Wall Friction Factor Research Articles

Analytical Study on Mechanism of Countercurrent Flow Limitation in Vertical Rectangular Channels.

A quantitative analysis of countercurrent flow limitation (CCFL) or flooding was successfully carried out using the existing experimental data for the vertical rectangular channels, adopting the criterion that the CCFL condition is determined by maximizing the falling water mass velocity with respect to the thickness of the falling water film for the whole flow channel, without any additional conditions. It was found that significant factors were the flow pattern, that is, which walls were wet, interfacial friction factor between liquid and gas based on the relative velocity, wall friction factors for laminar, transition and turbulent flow of liquid and gas, and aspect ratio of rectangular channels. Thus it was clarified that the analytical results give good predictions of the existing experimental data of an air-water system for vertical rectangular channels of 33 and 66 mm in channel width, 2.3 to 12.3 mm in channel gap, and 362 and 782 mm in channel length under atmospheric pressure.

Vorticity dynamics and scalar transport in separated and reattached flow on a blunt plate

Two‐dimensional calculations are performed for a Reynolds number of 1000 and an effective Prandtl number of unity to study the dynamics of large‐scale spanwise vortices with a passive scalar field in a separation and reattaching flow over a blunt plate. A triple decomposition technique is used to isolate the quasiperiodic fluctuations related to the large‐scale vortices shed from the separated shear layer. Three vortex shedding modes are identified in the reattachment zone, two of which involve partial pairings. The coherent vortices shed from the reattachment zone have a dominating effect on scalar transport, and act as ‘‘large‐scale mixers’’ by entraining wall scalar around their upstream periphery and free‐stream scalar on their lower downstream edge. There is a definite relationship between the phase‐averaged perturbations (due to the presence of coherent vortices) in the wall friction factor and wall scalar transport with their respective time mean maximums. On the other hand, although there does exist an explicit spatial relationship between the instantaneous stagnation point and instantaneous location of maximum wall scalar transport, there is no such relationship in the mean between the two locations, except that both are dependent on the vorticity dynamics in the reattachment region.

Optimal angle of attack in tube spinning

The angle of attack of the roller used in tube spinning has an essential effect on the build-up and bulge ahead of the roller, the variation of the inner diameter of the spun part, and the forces applied to the roller. Recognizing the importance of determining a proper angle of attack in practice, an analytical method of defining the optimal angle of attack in tube spinning is proposed on the basis of minimizing the resultant spinning force. The optimal angle of attack in forward and backward tube spinning in the form of a transcendental function of the relevant variables such as feed rate, reduction of wall thickness and friction factor, can be solved numerically by the Newton-Raphson method. The optimal angle of attack calculated according to the method proposed is in agreement with the data on desired angle of attack reported in the literature.

Estimation of shear stress in counter-current annular flow.

The accuracy to which the friction factor is correlated is important in counter-current flow (CCF) analysis using a two-fluid model. Current two-fluid model codes use correlations of friction factors developed for co-current flow, or correlations developed on the assumption of zero wall shear stress. An assessment of two-fluid model codes with these existing correlations shows that the downward flow rate of water is overestimated. An analytical model is developed to calculate the shear stress profile in a liquid film of the CCF in order to obtain information on the shear stress between the interface and the wall. Both this analysis and Bharathan's CCF data show that the wall shear stress acting on the falling water film is approximately of same order as the interfacial shear stress, and the correlation for co-current flow cannot be applied to CCF. Tentative correlations of interfacial and wall friction factors are developed based on the results of the present study.

Numerical analysis of laminar mixed convection in horizontal internally finned tubes

Steady, laminar, mixed convection in the fully developed region of horizontal internally finned tubes is investigated for the case of uniform heat input axially and uniform wall temperature circumferentially. The fluid flow and heat transfer characteristics are found to be dependent on a modified Grashof number Gr +, Prandtl number Pr, number of fins M and the relative fin height H. Governing differential equations are solved numerically for the parametric range M = 4 and 16, H = 0, 0.2, 0.5 and 0.8, Pr = 7 and Gr + = 0 to 2 × 10 6. Computed results include the secondary flow components, axial velocity and temperature distributions, wall heat flux, friction factor and average Nusselt number. Internal finning is found to retard the onset of significant free convective effects and to suppress the enhancements in friction factor and Nusselt number compared to smooth tubes. Satisfactory agreement is obtained between the present numerical results and previous experimental data.

Theory Versus Experiment for the Rotordynamic Coefficients of Labyrinth Gas Seals: Part I—A Two Control Volume Model

The basic equations are derived for a two-control-volume model for compressible flow in a labyrinth seal. The recirculation velocity in the cavity is incorporated into the model for the first time. The flow is assumed to be completely turbulent and isoenergetic. The wall friction factors are determined using the Blasius formula. Jet flow theory is used for the calculation of the recirculation velocity in the cavity. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order pressure distribution is found by satisfying the leakage equation while the circumferential velocity distribution is determined by satisfying the momentum equations. The first-order equations are solved by a separation of variable solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients.

Flow of Non-Newtonian Fluids in Curved Pipes : 1st Report, Numerical Analysis for Laminar Flow of Power-law Fluids

A steady fully-developed laminar flow of power-law fluids through curved pipes has been solved numerically under Dean numbers D l 1000, power-indices n=1∼0.5 and curvature radius ratios Rc=10∼100. Velocity profiles of a primary flow, stream lines of a secondary flow, distributions of wall shear stresses and friction factors are obtained. Effects of D, n and Rc upon flow characteristics are made clear.

Flow of non-Newtonian fluids in curved pipes. 1st report Numerical analysis for laminar flow of power-law fluids.

A steady fully-developed laminar flow of power-law fluids in curved pipes has been solved numerically for Dean numbers D<1000, power indices 0.5<n<1.0 and curvature radius ratios 10<Rc<100. Velocity profiles of primary flow, stream lines of secondary flow, distributions of wall shear stress and friction factors are obtained. Effects of D, n and Rc upon flow characteristics made clear.

Analysis of fully developed turbulent flow in an eccentric annulus.

An analysis is presented of fully developed turbulent flow in an eccentric annulus. An integral transformation technique (Kirchhoff transformation) is applied to eccentric annuli in a wide range of eccentricity and radius ratio. Velocity distributions, wall shear stress distributions and friction factors are calculated and compared with the literature. Although the analysis cannot predict the secondary flow in an eccentric annulus, the calculated results show good agreement with the experimental results in the literature.

An experimental study on hydrodynamics of a system in a pneumatic flash dryer

Pressure drop dependences on gas and solid flow rates and solid concentrations for a vertical pipe section and for a conical—cylindrical—conical chamber have been determined. Equations for a particle—wall friction factor have been obtained. Values of particle—wall friction factor for a vertical pipe section are in reasonable agreement with literature data. For a conical—cylindrical—conial chamber friction factors can be both positive and negative.

An experimental study of the three dimensional boundary layer on the end wall of a vortex chamber

Profiles of the radial and circumferential components of velocity have been measured in the end-wall boundary layer of a vortex chamber as part of an experimental and theoretical investigation of a confined, incompressible vortex flow. The profiles have been presented here for various radial positions and operating conditions and the main features of the boundary-layer have been discussed. Further, the circumferential profiles have been analysed by plotting them in two types of dimensionless coordinates. Also, the wall friction data corresponding to the circumferential direction have been plotted. Hence an empirical expression for the wall friction factor was obtained. The data presented here reveal some new features and provide new information on the end-wall boundary layer flow in a vortex chamber.

Aerated solids flow through a vertical standpipe below a pneumatically discharged bunker

An experimental investigation is described into the pneumatic discharge of sand ( d p = 140 μm) and of glass balk tini ( d p = 200 μm) from a bunker through vertical standpipes of various lengths up to 1.50 m and with diameters ranging from about 7 up to 13 mm. On the basis of a momentum balance, a relation could be established between the particle mass flow rate through the pipe, the pressure drop across the pipe, and the pipe length. In this relation two other quantities occur: the apparent density of the particulate mass, which appears to approach a limiting value with increasing pipe diameter, and the wall friction factor, which appears to be independent to pipe diameter within experimental accuracy.

Evaporating Fluid Flow in Pipes: A Theory for the Prediction of Phase Velocity, Pressure Drop and Critical Outlet Conditions for Evaporating Annular Flow in Pipes

The theory of evaporating flow given in this paper is believed to be an advance on what has hitherto been available in that it makes due allowance for the effect of vapour condensation which occurs simultaneously with vapour expansion. The basic theory is applicable without modification to any fluid undergoing evaporating flow in the annular mode, given suitable correlations for wall and interphase friction factors as defined in the paper. Preliminary correlations, which can only be very rough, are provided for water. A lot of experimental work on a variety of fluids would be required to achieve a position from which general correlations could be developed. The theory incidentally permits prediction of critical outlet conditions and some interesting comparisons with available experimental data have been made.

Closure to “Discussion of ‘Plane Turbulent Wall Jet Flow Development and Friction Factor’” (1963, ASME J. Basic Eng., 85, pp. 53–54)

Closure to “Discussion of ‘Plane Turbulent Wall Jet Flow Development and Friction Factor’” (1963, ASME J. Basic Eng., 85, pp. 53–54)