Flow In Rectangular Duct Research Articles

Specific aspects of turbulent flow in rectangular ducts

The essential ideas of investigations of turbulent flow in a straight rectangular duct are chronologically presented. Fundamentally significant experimental and theoretical studies for mathematical modeling and numerical computations of this flow configuration are analyzed. An important physical aspect of this type of flow is presence of secondary motion in the plane perpendicular to the streamwise direction, which is of interest from both the engineering and the scientific viewpoints. The key facts for a task of turbulence modeling and optimal choice of the turbulence model are obtained through careful examination of physical mechanisms that generate secondary flows.

AN ESTIMATION OF TURBULENT SECONDARY FLOW RESISTANCE IN RECTANGULAR DUCTS FROM A FLOW MODEL

Incompressible fluid flow in smooth rectangular ducts at working streamwise velocities is turbulent because of resistance of the four side-walls. A second feature of such flows is generation of secondary currents, though weak, in transverse cross sections. These secondary currents cause additional flow resistance, resulting in pressure drop in the direction of the primary flow. A number of experimental studies have been reported on the turbulence structure and consequent geometrical structures of the flow. In particular, the two diagonals and the pair of bisectors of the side walls divide a cross section into eight cells, in each of which vortical patches of motion take place. In this paper, it is shown that the vortical motion in a cell is kinematically analogous to the torsion problem of a prismatic isotropic elastic beam. Based on experimental results, the patch vortex in a cell is modeled to have elliptic shape with the major axis thrust toward a corner of the duct, giving a mathematical model of the flow field. Using the expressions for the transverse velocity components in the total momentum equation, with 1/pth power law where p ≈ 7 for the streamwise velocity, an equation is obtained between the side-wall resistance due to the secondary flow and the vorticity in each cell of division of the duct. Two particular cases are considered in numerical detail when the duct is square and when the height of the duct is one-half of the base length. For experimental validation of the side-wall resiatance formulae, additional experimental research is needed.

Comparison of Five Two-Equation Turbulence Models for Calculation of Flow in 90° Curved Rectangular Ducts

This paper presents a comparative study of five most widely used two-equation turbulence models in predicting the developing flows in two 90° curved rectangular ducts. These include the standard k-ε model, the shear stress transport k-ω model, and three low-Reynolds number k-ε models by Jones and Launder, Launder and Sharma, and Nagano and Hishida, respectively. The computational time for convergent solutions, streamwise and secondary velocities, pressure distributions as well as the Reynolds-averaged turbulence quantities resolved by these models are compared and validated against available experimental data. The purpose of this paper are to provide a detailed comparative verification for applying the five most widely used two-equation turbulence models to predicting curved rectangular duct flows, which are a kind of proto type flows in fluids engineering, and to provide a reference for the selection of turbulence models in predicting such flows in industrial applications.

Heat transfer and pressure drop characteristics of gas–liquid Taylor flow in mini ducts of square and rectangular cross-sections

The thermal and flow characteristics of gas–liquid Taylor flow in vertical mini square and rectangular ducts were studied numerically for water and ethylene glycol as the liquid phase and nitrogen as the gas phase. The effects of fluid properties, flow parameters, and aspect ratio on the bubble shape, recirculation time, friction factor, and Nusselt number are discussed. The results indicate that the gas phase is confined by the tube wall in square and rectangular tubes leading to an asymmetrical Taylor bubble at low Capillary numbers, while an axisymmetric bubble is formed at high Capillary numbers. The liquid film thicknesses in the square and rectangular ducts are not uniform with a thicker liquid film formed at the tube corner. The recirculation region decreases and the dimensionless recirculation time increases with increasing Capillary number, which means that the intensity of recirculation decreases with increasing Capillary number. The friction factor decreases with increasing two-phase mixing velocity and aspect ratio and increases in gas void fraction, while the reverse is true for the two-phase Nusselt number. Compared with the ethylene glycol/nitrogen cases, the addition of Taylor bubble plays a more significant role on the pressure drop increase and heat transfer enhancement for the water/nitrogen cases because of the larger recirculation volume and smaller dimensionless recirculation time. Two empirical correlations are developed to predict the apparent slug Nusselt number and the film-to-slug Nusselt number for gas–liquid Taylor flow in square and rectangular ducts.

Numerical investigation of a space-fractional model of turbulent fluid flow in rectangular ducts

Models containing fractional derivatives are among the most promising new approaches for description of turbulent flows. In the present work, a steady-state flow in a duct is considered under the condition that the turbulent diffusion is governed by a fractional power of the Laplace operator. To study numerically flows in rectangular channels, finite-difference approximations are employed. The resulting discrete problem is solved by a preconditioned conjugate gradient method. At each iteration, the problem with a fractional power of the grid Laplace operator is solved. Predictions of turbulent flows in ducts at different Reynolds numbers are presented via mean velocity fields.

Ceramic Monolith Heat Exchanger - A Theoretical Study and Performance Analysis

A ceramic monolith heat exchanger has been learnt for finding out heat transfer performance and effectiveness on computing numerically and ξ-NTU method. In entire domain computation numerically has been performed along with fluid region in rectangular ducts of exhaust gas side, ceramic core and rectangular duct fluid region in air side with the air exhaust in direction of cross flow. Additionally, the heat exchanger has been examined for estimating the functionality via ξ-NTU technique that is conventional along numerous Nusselt number links for rectangular duct flow for the literature. Based on the research, it has been performed on the ceramic heat exchangers and on the ceramic materials and the demand in utilizing the ceramic materials in heat exchangers. Then the recuperator is modeled by using GAMBIT and it is analyzed using FLUENT. The effectiveness and the heat transfer rate are also calculated. Then those outcomes have been assessed along the experimental data. By comparison of both functionality by computing numerically and the ξ-NTU technique, the efficiency by ξ-TU technique has been identified to be nearest to product by the numerical computation among the associative of 2.15% when Stephan's Nusselt number association has been adapted to the ξ-NTU technique within numerous connections. The total heat transfer and effectiveness by ξ-NTU method relative errors utilizing five Nusselt number correlations from literature have been lesser than 14.5% comparative to numerical computation. Associated to Nusselt number correlations, the entire heat transfer utilizing ξ-NTU technique with Stephan's correlation is highly nearest to numerical computation. For that reason, the exit temperature by ξ-NTU method with Stephan's correlation simulates within 1.2% of the relative error for exhaust exist temperature and 0.45% for the air exit temperature assessed against the numerical computation. Overall heat transfer coefficient's relative errors by ξ-NTU technique utilizing five Nusselt number correlations for the literature have been more than 17.5% to that on computing numerically.

Theoretical Study and Analysis on Performance Enhancement of a Ceramic Monolith Heat Exchanger

Background/Objectives: Ceramic heat exchangers are preferred in most high temperature applications due to its high temperature stability and corrosion resistance. Evaluation of performance of the heat exchanger under different circumstances helps us to select suitable design for certain application. Methods/Statistical Analysis: This work investigated the functioning capability of a ceramic heat exchanger, determining pressure drop and the heat transfer theoretically by Ɛ-NTU method by using silicon carbide and aluminium nitride as heat exchanger material. The performance of both the ceramic material under the desired condition was compared. A heat exchanger possess ducts that is rectangular to exhaust gas, ducts which are rectangular for air and exhaust gases, a core made of ceramic along with air in the cross-flow direction. Findings: Heat exchanger has been investigated involving conventional Ɛ-NTU technique with numerous Nusselt number correlations from the literature for characterizing the rectangular duct flow. Theoretical analyses reveal that, while using aluminium nitride as the heat exchanger material the performance parameters such as overall heat transfer got increased by 4.5-5%, effectiveness by 3% and heat transfer rate by same 3% relative to silicon carbide as the heat exchanger material. Applications/Improvements: Analysis on performance enhancement of all other heat exchanger.

矩形ダクト流における局在乱流構造の成長過程

矩形ダクト流における局在乱流構造の成長過程

矩形管内流における熱泳動によるナノ粒子付着現象に関する数値的研究

In high thermal gradient environment, nano particles often adhere on wall surfaces of fluid machinery due to thermophoresis effects, which results in energy loss. Its deposition mechanism has not been clarified yet. In this study, we perform numerical simulations of a rectangular duct flow with a flat plate to investigate nano-particle motion and its deposition phenomenon. The Euler-Lagrange coupling method is employed to reproduce interaction between particles and the flow field. The results show that the thermophoresis dominates nano-particle motion and the deposition layer forms around the flat plate on the low temperature wall of the duct. Due to the adiabatic deposition layer, however, the thermophoresis effect decreases.

Numerical and experimental investigations of shape and location of vortex generators on fluid flow and heat transfer in a constant heat-fluxed rectangular duct

A numerical and experimental study was conducted for heat transfer enhancement and fluid flow in a constant heat-fluxed rectangular wooden duct fitted with two shapes of vortex generators (circular and square). These vortex generators are of the same area and placed at two different locations ([Formula: see text] and [Formula: see text]) ahead of the heater set and for Reynolds number from 32,000 to 83,000. The numerical and experimental results show an enhancement of heat transfer with the presence of vortex generators. This enhancement depends on the shape and location. Also, the numerical results show saving of 27% of the heater power with the presence of vortex generator. The experimental results of temperature distribution, Nusselt number distribution, effectiveness distribution, and pressure drop values of flow over heaters with vortex generators were reported and compared with the flow over heaters without vortex generators. The results show that heat transfer was enhanced by 2.186%−3.75% using circular type, and it enhanced by 1.3%−1.94% using square type. Also, pressure drop at the outlet of the duct increases by 166.7%−400% when using circular vortex generators and increases by 133.3%−300% when using square vortex generators. These values were obtained for the velocity ranging between 4 and 10 m/s and when vortex generators were placed at location [Formula: see text]. Finally, correlation equations for Nusselt number were obtained at location [Formula: see text] ahead of the heater set.

Numerical Simulation of Flow in Rectangular Duct with Different Obstruction Heights

Numerical Simulation of Flow in Rectangular Duct with Different Obstruction Heights

A hybrid finite difference–boundary element procedure for the simulation of turbulent MHD duct flow at finite magnetic Reynolds number

A conservative coupled finite difference–boundary element computational procedure for the simulation of turbulent magnetohydrodynamic flow in a straight rectangular duct at finite magnetic Reynolds number is presented. The flow is assumed to be periodic in the streamwise direction and is driven by a mean pressure gradient. The duct walls are considered to be electrically insulated. The co-evolution of the velocity and magnetic fields as described respectively by the Navier–Stokes and the magnetic induction equations, together with the coupling of the magnetic field between the conducting domain and the non-conducting exterior, is solved using the magnetic field formulation. The aim is to simulate localized magnetic fields interacting with turbulent duct flow. Detailed verification of the implementation of the numerical scheme is conducted in the limiting case of low magnetic Reynolds number by comparing with the results obtained using a quasistatic approach that has no coupling with the exterior. The rigorous procedure with non-local magnetic boundary conditions is compared with simplified pseudo-vacuum boundary conditions and the differences are quantified. Our first direct numerical simulations of turbulent Hartmann duct flow at moderate magnetic Reynolds numbers and a low flow Reynolds number show significant differences in the duct flow turbulence, even at low interaction level between the flow and magnetic field.

Localized turbulence structures in transitional rectangular-duct flow

Direct numerical simulations of transitional flow in a rectangular duct of cross-sectional aspect ratio $A\equiv s/h=1$–9 ($s$ and $h$ being the duct half-span and half-height, respectively) have been performed in the Reynolds number range $\mathit{Re}\equiv u_{b}h/{\it\nu}=650$–1500 ($u_{b}$ and ${\it\nu}$ being the bulk velocity and the kinematic viscosity, respectively) in order to investigate the dependence on the aspect ratio of spatially localized turbulence structures. It was observed that the lowest Reynolds number $\mathit{Re}_{T}$, estimated in a specific way, for localized (transiently sustaining) turbulence decreases monotonically from $\mathit{Re}_{T}=730$ for $A=1$ (square duct) with increasing aspect ratio, and for $A=5$ it nearly attains a minimal value $\mathit{Re}_{T}\approx 670$ that is consistent with the onset Reynolds number of turbulent spots in a plane channel ($A=\infty$). Turbulent states consist of localized structures that undergo a fundamental change around $A=4$. At $\mathit{Re}=\mathit{Re}_{T}$ turbulence for $A=1$–$3$ is streamwise-localized similar to turbulent puffs in pipe flow, while for $A=5$–9 turbulence at $\mathit{Re}=\mathit{Re}_{T}$ is also localized in the spanwise direction, similar to turbulent spots in plane channel flow. This structural change in turbulent states at $\mathit{Re}=\mathit{Re}_{T}$ is attributed to the exclusion of turbulence from the vicinity of the duct sidewalls in the case of a wide duct with $A\gtrsim 4$: here the friction length on the sidewalls is so long that the size (around 100 times the friction length) of a self-sustaining minimal flow unit of streamwise vortices and streaks is larger than the duct height and, therefore, it cannot be accommodated.

Influence of temperature dependent conductivity of a nanofluid in a vertical rectangular duct

Natural convective heat transfer and fluid flow in a vertical rectangular duct filled with a nanofluid is studied numerically assuming the thermal conductivity to be dependent on the fluid temperature. The transport equations for mass, momentum and energy formulated in dimensionless form are solved numerically using finite difference method. Particular efforts have been focused on the effects of the thermal conductivity variation parameter, Grashof number, Brinkman number, nanoparticles volume fraction, aspect ratio and type of nanoparticles on the fluid flow and heat transfer inside the cavity. It is found that the flow was enhanced for the increase in Grashof number, Brinkman number and aspect ratio for any values of conductivity variation parameter and for regular fluid and nanofluid. The heat transfer rate for regular fluid is less than that for the nanofluid for all governing parameters.

Entropy Generation and Optimization Analysis for Gas Flow in Rectangular Ducts with Volumetric Radiation

Entropy generation of a radiative participating gas flow in rectangular ducts is studied. The thermodynamic efficiency for high-temperature flow is also defined. The critical thermodynamic regions for absorption, emission, and scattering processes in the rectangular ducts are identified, and the aspect ratio for minimum entropy generation is determined. The study is extended by considering the thermodynamic effects of Reynolds number, Boltzmann number, and average transverse Nusselt number. It is shown that the total entropy generation rate and the transport efficiency of duct flows can be controlled through Reynolds number, Boltzmann number, and Nusselt number.

Free convective flow in a vertical rectangular duct filled with porous matrix for viscosity and conductivity variable properties

Abstract Free convection over a vertical rectangular duct filled with porous matrix with variable viscosity and variable thermal conductivity is studied in this paper. We consider the two-dimensional steady laminar flow and Brinkman–Forchheimer extended Darcy model to define the porous medium. Using the appropriate variables the basic governing equations are transformed to non-dimensional governing equations. The fluid viscosity is assumed to vary exponentially with temperature whereas the thermal conductivity is assumed to vary linearly with temperature. One of the vertical walls of the duct is cooled with constant temperature while the other wall is heated to constant but different temperature. The governing coupled nonlinear momentum and energy equations are solved numerically using finite difference method. The effect of pertinent parameters such as variable viscosity, variable thermal conductivity, Darcy number, inertial parameter, Grashof number, Brinkman number and aspect ratio on the velocity, temperature, volumetric flow rate, shear stress and heat transfer are discussed.

Numerical Study of Turbulent Flow and Convective Heat Transfer Characteristics in Helical Rectangular Ducts

Three-dimensional turbulent forced convective heat transfer and its flow characteristics in helical rectangular ducts are simulated using SST k–ω turbulence model. The velocity field and temperature field at different axial locations along the axial direction are analyzed for different inlet Reynolds numbers, different curvatures, and torsions. The causes of heat transfer differences between the inner and outer wall of the helical rectangular ducts are discussed as well as the differences between helical and straight duct. A secondary flow is generated due to the centrifugal effect between the inner and outer walls. For the present study, the flow and thermal field become periodic after the first turn. It is found that Reynolds number can enhance the overall heat transfer. Instead, torsion and curvature change the overall heat transfer slightly. But the aspect ratio of the rectangular cross section can significantly affect heat transfer coefficient.

NASA Trapezoidal-Wing Simulation Using Stress-, and One- and Two-Equation Turbulence Models

The Wilcox 2006 stress- model (also referred to as WilcoxRSM-w2006) has been implemented in the NASA Langley Research Center code CFL3D, and used to study a variety of two-dimensional and three-dimensional configurations. It predicted a variety of basic cases reasonably well, including secondary flow in a supersonic rectangular duct. One- and two-equation turbulence models that employ the Boussinesq constitutive relation were unable to predict this secondary flow accurately because it is driven by normal turbulent-stress differences. For the NASA trapezoidal wing at high angles of attack, the WilcoxRSM-w2006 model predicted lower maximum lift than the experiment, similar to the results of a two-equation model.

Effects of temperature-dependent viscosity on fluid flow and heat transfer in a helical rectangular duct with a finite pitch

An incompressible fully developed laminar flow in a helical rectangular duct having finite pitch and curvature with temperature-dependent viscosity under heating condition is studied in this work. Both the cases of one wall heated and four walls heated are studied. The cross-sectional dimensions of the rectangular duct are 2a and 2b. The aspect ratio n=2b/2a is 0.5. Water is used as the fluid and Reynolds number (Re) is varied in the range of 100 to 400. The secondary flow with temperature-dependent viscosity is enhanced markedly as compared to constant viscosity. An additional pair of vortices is obtained near the center of the outer wall at Re=400 for the model of four walls heated with temperature-dependent viscosity, y, while for constant viscosity, the appearance of two additional vortices near the outer wall cannot be found. Besides, the axial velocity decreases and the temperature increases at the central region of the rectangular duct when the temperature-dependent viscosity is considered. Due to the decrease of the viscosity near the walls, the friction factor obtained with temperature-dependent viscosity is lower than that of constant viscosity, while the convective heat transfer for temperature-dependent viscosity is significantly enhanced owing to the strengthened secondary flow. Especially for four heated walls, the effects of viscosity variation on the flow resistance and heat transfer are more significant.

Research on frictional resistance of bubbly flow in rolling rectangular ducts

For a flow system in a marine vehicle, rolling motion induced by ocean environment usually imposes a periodical force on the system. Experimental investigation was conducted on frictional resistance of bubbly flow in three rectangular ducts in rolling motion. The cross-sections of the three ducts have the same width of 43mm but different heights of 1.41mm, 3.25mm and 9.96mm. Rolling motion can easily cause the fluctuation of frictional pressure in the rectangular duct with larger height, therefore, a narrow duct is beneficial to restrain the effect of rolling motion on frictional resistance of bubbly flow. The additional pressure drop in ducts with heights of 1.41mm and 3.25mm can be neglected. Increasing the gas flow rate and the rolling amplitude or decreasing the rolling period would result in the increase of the fluctuation amplitude of the frictional pressure. A new correlation by modifying the parameter C in the Chisholm correlation was acquired to describe the hydrodynamic performance of bubbly flow for rectangular ducts in rolling motion, showing a good agreement with the experimental data.