Solution Of Laminar Flow Research Articles

Laminar and turbulent natural convection in an enclosed cavity

The paper presents a computational method used to obtain solutions of the buoyancy-driven laminar and turbulent flow and heat transfer in a square cavity with differentially heated side walls. A series of Rayleigh numbers, rangingfrom 10 3 to 10 16 was studied. Donor-cell differencing is used, and mesh-refinement studies have been performed for all Rayleigh numbers considered. The turbulence model used for Rayleigh numbers greater than 10 6 is a ( k ~ ε) two-equation model of turbulence, that includes gravity ~ density gradient interactions. The results are presented in tabular and graphical form, and as correlations of the Nusselt and Rayleigh numbers. Furthermore, the results for Rayleigh numbers up to 10 6 are compared with the benchmark numerical solution of de Vahl Davis.

A "Similarity" Solution for Laminar Swirling Core Flows

Spurk, J. H. and Gerber, N., Dust Collection Efficiency for Power Law Bodies in Hypersonic Flight, AIAA Journal, Vol. 10, June 1972, pp. 755-761. Peddieson, J. and Lyu, C.-H., Supersonic Two-Phase Flow Past a Cone, Proceedings of the 10th Southeastern Seminar on Thermal Sciences, edited by Watts and Sogin, Tulane Univ., New Orleans, La., 1974, pp. 467-482. Barren, R. M. and Wiley, J. T., Remarks on Dusty Hypersonic Wedge Flow, AIAA Journal, Vol. 17, March 1979, pp. 317-318. Barren, R. M. and Wiley, J. T., Newtonian Flow Theory for Slender Bodies in a Dusty Gas, Journal of Fluid Mechanics, Vol. 108, July 1981, pp. 147-157.

Finite element solutions for laminar and turbulent compressible flow

AbstractThe time‐split finite element method is extended to compute laminar and turbulent flows with and without separation. The examples considered are the flows past trailing edges of a flat plate and a backward‐facing step. Eddy viscosity models are used to represent effects of turbulence. It is found that the time‐split method produces results in agreement with previous experimental and computational results. The eddy viscosity models employed are found to give accurate predictions in all regions of flow except downstream of reattachment.

An analytic benchmark solution to the linear, time-dependent isothermal laminar flow fission-product plateout problem

The time-dependent convective-diffusion equation with radioactive decay is solved analytically in axisymmetric cylindrical geometry for laminar and slug velocity profiles under isothermal conditions. Concentration-dependent diffusion is neglected. The laminar flow solution is derived using the method of separation of variables and Frobenius' technique for constructing a series expansion about a regular singular point. These solutions, which describe the transport of fission products in a flowing stream, are then used to determine the pointwise and integrated concentrations of radioactive material deposited on a conduit wall using a standard mass-transfer model. Extensive parametric investigations have been conducted by varying the wall mass-transfer coefficient, diffusion coefficient, flow velocity, pipe radius and species half-life in the deposition models. The computational results indicate that the plateout estimates for the slug flow model are typically 5–100% greater than for the laminar model. The effect of axial diffusion is necessarily negligible for Péclet numbers greater than 100. Little increased plateout is observed for Péclet numbers less than 100; an additional 8% is predicted for a Péclet number of 20 if axial diffusion is included. Characteristic stream, wall and integrated deposition profiles are shown. Representative results from the analysis of fission-product deposition measurements for diffusion tubes in the Fort St Vrain high-temperature gas-cooled reactor plateout probe are presented. Using single-region slug and laminar models, the wall mass-transfer coefficients, diffusion coefficients and inlet concentrations are determined using least-squares analysis. The diffusion coefficients and inlet concentrations are consistent between tubes. The computed diffusion coefficients and wall mass-transfer coefficients are in agreement with known literature values. The analysis indicates that little difference can be discerned between computed laminar and slub flow-model parameters unless accurate data is obtained under strictly regulated conditions.

The Effect of Inlet and Exit Losses on Free Convective Laminar Flow in the Trombe Wall Channel

A numerical solution for two-dimensional free convective laminar flow in the Trombe wall channel has recently been presented by Akbari and Borgers [1]. Their analysis assumed no flow losses in the channel entrance and exit, other than the exit dynamic head (loss coefficient k = 1), however the actual coefficient for combined inlet and exit losses is probably 2 < k < 5. In the present study, the convective terms of the momentum and energy equations are linearized through an Oseen-type approximation. A closed-form series solution to the resulting partial differential equations is obtained. Results are presented for dimensionless temperature and velocity field, flow rate and heat transfer; in terms of loss coefficient, surface temperature ratio, and Grashof number. As expected, vent loss reduces flow rate significantly: for loss coefficient k = 5, flow rate is reduced by ∼70 percent relative to k = 1. Surprisingly, at high Grashof number, vent loss can cause a significant (∼60 percent) increase in heat transfer. Reduction in flow rate occurs entirely due to flow velocity decrease in the region near the channel center, which contributes negligibly to the total heat delivery.

Natural Convection Heat Transfer in a Confined-Flow Geometry

A finite element method of solution for laminar convection flows was used to obtain the flow, temperature, and heat transfer distributions for a heated copper block immersed in a tank of water simulating the debris tray cooling problem that can result after a core meltdown in a liquid-metal-cooled fast breeder reactor. Careful iteration has allowed the solution to be taken up to the onset of turbulence value of Gr X Pr approx. = 5 X 10/sup 7/. Comparison of the numerical solution with experimental results shows very good agreement. Local and average Nusselt numbers for this confined-flow situation are then derived from the solution, and it is shown that the existing correlations for flat plates in an infinite medium can be used to predict to a first approximation the behavior in the more complex geometries simulating the debris tray.

Experimental study of viscoelastic effectives in a cylinder-plane lubricated contact

This experimental study is related to the flow between a stationary small diameter needle and a moving drum of much larger diameter, seen as a moving plane. Our visualisation experimental set-up adds new results regarding the flow behaviour of a polymer solution. This flow is compared to that of a Newtonian fluid used under the same kinematic conditions. Important differences between Newtonian and polymeric flows concern mainly streamlines, stagnation point positions, and reverse flow. A second experimental set-up enabled us to obtain normal stress profiles along the needle wall and the flow rate through the gap. Reslts related to Newtonian flows are compared to the well-known analytical solutions for a bidimensional laminar flow.

Numerical Solutions for Laminar Flow and Heat Transfer in a Periodically Converging-Diverging Tube, with Experimental Confirmation

Numerical Solutions for Laminar Flow and Heat Transfer in a Periodically Converging-Diverging Tube, with Experimental Confirmation

Application of Gyarmati's variational principle to laminar stagnation flow problem

Gyarmati's principle for the evolution of irreversible processes has been applied to construct the variational solutions of laminar stagnation flow of incompressible Newtonian fluid in two dimensions. Variational solutions obtained in three different representations approximate closely the exact numerical result of longitudinal velocity component and the Gyarmati's principle in force representation yield the same result as obtained by Doty and Blick with the help of local potential method of Glansdorff and Prigogine.

Numerical Analysis of a Periodically Varying Flow in a Circular Tube Containing a Slightly Compressible Fluid

Pressure and cross-sectional mean velocity of a periodically varying flow in a circular tube containing a slightly compressible fluid are numerically calculated by the method of characteristics and the finite-difference technique by using wall shear stress evaluated from the cross-sectional distribution of instantaneous axial velocities. The present numerical solutions for a pulsating laminar flow agree with the analytical ones and the calculated results for water hammer show a good agreement with the experimental ones reported by Holmboe and Rouleau (1967). In case of a pulsating turbulent flow, the influences of frequency and Reynolds number on the pressure, the velocity, and the wall shear stress profiles are shown schematically, and the critical condition for an incompressible fluid flow is presented. At middle frequencies, calculated results in a previous paper deviate a little from the experimental data, but the present results agree well with the same data.

Unsteady Compressible Laminar Boundary-Layer Flow within a Moving Expansion Wave

Numerical solutions for the unsteady compressible laminar boundary-layer flow developed within a centered expansion wave are obtained for two wall thermal conditions, isothermal and adiabatic. The Howarth's transformation, similarity transformation via one-parameter groups, and then series expansion are employed for the solutions. The solutions are of second-order accuracy and are shown to improve over the Hall's zero-order solution for the temperature distribution in the boundary layer. It is shown that both velocity and temperature boundary layer grow rapidly behind the expansion wavefront but attenuate further downstream. If the wall temperature is held at the undisturbed temperature, the heat transfer occurs from the wall to the expanding gas. The rate of heat transfer increases from the wavefront to approximately £ = 0.35 behind the wave where maximum heat transfer is observed. The isothermal wall temperature is found to be higher than the adiabatic wall temperature by a factor (1 + 0.335£).

A Surface Integral Numerical Solution for Laminar Developed Duct Flow

A surface integral numerical solution for laminar developed flow in ducts of arbitrary shape cross sections is presented. The method is general for any two-dimensional duct with simple or multiple connected regions cross section. The solutions provide information for velocity distribution, friction factor, and wall shear stress. As an application of the present method, solutions for flow in circular and rectangular ducts are obtained. These solutions are used to compare the obtained results and the corresponding exact analytical solutions. Moreover, in order to illustrate the general use of the present scheme, a solution for the case of circular duct containing rod clusters is obtained. The method proved to have several interesting features and advantages over other conventional numerical and analytical techniques.

Self-similar solutions of navier-stokes equations for rotational flow of incompressible fluid in a round pipe

Self-similar solutions of Navier—Stokes equations are obtained for rotational and laminar flows in a round pipe with porous and impermeable walls. Longitudinal and circular velocity components are assumed to be linear functions of the longitudinal coordinate. The obtained system of ordinary differential equations is numerically integrated. Solutions for laminar flows are not unique in the investigated here range of parameter variation that defines the intensity of suction and injection of fluid. Solutions for rotational and laminar flows in pipes with porous walls, which are characteristic of the boundary value problem, are treated separately. Curves of radial distribution of velocity components of rotational and laminar flows are presented for several intensities of sucking and injection. Curves and tables of integral characteristics of flow are also presented.

Self-similar solution of unsteady compressible three-dimensional stagnation-point boundary layers

The self-similar solution of the unsteady laminar compressible boundary-layer flow with variable properties at a three-dimensional stagnation point with mass transfer has been obtained when the free-stream velocity varies inversely as a linear function of time. The resulting ordinary differential equations have been solved numerically using an implicit finite-difference scheme. The results are found to be strongly dependent on the parameter characterizing the unsteadiness in the free-stream velocity. The velocity profiles show some features not encountered in steady flows.

Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a non-isothermal vertical flat plate

Laminar free convection boundary layer flow of a thermomicropolar fluid past a non-isothermal vertical flat plate has been studied in detail. It has been established that the flow problem has similarity solutions when the variation in the temperature of the plate is a linear function of the distance from the leading edge measured along the plate. The resulting system of the nonlinear ordinary differential equations has been solved numerically by “Shooting Method” for various values of the material parameters. The effects of these parameters has been studied on the velocity and microrotation fields graphically. Also “Tables” have been given for the values of temperature, skin-friction parameter, microrotation gradient on the wall and Nusselt number. Two types of boundary conditions are prescribed for the microrotation on the wall.

Taylor diffusion for a natural convective flow through a vertical channel

Dispersion of a solute in natural convective laminar flow through a vertical channel is investigated when there is a uniform axial temperature variation along the walls. It is observed that the effective Taylor diffusion coefficient is oscillatory in nature for small and moderate values of Rayleigh number r and it increases gradually with increase in Rayleigh number ( r > 3.0).

Thermodynamic method to two dimensional stagnation flow and heat transfer

The purpose of this paper is to develop a variational technique, using the variational principle of non-equilibrium thermodynamics for the solution of laminar stagnation point flow and heat transfer in two dimensions. The governing principle of dissipative processes is formulated for the problem and then using the boundary conditions of the system the elementary trial functions of third degree are assumed for the flow and temperature fields in the vicinity of the wall. The viscous and thermal boundary layer thicknesses, the skin friction and the rate of heat transfer from the wall to the fluid are obtained. It is found that these new approximate results are quite close to the exact known ones. These results are better than those of the Karman-Pohlhausen technique.

A Study of Heat Transfer in a Rotating Cylindrical Tube

The paper reports the results of a numerical solution for laminar fluid flow and heat transfer in the developed region of a tube rotating about a parallel axis. The results cover a wide range of Prandtl number and the eccentricity and Coriolis effects are included in the solution. By transforming the variables in the governing equations, it is shown that the Rayleigh and Reynolds numbers only occur as the product Ra Re, and at large Prandtl number an asymptotic solution is defined by the product Ra Re Pr and the eccentricity alone. The numerical solution of the full governing equations confirms this and indicates that for sufficiently large radius of rotation Nu = f(Ra Re Pr) is a good approximation over a wide range of Prandtl number. The Fanning friction factor is better described by Gr Re. The solution is compared with other analyses and experimental data for air, water, and glycerol.

Convective diffusion with homogeneous and heterogeneous reactions in a tube

A new complete solution for laminar flow with axial diffusion and first-order homogeneous and wall reactions in a tube is presented. The solution is in terms of an eigenfunction series expansion. Effects of axial diffusion, homogeneous reaction, and wall reaction on the concentration field are discussed. Comparison of the simplified results derived from the present analysis by neglecting axial diffusion and wall reaction with those of previous workers shows good agreement. Conditions are established for the necessity of applying the present results to describe the system accurately. 11 figures.

Dispersion of solutes in combined free and forced convective flow through a channel

Dispersion of a solute in combined free and forced convective laminar flow through a parallel plate channel has been considered, when there is a uniform axial temperature variation along the channel walls. It is observed that the effective Taylor diffusion coefficient increases with increase in Grashof number and also the interesting fact that it is same for both heating and cooling of the plates.