is studied numerically by an implicit turbulence model for large eddy simulation (LES). Because of a high temperature difference between two walls and turbulent flow, the compressibility and viscosity of fluid should be taken into consideration simultaneously. Methods of the Roe scheme, preconditioning, and dual time stepping coordinating an implicit turbulence model for LES are used for resolving the effect of the compressibility of fluid on a low speed flow field. The magnitudes of Re _τ based on the friction velocity changing from 180 to 940, with the high temperature difference of two walls of 500 k are conducted. The results of the mean velocity profiles and turbulent intensities are in good agreement with the benchmark DNS data obtained by spectral codes from a low Reynolds number (Re _τ  = 180) to a high Reynolds number (Re _τ  = 940). Besides, the larger the Re _τ is, with the exception of acquirement of larger average Nusselt number, the more drastic variation of local instantaneous Nusselt number is observed.     

Heat- mass transfer and flow characteristics of two-phase countercurrent annular flow in a vertical pipe

Experimental and theoretical results on flow, heat and mass transfer characteristics for the countercurrent flow of air and water in a vertical circular pipe are compared. An experimental setup was designed and constructed. Hot water is introduced through a porous section at the upper end of a test section and flows downward as a thin liquid film on the pipe wall while the air flows countercurrently. The air and water flow rates used in this study are those before the flooding is reached. A developed mathematical model is separated into three parts: A high Reynolds number turbulence model, in which the local state of turbulence characteristics consists of the turbulent kinetic energy (k) and its dissipation rate (ϵ).The transport equations for both k and s are solved simultaneously with the momentum equation to determine the kinetic turbulence viscosity, the pressure drop, interfacial shear stress and then the friction factor at the film/core interface; Heat and mass transfer models are proposed in order to estimate the distribution of the temperature and the mass fraction of water vapor in gas core. The results from the model are compared with the present experimental ones. It can be shown from the present study that the influence of the interfacial wave phenomena is significant to the pressure loss, and the heat and mass transfer rate in the gas phase.     

岛屿地貌单元的湍流能耗物理模型试验

岛屿地貌单元是珠江三角洲发育演变过程中的沉积核心,研究其消能机制,对理解河口动力过程及三角洲发育演变有重要意义。通过建立岛屿地貌单元的湍流能耗特性概化物理模型,基于16 MHz ADV采集高频流速数据,统计了时均及湍流特征量,并利用惯性耗散法分析了岛屿地貌单元的湍流动能耗率。结果表明,相同控制条件下岛屿地貌单元的形态阻力致使尾流中紊动强度量值为明渠的2~3倍,湍流剪切应力及湍流动能较明渠水流的大近1个数量级,湍流动能耗散率比明渠水流湍流动能耗散率大1~2个数量级。岛屿地貌单元的局部形态阻力导致尾流时均流速的空间梯度、切应力增大是湍流能耗率增大的原因。岛屿地貌单元的汇流作用增加了下游尾流区的水流掺混,并在尾流区域形成大量微尺度涡,导致区域湍流能耗作用增强,有利于岛屿沉积核心发育。研究成果有助于理解河口动力及三角洲的发育演变过程。     

DNS of fully developed turbulent heat transfer of a viscoelastic drag-reducing flow

A direct numerical simulation (DNS) of turbulent heat transfer in a channel flow with a Giesekus model was carried out to investigate turbulent heat transfer mechanism of a viscoelastic drag-reducing flow by additives. The configuration was a fully-developed turbulent channel flow with uniform heat flux imposed on both the walls. The temperature was considered as a passive scalar with the effect of buoyancy force neglected. The Reynolds number based on the friction velocity and half the channel height was 150. Statistical quantities such as root-mean-square temperature fluctuations, turbulent heat fluxes and turbulent Prandtl number were obtained and compared with those of a Newtonian fluid flow. Budget terms of the temperature variance and turbulent heat fluxes were also presented.     

Three‐dimensional turbulent forced convection around a hot cubic block exposed to a cross‐flow and an impinging jet

A numerical study of a three‐dimensional, turbulent, forced convection flow around a hot cubic block exposed to cross‐flow and an impinging jet is carried out. The standard k‐ε turbulence model is used to study the effects of Reynolds number ratio on the flow and heat transfer. For each value of the Reynolds number of the jet, the Reynolds number ratio is equal to 1, 1.5, and 2. The influence of the channel height and the jet axis location are also examined. The governing equations are solved by using Ansys Fluent software 14.5. Results show that the heat transfer increases with the increase in the Reynolds number ratio. At the top of the cube, better cooling occurs with an increase in the speed of the impinging jet. A reduction in the height of the channel and the displacement of the axis of the jet toward the channel inlet improve the heat transfer. Our simulations are compared with experimental data found in the literature, using different turbulence models.     

Temperature-Invariant Scaling for Compressible Turbulent Boundary Layers with Wall Heat Transfer

In a recent paper by Zhang et al. in 2012, a Mach number-invariant scaling was proposed to account for the effect of variation of free-stream Mach number in supersonic turbulent boundary layers. The present work focuses on the effect of variation of wall temperature with strong heating and cooling at the wall. Direct numerical simulation is used to study scaling and turbulence structure of a spatially evolving Mach 2 supersonic boundary layer at a friction Reynolds number of 500. A new scaling law is proposed to account for temperature-dependent fluid-property variations. This universal scaling appears superior to the existing models with the novelty that it applies not only for the mean-velocity profile but also extends to the turbulent transport, production, and dissipation terms in the budget of the turbulent kinetic energy.     

Large eddy simulation of stably stratified turbulent open channel flows with low- to high-Prandtl number

Large eddy simulation of thermally stratified turbulent open channel flows with low- to high-Prandtl number is performed. The three-dimensional filtered Navier-Stokes and energy equations under the Boussinesq approximation are numerically solved using a fractional-step method. Dynamic subgrid-scale (SGS) models for the turbulent SGS stress and heat flux are employed to close the governing equations. The objective of this study is to reveal the effects of both the Prandtl number (Pr) and Richardson (Ri_τ) number on the characteristics of turbulent flow, heat transfer, and large-scale motions in weakly stratified turbulence. The stably stratified turbulent open channel flows are calculated for Pr from 0.1 up to 100, Ri_τ from 0 to 20, and the Reynolds number (Re_τ) 180 based on the wall friction velocity and the channel height. To elucidate the turbulent flow and heat transfer behaviors, some typical quantities, including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and the structures of the velocity and temperature fluctuations, are analyzed.     

Numerical Analysis of Turbulent Flow in a Small Helically Segmented Finned Tube Bank

A full finned tube bank is represented as a small finned tube bank in order to analyze numerically mean properties behavior in the streamwise direction. The main goal is to obtain criteria for implementing periodic boundary conditions in a single isolated finned tube module. The simulation is carried out with the Reynolds Averaged Navier–Stokes method and the turbulence effect is modeled with the Renormalization Group k-? model. The complex geometry of finned tube is represented by means of a cut-cell method. Numerical results are compared with experimental data, experimental visualizations, and semi-empirical correlations. Predictions show an adequate hydrodynamics and heat transfer representation. Additionally, mean properties in the streamwise direction show quasi-sinusoidal behavior, and the heat transfer presents approximately identical values in every finned tube in the fully developed flow zone. Therefore, periodic boundary conditions for turbulent kinetic energy and its dissipation rate and a constant wall heat flux condition in the fully developed flow are proposed in numerical simulations on a single isolated finned tube module.     

Implications concerning rod bundle crossflow mixing based on measurements of turbulent flow structure

An experimental study was performed to investigate the effect of flow channel geometry on fully developed turbulent flow in “clean” rod bundle flow channels. This information was sought to obtain a better understanding of crossflow mixing between rod bundle subchannels. The experiments were performed in water with a Reynolds number range from 50 000 to 200 000. The experimental flow models considered pitch-to-diameter ratios of 1.25 and 1.125. Axial components of velocity, turbulence intensity and Eulerian autocorrelation function were the primary measurements. The autocorrelation function provided an indication of the dominant frequency of turbulence and an estimate of the longitudinal macroscale by using Taylor's hypothesis. A limited amount of lateral component turbulence intensity data was also obtained.The experimental results show that rod gap spacing (pitch-to-diameter ratio) is the most significant geometric parameter affecting the flow structure. Decreasing the rod gap spacing increases the turbulence intensity, longitudinal macroscale, and the dominant frequency of turbulence. These turbulence parameters are rather insensitive to Reynolds number.The results indicate that macroscopic flow processes exist adjacent to the rod gap. This includes secondary flows and increased scale and frequency of flow pulsations when the rod gap spacing is reduced. When interpreted in terms of crossflow mixing, the results are consistent with present crossflow mixing correlations.