Duct Of Square Cross-section Research Articles

A computational study of a new design configuration for a turbulence tunnel

A new kind of turbulence tunnel, the pure coherent shear source turbulence tunnel, proposed to produce high Reynolds number, approximately homogeneous isotropic turbulence is studied computationally. The Reynolds-averaged Navier–Stokes equations, along with the standard k − ϵ model for closure, are solved in the computations. The tunnel design studied here consists of a duct of square cross section with a plane at one end consisting of an array of round jets and suction vents. This plane, referred to as the momentum source plane (MSP), also a zero net-mass flux plane, forces the flow into the tunnel. The flow field inside consists of an advection-dominated region where the jets merge to form a combined flow, and an advection-free near-homogeneous turbulence region. Turbulence statistics in the advection-dominated and advection-free regions of the flow field, and the effect of parameters associated with the forcing that affects these statistics are studied. A plateau of turbulence statistics with rms of fluctuations as high as 0.8 times the mean advective velocity scale for the tunnel section, U T , is obtained in a region with negligible mean advection. The effect of geometrical configuration at the MSP on the turbulence quantities in the advection free region is studied. The Reynolds number based on Taylor length scale of the turbulence produced is estimated to be of the order of 350 in a tunnel of size 0.5 × 0.5 m2.

Computational Analyses of Flow and Heat Transfer at 60° Position of 180° Curved Duct of Square Cross-Section

3D computational analyses are achieved to predict seriously the influences of thermal buoyancy strength and Dean number on Dean vortices, flow behavior and the rate heat transfer through 180° curved channel of square cross-sectional form. The work shows many results, so this paper emphasizes only on the results of 60° cross-sectional position of the bend duct. The principal partial equations of continuity, momentum and energy are considering in three dimensions under the following assumptions: flow is incompressible and laminar, and it is solved in steady-state. The aforementioned equations are subjected to suitable boundary conditions under following range as: Dean number of De = 125 to 150, Richardson number of Ri = 0 to 2 at fixed value of Prandtl number Pr = 1. The principal results of this work are illustrated as streamline and isotherm contours to draw to flow patterns and temperature distributions respectively. The axial velocity profile is shown versus above conditions, the local Nusselt number is also presented along the wall of 60° cross-sectional position. The results show that the thermal buoyancy can balance the effect of centrifugal force of fluid particles at the angular position of 60°.

Experimental investigation of flame propagation in a meso-combustor

The present work aims to study the quenching of propagating flames in meso-combustors for which dimensions are of the order of quenching distances of hydrocarbon fuels. Combustion of gaseous fuels and subsequent flame propagation in a meso-scale combustor duct of square cross-section is studied experimentally. Premixed mixtures of methane, propane, and ethylene with air are considered. Two different variants of flame propagation states are found to occur in the meso-combustor, viz., one undergoing flame propagation till the combustor entry and quenching at the step and the other undergoing wall quenching. Regime transitions across these flame states are mapped comprehensively over a wide range of operating conditions. The radius of curvature of the flame and the dead space between the flame and the wall are determined for those conditions with the aid of curve fitting and image processing techniques using Matlab software. The spatial and temporal variation of both these parameters show a drastic increase during quenching in the wall-quenched case, while it remains nearly constant in the step quenched case. With increasing duct Reynolds number, the flame propagates slower, and the heat conduction to the wall leads to a decrease in the dead space and flattening of the flame, particularly at equivalence ratios corresponding to lower flame speeds. This flame-wall interaction is found to be low for methane, resulting in more heat loss and thereby wall-quenched flames compared to propane and ethylene. None of the ethylene flames were found to suffer wall quenching thereby making it a suitable fuel for meso-/micro-combustors among the three fuels used in the present work.

3D Simulation of Incompressible Poiseuille Flow through 180° Curved Duct of Square Cross-section under Effect of Thermal Buoyancy

In this paper, three-dimensional numerical simulations are carried out to investigate and analyze the gradual effects of thermal buoyancy strength on laminar flow of an incompressible viscous fluid and heat transfer rate inside a 180° curved channel of square cross-section. The governing equations of continuity, momentum and energy balance are obtained and solved numerically using finite volume method. The effect of Dean number, De, and Richardson number, Ri, on dimensionless velocity profiles and Nusselt number are examined for the conditions: De = 125 to 150, Ri = 0 to 2 at Pr = 1. The mean results are illustrated in terms of streamline and isotherm contours to interpret the flow behaviors and its effect on heat transfer rate. Dimensionless velocity profiles and the local Nusselt number at the angle 0° and 90° are presented and discussed. Also, the average Nusselt number on surfaces of curved duct is computed. The obtained results showed that by adding thermal buoyancy to computed domain, some early Dean vortices are observed at the angle 0° and new sort are observed at 90°. Furthermore, increase in Dean number increases the heat transfer rate. In other hand, increase in Richardson number decreases the average Nusselt number of 180° curved duct.

3D Simulation of Dean Vortices at 30° Position of 180° Curved Duct of Square Cross-Section under Opposing Buoyancy

3D numerical simulations are performed to analyze correctly the effect of opposing thermal buoyancy and Dean number on Dean vortices, fluid flow and heat transfer through 180° curved duct of square cross-section. Due to tremendous found results, this works emphasizes only at the position 30° of the bend portion. The governing equations involving momentum, continuity and energy are solved in three dimensions under these assumptions: the flow is laminar, steady-state and incompressible. The present study is investigated in the range of these conditions: Dean number of De = 125 to 150, Richardson number of Ri = 0 to 2 at Pr = 1. The principal obtained results are represented in forms of streamlines and isotherms to analyze and to discuss the found physical phenomena. The local Nusselt number along the wall of square cross-section is also computed and presented. The main found point is that the opposing thermal buoyancy has a tendency to eliminate the effect of centrifugal force at the position 30° of bend portion of 180° curved duct.

Numerical Analysis of Spatial Hydrodynamic Stability of Shear Flows in Ducts of Constant Cross Section

A technique for analyzing the spatial stability of viscous incompressible shear flows in ducts of constant cross section, i.e., a technique for the numerical analysis of the stability of such flows with respect to small time-harmonic disturbances propagating downstream is described and justified. According to this technique, the linearized equations for the disturbance amplitudes are approximated in space in the plane of the duct cross section and are reduced to a system of first-order ordinary differential equations in the streamwise variable in a way independent of the approximation method. This system is further reduced to a lower dimension one satisfied only by physically significant solutions of the original system. Most of the computations are based on standard matrix algorithms. This technique makes it possible to efficiently compute various characteristics of spatial stability, including finding optimal disturbances that play a crucial role in the subcritical laminar–turbulent transition scenario. The performance of the technique is illustrated as applied to the Poiseuille flow in a duct of square cross section.

Numerical Analysis of 2-D and 3-D MHD Flows Relevant to Fusion Applications

The analysis of many fusion applications such as liquid-metal blankets requires application of computational fluid dynamics (CFD) methods for electrically conductive liquids in geometrically complex regions and in the presence of a strong magnetic field. A current state of the art general purpose CFD code allows modeling of the flow in complex geometric regions, with simultaneous conjugated heat transfer analysis in liquid and surrounding solid parts. Together with a magnetohydrodynamics (MHD) capability, the general purpose CFD code will be a valuable tool for the design and optimization of fusion devices. This paper describes an introduction of MHD capability into the general purpose CFD code CFX, part of the ANSYS Workbench. The code was adapted for MHD problems using a magnetic induction approach. CFX allows introduction of user-defined variables using transport or Poisson equations. For MHD adaptation of the code three additional transport equations were introduced for the components of the magnetic field, in addition to the Poisson equation for electric potential. The Lorentz force is included in the momentum transport equation as a source term. Fusion applications usually involve very strong magnetic fields, with values of the Hartmann number of up to tens of thousands. In this situation a system of MHD equations become very rigid with very large source terms and very strong variable gradients. To increase system robustness, special measures were introduced during the iterative convergence process, such as linearization using source coefficient for momentum equations. The MHD implementation in general purpose CFD code was tested against benchmarks, specifically selected for liquid-metal blanket applications. Results of numerical simulations using present implementation closely match analytical solutions for a Hartmann number of up to 1500 for a 2-D laminar flow in the duct of square cross section, with conducting and nonconducting walls. Results for a 3-D test case are also included.

CFD study of forced convective heat transfer enhancement in a 90° bend duct of square cross section using nanofluid

In this paper, the forced convective heat transfer enhancement with nanofluids in a 90° pipe bend has been presented. Numerical investigation is carried out for the turbulent flow through the pipe employing finite volume method. The governing differential equations are discretized using hexahedral cells, and the resulting algebraic equations are solved using Commercial solver Fluent 6.3. In order to close the time averaged Navier–Stokes equations, the two-equation k–ɛ turbulence model with a standard wall function have been used. The duct Reynolds number is varied in the range of 2,500–6,000. It is observed that the heat transfer is enhanced significantly by varying the volume fraction of the nanofluid. It is also found that the heat transfer is increased with Reynolds number. A strong secondary flow is observed due to the presence of the wall. Turbulent kinetic energy near outer wall is found to be higher than the inner wall of the bend. A comparative assessment for the heat transfer enhancement with different types of nanofluids is also presented. The computed results of area weighted average Nusselt numbers are validated with some of the existing literature.

Laminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition

The problem of fluid flow and heat transfer was studied for flow inside twisted duct of square cross-section. Three-dimensional numerical solutions were obtained for steady fully developed laminar flow and for uniform wall heat flux boundary conditions using commercially available software. Reynolds number range considered was 100–3000. Twist ratio used are 2.5, 5, 10 and 20. Fluids considered are in Prandtl number range of 0.7–20. Product of friction factor and Reynolds number is found to be a function of Reynolds number and maximum values are observed for a twist ratio of 2.5 and Reynolds number of 3000. Maximum Nusselt number is observed for the same values along with Prandtl number of 20. Correlations for friction factor and Nusselt number are developed involving swirl parameter. Local distribution of friction factor ratio and Nusselt number across a cross-section is presented. Based on constant pumping power criteria, enhancement factor is defined to compare twisted ducts with straight ducts. Selection of twisted square duct is presented in terms of enhancement factor. It is found that twisted duct performs well in the laminar region for range of parameters studied. Heat transfer enhancement for Reynolds number of 3000 and Prandtl number of 0.7 for twist ratio of 2.5, 5, 10, and 20 is 20%, 17.8%, 16.1% and 13.7%, respectively. The results are significant because it will contribute to development of energy efficient compact size heat exchangers.

Development of secondary flows in viscoelastic curved ducts and the influence of outlet region

This paper presents numerical simulations of Newtonian and viscoelastic flows through a 180° curved duct of square cross section with a long straight outlet region. A particular attention is paid to the development of the flow in the output rectangular region after the curved part. The viscoelastic fluid is modeled using the constitutive equation proposed by Phan–Thien–Tanner (PTT). The numerical results, obtained with a finite-volume method, are shown for three different Dean numbers (125,137,150) and for three Deborah numbers (0.1,0.2,0.3). The necessary outlet length to impose boundary conditions is presented and discussed for these cases. Streamlines and vortex formation are shown to illustrate and analyze the evolution of the secondary flow in this region.

Heat Transfer in Coiled Square Tubes for Laminar Flow of Slurry of Microencapsulated Phase Change Material

Passive heat transfer enhancement using a slurry of microencapsulated phase-change material (MEPCM) flowing in a laminar regime through a coiled duct of square cross section was evaluated. The phase-change material is n-octadecane. The flow behavior and heat transfer performance of water and MEPCM suspensions in various configurations (conical spiral, in-plane spiral, and helical spiral) of coiled tubes of square cross section was investigated. The results are compared with those for water as the base fluid flowing through a straight tube. A computational fluid dynamics (CFD) approach is used to simulate the laminar flow of water with MEPCM suspension in these geometries. The liquid suspension properties are expressed as functions of the volumetric concentration of MEPCM particles and the temperature. Improved heat transfer performance was obtained as the concentration of MEPCM suspension increased from 1 to 10%. However, the overall performance in terms of the pumping power consumed for unit heat transferred worsened.

Numerical Analysis of the Flow in a Curved Duct

The Secondary flow in a curved duct of square cross-section, is investigated numerically using the spectral method. The walls of the duct except the outer wall rotate around the centre of curvature and an azimuthal pressure gradient is imposed. Multiple solutions are obtained at the same flow condition. It is also found that the secondary flow in a cross-section consists of two-vortex, four-vortex, eight-vortex or even non-symmetric vortex with respect to the centre line of the cross-section. The linear stability analysis for the multiple solution is also carried out to investigate the actual flow patterns.

A self-adjusting flow dependent formulation for the classical Smagorinsky model coefficient

In this paper, we propose an efficient formula for estimating the model coefficient of a Smagorinsky model based subgrid scale eddy viscosity. The method allows vanishing eddy viscosity through a vanishing model coefficient in regions where the eddy viscosity should be zero. The advantage of this method is that the coefficient of the subgrid scale model is a function of the flow solution, including the translational and the rotational velocity field contributions. Furthermore, the value of model coefficient is optimized without using the dynamic procedure thereby saving significantly on computational cost. In addition, the method guarantees the model coefficient to be always positive with low fluctuation in space and time. For validation purposes, three test cases are chosen: (i) a fully developed channel flow at ${\mathop{\rm Re}\nolimits} _\tau = 180,\,395$ Re τ=180,395, (ii) a fully developed flow through a rectangular duct of square cross section at ${\mathop{\rm Re}\nolimits} _\tau = 300$ Re τ=300, and (iii) a smooth subcritical flow past a stationary circular cylinder, at a Reynolds number of ${\mathop{\rm Re}\nolimits} = 3900$ Re =3900, where the wake is fully turbulent but the cylinder boundary layers remain laminar. A main outcome is the good behavior of the proposed model as compared to reference data. We have also applied the proposed method to a CT-based simplified human upper airway model, where the flow is transient.

Parametric study on the three-dimensional distribution of velocity of a FENE-CR fluid flow through a curved channel

In order to better understand the three-dimensional non-Newtonian flow in an 180° curved duct of square cross-section, simulations were carried out considering an incompressible viscoelastic fluid, which follows the non-linear FENE-CR model, having constant shear viscosity. A fully implicit finite-volume method was used for the solution of the governing equations. Numerical simulations were performed for different Reynolds and Weissenberg numbers, and by varying the model parameters, namely the retardation ratio (β) and the extensibility (L2). The aim was to analyse the development and distribution of velocity field in the cross-sections along the curved channel and as a consequence to understand the variation of maximum velocity with these parameters. The results reveal complex changes with increasing extensibility and decreasing retardation parameter, which are associated to transition from one to two pairs of vortices in the secondary flow. Comparison with the literature confirms and reveals that the absence of shear-thinning delays this transition.

Bifurcation Phenomena of Secondary Flows in Curved Duct of Square Cross-Section

Based on the flow model and its mathematical description in curvilinear coordinates, the steady and fully developed laminar flow in the curved pipe of square cross-section was simulated by the Galerkin method. The results show that the eye points of the secondary flow vortex at low Reynolds numbers almost locate at the position of 0.457 on the vertical axis, the axial velocity maximum shifts inward or outward when the pipe curvature parameter and flow conditions change. Furthermore the bifurcation flow is studied to draw the bifurcation state diagram, and the Reynolds number corresponding to the bifurcation point of the four-vortex solution is accurately equal to 300.1.

Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers

AbstractHigh-resolution direct numerical simulations are conducted to analyse turbulent states of the flow of an electrically conducting fluid in a duct of square cross-section with electrically insulating walls and imposed transverse magnetic field. The Reynolds number of the flow is $1{0}^{5} $ and the Hartmann number varies from $0$ to $400$. It is found that there is a broad range of Hartmann numbers in which the flow is neither laminar nor fully turbulent, but has laminar core, Hartmann boundary layers and turbulent zones near the walls parallel to the magnetic field. Analysis of turbulent fluctuations shows that each zone consists of two layers: the boundary layer near the wall characterized by small-scale turbulence and the outer layer dominated by large-scale vortical structures strongly elongated in the direction of the magnetic field. We also find a peculiar scaling of the mean velocity, according to which the reciprocal von Kármán coefficient grows nearly linearly with the distance to the wall.

Instabilities and turbulence in magnetohydrodynamic flow in a toroidal duct prior to transition in Hartmann layers

AbstractFlow of an electrically conducting fluid in a toroidal duct of square cross-section is analysed. The flow is driven by the azimuthal Lorentz force resulting from the interaction between the radial electric currents created by the difference of electric potential maintained between the cylinder walls and the strong magnetic field imposed in the axial direction. The flow geometry and the value of the Hartmann number correspond to the experiment of Moresco & Alboussière (J. Fluid Mech., vol. 504, 2004, pp. 167–181). The purpose of the analysis is to reveal the flow features at Reynolds numbers below the threshold of transition to turbulence in Hartmann layers. We find that the flow experiences a complex evolution. The laminar base flow experiences the first instability at the Reynolds number significantly smaller than that of the threshold. The instability is axisymmetric and oscillatory. Turbulence appears at a slightly higher Reynolds number. Right up to the Hartmann layer instability, the turbulence remains localized in a layer near the outer cylinder wall. It is demonstrated that the turbulence may affect the transition in the Hartmann layers via unsteady forcing of the outer flow.

Numerical simulation of magnetohydrodynamic flow in a toroidal duct of square cross-section

We present numerical simulation results of the quasi-static magnetohydrodynamic (MHD) flow in a toroidal duct of square cross-section with insulating Hartmann walls and conducting side walls. Both laminar and turbulent flows are considered. In the case of steady flows, we present a comprehensive analysis of the secondary flow. It consists of two counter-rotating vortex cells, with additional side wall vortices emerging at sufficiently high Hartmann number. Our results agree well with existing asymptotic analysis. In the turbulent regime, we make a comparison between hydrodynamic and MHD flows. We find that the curvature induces an asymmetry between the inner and outer side of the duct, with higher turbulence intensities occurring at the outer side wall. The magnetic field is seen to stabilize the flow so that only the outer side layer remains unstable. These features are illustrated both by a study of statistically averaged quantities and by a visualization of (instantaneous) coherent vortices.

Vortex Patterns of the Flow in a Curved Duct

The vortex patterns of the secondary flow in a curved duct of square cross-section are numerically investigated. The flow is driven by the axial pressure gradient as well as the walls rotation of the duct except the outer wall around the center of curvature. When the rotation is in the same direction as the negative pressure gradient, the secondary flow shows complicated multiple patterns, which consists of two-vortex, four-vortex, eight-vortex or even non-symmetric secondary flow pattern. An analysis of linear stability on the flow is also carried out to distinguish possible flow patterns among multiple steady solutions.

Fast computation of optimal disturbances for duct flows with a given accuracy

This work is devoted to the numerical analysis of small flow disturbances, i.e. velocity and pressure deviations from the steady state, in ducts of constant cross sections. The main emphasis is put on the disturbances causing the most kinetic energy density growth, the so-called optimal disturbances, whose knowledge is important in laminar-turbulent transition and robust flow control investigations. Numerically, this amounts to computing the maximum amplification of the 2-norm of a matrix exponential exp{tS} for a square matrix S at t ≥ 0. To speed up the computations, we propose a new algorithm based on low-rank approximations of the matrix exponential and prove that it computes the desired amplification with a given accuracy. We discuss its implementation and demonstrate its efficiency by means of numerical experiments with a duct of square cross section.