Laminar Duct Flow Research Articles

Unsteady Laminar Duct Flow With a Given Volume Flow Rate Variation

In this paper we give a procedure to obtain analytical solutions for unsteady laminar flow in an infinitely long pipe with circular cross section, and in an infinitely long two-dimensional channel, created by an arbitrary but given volume flow rate with time. In the literature, solutions have been reported when the pressure gradient variation with time is prescribed but not when the volume flow rate variation is. We present some examples: (a) the flow rate has a trapezoidal variation with time, (b) impulsively started flow, (c) fully developed flow in a pipe is impulsively blocked, and (d) starting from rest the volume flow rate oscillates sinusoidally. [S0021-8936(00)01702-5]

Laminar flow in certain ducts of symmetric cross section

AbstractViscous flow in certain symmetrical ducts can be solved by a modified Levy's method with internal matching. The method is simple, efficient and accurate. Approximate analytic formulas are also derived for the extreme cases. It is found that cutting convex corners has little effect on the flow rate, but a centered core, however slender, decreases flow dramatically. The graphs for flow rates are useful for the design of ell, cross and nested square ducts and also for the prediction of the permeability of parallel‐structured porous media.

Richardson’s Annular Effect in Oscillating Laminar Duct Flows

Technical Briefs Richardson’s Annular Effect in Oscillating Laminar Duct Flows A. Yakhot, A. Yakhot Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva 84105, Israel Search for other works by this author on: This Site PubMed Google Scholar M. Arad, M. Arad Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva 84105, Israel Search for other works by this author on: This Site PubMed Google Scholar G. Ben-Dor G. Ben-Dor Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva 84105, Israel Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information A. Yakhot Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva 84105, Israel M. Arad Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva 84105, Israel G. Ben-Dor Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva 84105, Israel J. Fluids Eng. Mar 1998, 120(1): 209-211 (3 pages) https://doi.org/10.1115/1.2819652 Published Online: March 1, 1998 Article history Received: February 7, 1997 Revised: July 21, 1997 Online: December 4, 2007

Laminar flow in annuli ducts with constant wall temperature

The Galerkin integral method is applied to calculate the Nusselt number for laminar flow in annuli ducts imposed by constant wall temperature at the boundaries. The flow is assumed to be hydrodynamically fully developed, laminar, and Newtonian. The thermally fully developed temperature can be obtained when the local Nusselt number approaches asymptotically to constant value. A three-term solution or even two-term solution provides accurate predictions for annuli duct having a larger aspect ratio b/a. However, for duct with a smaller aspect ratio, a larger number of basis functions must be used.

Particle Deposition with Thermophoresis in Laminar and Turbulent Duct Flows

ABSTRACT A numerical simulation procedure for studying deposition of aerosol particles in duct flows including the effect of thermal force under laminar and turbulent flow conditions is developed. An improved model for thermophoretic force acting on small particles is presented. Perturbation based analytical expressions for velocity and temperature profiles are used in the analysis for the laminar duct flow. The Reynolds stress transport model (RSM) of the FLUENT code is used to evaluate the mean flow and temperature fields for the turbulent duct flow case. The instantaneous fluctuation velocity field is generated by the continuous filtered white noise model. Effects of Brownian diffusion, thermophoresis, lift force, and gravity are included in the computation. Ensembles of particle trajectories are generated and statistically analyzed. Particle dispersion from a point source in the presence of a temperature gradient field in laminar and turbulent duct flows is studied. For an initially uniform concentrat...

Laminar buoyant magnetohydrodynamic flow in vertical rectangular ducts

The buoyancy-driven laminar magnetohydrodynamic flow in long vertical channels is investigated. It is assumed that the channels have a rectangular cross section with one pair of walls aligned with the strong uniform magnetic field. The walls may have arbitrary electrical conductance. Using asymptotic methods, solutions are derived for general temperature distributions inside the ducts. Results are shown for different values of the control parameters. One finds the typical subregions for the flow inside the duct, namely the inviscid core, surrounded by viscous Hartmann layers and side layers. The character of the solution inside these regions may deviate from what is expected by a comparison with the classical solutions for pressure-driven duct flows. The main difference is that the flow in the core not necessarily exhibits a two-dimensional behavior. Most surprising, however, is the fact, that high-velocity jets are observed for the first time along perfectly conducting sidewalls. These jets are able to carry a major part of the flow rate.

Friction factors for fully developed laminar flow in ducts confined by corrugated parallel walls

Straight ducts of constant cross-section with sinusoidally curved walls may be found in plate heat exchangers as well as in packing structures used in mass transfer operations or in catalytic reactors. Frictional pressure drop, in the case of fully developed laminar flow, depends on the shape of the cross-section. It is characterized by a generalized form of Poiseuilles law: ( ξ · Re) = K. Two types of cross-section formed by two parallel sinusoidally corrugated walls, with the amplitude a ̂ , the wave length A and the distance 2 a ̂ are regarded. The two sine walls may be either phase shifted by Π, so that the walls touch each other and form an arbitrary number of equal tubelike ducts, or they may be in phase, so that the duct is similar to the one formed by two parallel planes. In both limits the values of K were numerically calculated for a number of aspect ratios 2 a ̂ / A . The whole range of aspect ratios has been covered by fitting polynomials in order to allow for interpolation of the calculated values.

Estimation of inlet temperature profile in laminar duct flow

The inverse analysis using conjugate-gradient method of minimization with an adjoint equation is presented for estimating the transversal variation of inlet temperature from temperature measurements taken at downstream location in a parallel-plate duct. The advantage of the method is that no prior information is needed for the functional form of spacewise variation of the unknown inlet temperature. The effects of the number of measurements N as well as the distribution of the measurements in the transversal direction, axial locations of the sensor, measurement errors, and functional form of the unknown inlet temperature on the accuracy of estimations are investigated. Inlet temperature distribution involving slope discontinuities was found difficult to estimate.

Simultaneous estimation of fluid thermal conductivity and heat capacity in laminar duct flow

An inverse analysis is applied to identify simultaneously the constant thermal conductivity k and heat capacity C of the fluid in liminar forced convection inside a circular duct from the knowledge of transient temperature measurements taken at a single location in the downstream region. Transient temperatures are generated by suddenly applying a constant wall heat flux over a finite length of the duct at the inlet region. The iterative algorithm of Levenberg-Marquardt method is used to solve the resulting system of algebraic equations in the minimization procedure. The effects of sensor location both in the axial and radial directions, heated length of the duct, magnitude of applied wall heat flux, the number of measurements, and errors involved in the measured data on the accuracy of estimations are studied.

First- and higher-order effects of curvature and torsion on the flow in a helical rectangular duct

A series expansion method is employed to determine the first-order terms in curvature ε and torsion η of fully developed laminar flow in helical square ducts and in helical rectangular ducts of aspect ratio two. The first-order solutions are compared to solutions of the full governing equations. For toroidal square ducts with zero pitch, the first-order solution is fairly accurate for Dean numbers,De=Reε1/2, up to about 20, and for straight twisted square ducts the first-order solution is accurate for Germano numbers,Gn= ηRe, up to at least 50 whereReis the Reynolds number. Important conclusions are that the flow in a helical duct with a finite pitch or torsion to the first order (i.e. with higher-order terms in ε and η neglected) is obtained as a superposition of the flow in a toroidal duct with zero pitch and a straight twisted duct; that the secondary flow in helical non-circular ducts for sufficiently smallReis dominated by torsion effects; and that for increasingRe, the secondary flow eventually is dominated by effects due to curvature. Torsion has a stronger impact on the flow for aspect ratios greater than one. A characteristic combined higher-order effect of curvature and torsion is an enlargement of the lower vortex of the secondary flow at the expense of the upper vortex, and also a shift of the maximum axial flow towards the upper wall. For higher Reynolds numbers, bifurcation phenomena appear. The extent of a few solution branches for helical ducts with finite pitch or torsion is determined. For ducts with small torsion it is found that the extent of the stable solution branches is affected little by torsion. Physical velocity components are employed to describe the flow. The contravariant components are found useful when describing the convective transport in the duct.

Laminar Fluid Transients in Conduits of Arbitrary Cross Section

Conduit cross sections of nonelementary shape are the rule in biological fluid systems. Because of mathematical and experimental difficulties, however, relatively little is known about the dynamics of flow in these vessels, particularly under time-varying conditions, although knowledge of the fluid motion therein in terms of properties such as driving head, velocity, and wall shear stress is clearly essential for proper diagnosis of a flow problem. This paper presents an analytical method for solving problems of unsteady laminar flow in long ducts of arbitrary cross section. The implied assumption of parallel flow renders the mathematical situation linear, but the proposed method is far from conventional because it allows consideration of almost any cross-sectional configuration conceivable. This novel approach is made possible by joining a steady-state superposition method for creating new conduits from known basic shapes with a regular perturbation scheme found suitable for dealing with fluid transients...

Twisted tape vortex generators in duct flow: Flow field and heat and mass transfer

The flow field in a rectangular duct behind a row of twisted tape vortex generators is investigated by means of laser-Doppler anemometry (LDA) and a mass transfer measuring method. The experimental apparatus consists of an open flow wind tunnel with a test section of three rectangular ducts. A row of twisted tape vortex generators is installed in each duct, which produces a regular field of longitudinal vortices. The flow velocity field behind the vortex generators is measured by LDA, and then the amplitude of the cross-flow velocity distribution Δu 2 of the main flow velocity in the center of the duct is determined. The amplitude of this velocity distribution describes the downstream damping of vortices. The local mass transfer is measured in the same duct with a photometric method, and the local mass transfer and the cross-flow amplitude of the mass transfer distribution corresponding to the amplitude of the velocity distribution is determined. The results show that the damping of the vortices can be investigated either by LDA measurements of the velocity field or by measuring the mass transfer distribution with the mass transfer measuring method. The analogy between the decay of the velocity and mass transfer amplitude with this vortex generator is evident but must still be proved for other types of vortex generators and duct geometries. The knowledge of the vortex damping is of particular importance for optimization of heat and mass transfer equipment. Then the distance to the next row of vortex generators can easily be optimized, leading to optimal improvement in heat and mass transfer along the whole surface of the duct. In laminar duct flow the existing range of the vortices downstream of the vortex generators gets smaller with the Reynolds number. The largest amplification of the vortices here takes place at Re /2~ 2500.

Study on friction factor of developing and developed laminar flow in annular-sector ducts

The pressure drops of laminar developing and developed flow in annular-sector ducts with small round corner have been investigated experimentally. Numerical simulation has been performed to study the effect of the small round corner on the friction factor in the developed region. It has been found that with the increase in corner radius, the value off Re decreases. In the range ofr c/rofrom 0.031 to 0.12, the decrease inf Re varies from 0.048% to 0.1% for the five apex angle computed.

An Equation for Laminar Flow Heat Transfer for Constant Heat Flux Boundary Condition in Ducts of Arbitrary Cross-Sectional Area

We can calculate the heat transfer in ducts of arbitrary cross section with the definition of the equivalent diameter only in turbulent flow. In laminar flow, it is not sufficient to define an equivalent diameter, because the boundary layer of each wall is influenced by another wall. Therefore, one needs additional quantities to describe the heat transfer and pressure drop. This is shown for pressure drop calculations by Yilmaz and heat transfer for constant wall temperature by Yilmaz and Cihan. In these works, by using other quantities, it was possible to obtain general equations for pressure drop and heat transfer for constant wall temperature. In the present work, an equation for heat transfer for the boundary condition of constant heat flux at the wall for laminar developed flow in ducts of arbitrary cross-sectional area is given. 14 refs., 1 fig., 4 tabs.

Integral transform solution of developing laminar duct flow in Navier‐Stokes formulation

AbstractThe generalized integral transform technique is employed in the hybrid numerical‐analytical solution of the Navier‐Stokes equations in streamfunction‐only formulation, which govern the incompressible laminar flow of a Newtonian fluid within a parallel plate channel. Owing to the analytic nature of this approach, the outflow boundary condition for an infinite duct is handled exactly, and the error involved in considering finite duct lengths is investigated. The present error‐controlled solutions are used to inspect the relative accuracy of previously reported purely numerical schemes and to compare Navier‐Stokes and boundary layer formulations for various combinations of inlet conditions and Reynolds number.

Maximum gas flow in circular ducts at various pressures: an approximate approach

An approximate solution is given for the prediction of the gas flow rate depending on the pressure drop for compressible laminar flow in circular ducts. The pressure and pressure drop range from high to low values, i.e. both Newtonian flow and Knudsen flow as well as the transition regime have to be modelled. The resulting equations are easy to handle and may be sufficient to serve engineering purposes. A numerical example displaying how fast a vessel can be evacuated is also included in the paper.

Solution of the laminar duct flow problem by a boundary integral equation method

A boundary integral equation method is proposed for approximate numerical and exact analytical solutions to fully developed incompressible laminar flow in straight ducts of multiply or simply connected cross-section. It is based on a direct reduction of the problem to the solution of a singular integral equation for the vorticity field in the cross section of the duct. For the numerical solution of the singular integral equation, a simple discretization of it along the cross-section boundary is used. It leads to satisfactory rapid convergency and to accurate results. The concept of hydrodynamic moment of inertia is introduced in order to easily calculate the flow rate, the main velocity, and the fRe-factor. As an example, the exact analytical and, comparatively, the approximate numerical solution of the problem of a circular pipe with two circular rods are presented. In the literature, this is the first non-trivial exact analytical solution of the problem for triply connected cross section domains. The solution to the Saint-Venant torsion problem, as a special case of the laminar duct-flow problem, is herein entirely incorporated.

Fully developed flow and heat transfer in semi-elliptical ducts

A control volume-based numerical solution is described for the fully developed laminar flow and heat transfer in ducts of semi-elliptical cross section. Both an isothermal and a uniform axial heat flux condition on the duct walls have been considered. Numerical results for velocity and temperature profiles, friction factor, pressure defect, and Nusselt number are presented for a wide range of duct aspect ratios from 0.1 to 0.999. Comparison with earlier numerical results for the limiting case of semicircular duct and with analytical solution for fully elliptical ducts is excellent. For ducts in which the baseplate is on the major axis, friction factor and Nusselt number for the uniform heat flux condition increase as the aspect ratio decreases, with values for the lowest aspect ratio of 0.1 being about 25 percent larger than those for a semicircular duct. For ducts with the baseplate on the minor axis, all characteristics exhibit a nonmonotonic behavior with respect to the aspect ratio. While the maximum velocity and pressure defect exhibit a mild maximum for aspect ratio of 0.6, the friction factor and Nusselt number exhibit a minimum at the same aspect ratio. The ratio of Nusselt number to friction factor is higher for semi-elliptical ducts in comparison to that for other ducts, such as sinusoidal, circular segmental, and isosceles triangular ducts.

Solution of the laminar duct flow problem by a boundary integral equation method

Solution of the laminar duct flow problem by a boundary integral equation method

On turbulent drag and heat transfer reduction phenomena and laminar heat transfer enhancement in non-circular duct flow of certain non-Newtonian fluids

The fascinating friction drag and heat transfer reduction phenomena associated with turbulent flows of so-called ‘drag-reducing fluids’ are not well understood. It is believed that elastic fluid properties are strongly related to these phenomena. However, not all drag-reducing fluids are viscoelastic, nor are all viscoelastic fluids drag-reducing, suggesting that drag reduction and viscoelasticity are probably incidentally accompanying phenomena. Furthermore, the limited research to date has revealed considerable heat transfer enhancement (virtually without friction drag increase) in laminar non-circular duct flows with certain polymer solutions, and has shown that all utilized fluids were indeed viscoelastic 1.It is argued here that turbulence suppression (i.e. flow laminarization), due to flow-induced anisotropic fluid structure and properties, is a determining factor for the reduction phenomena—not the fluid elasticity—while the latter may be a major cause for the laminar heat transfer augmentation. It is certain that many challenges in this interesting and useful area will keep researchers very busy well into the next century and beyond.