Velocity Profile Of Turbulent Flow Research Articles

Numerical study of a nanofluid-based receiver for linear Fresnel collectors

In concentrated solar technologies, the use of volumetric receivers instead of surface receivers may help to achieve higher solar collection efficiencies. This paper reports a simplified model that computes the concentrated solar radiation absorption and energy transport by advection in the volumetric receiver of a linear Fresnel collector. The proposed linear Fresnel collector is intended for use in industrial solar heat processes. The receiver consists of a rectangular channel whereby flows a nanofluid composed of thermal oil and graphite nanoparticles. The bottom wall of the channel is a glass, while the upper wall is a highly reflective surface that is well insulated. The light absorption into the nanofluid was solved using the Rayleigh dispersion, while the convection was solved with a simplified velocity profile for turbulent flow (power law) and incorporating a radiative source term in the energy equation. All equations were discretized by using finite volumes and were coded in Python language. Receiver efficiencies in the range of 92–96% were found for temperatures of 403–343K. The results show that the volumetric fraction (optical depth) drives the way the radiation is absorpted, and in consequence, the temperature profile and the receiver efficiency. For low optical depths, the solar absorption is low, resulting in high reflected radiation losses. Contrarily, high optical depths mean high solar absorption, consequently, the temperature close to the glass increases, and the convection losses are higher. The results suggest that values of optical depth close to 2.3 are optimum to obtain the highest receiver efficiency.

Numerical analysis of liquid flow measurement using multipath ultrasonic phased array flowmeter

In this paper, multipath ultrasonic flowmeter using phased array transducer is introduced to measure the flowrate. In the proposed flowmeter, the path velocities are achieved by dynamic beam steering via phased array sensor then numerical integration is used to calculate the flowrate. Turbulent flow profile through a straight pipe, flow field downstream of single bend, and double bend are studied in this paper. For each case, the influence of the number of paths, beam angle, and installation angle on the performance of the proposed flowmeter is discussed. Because of symmetric velocity profile for turbulent flow through the straight pipe, relative errors are not dependent on the installation angle and its minimum value is obtained 0.03 % under [±56.6°, 0] path arrangement. Relative errors after single and double bend depend on the installation angle due to the asymmetric flow field. In 3-path configuration, for velocity profile after single bend and double bend, the minimum error range is 1.35 % and 2.38 % under [±55o, 0] and [±45o, 0] path arrangement, respectively. In 5-path arrangement, after single bend and double bend, the minimum error range is achieved by 0.14 % and 1.03 % under [±70o, ±35o, 0] and [±65o, ±25o, 0], respectively. The validity of multipath ultrasonic phased array flowmeter after the single bend in Re = 2 × 105 to 106 has been examined with the computational fluid dynamics simulation. The maximum absolute relative error under [±55o,0] and [±70o,±35o,0] was achieved at about 3 % and 1.8 % respectively.

Curvature effects on the velocity profile in turbulent pipe flow

Prandtl and von Kármán have developed the famous log-law for the mean velocity profile for turbulent flow over a plate. The log-law has also been applied to turbulent pipe flow, though the wall surface is curved (in span-wise direction) and has finite diameter. Here we discuss the theoretical framework, based on the Navier-Stokes equations, with which one can describe curvature effects and also the well-known finite-size effects in the turbulent mean-velocity profile. When comparing with experimental data we confirm that the turbulent eddy viscosity must contain both curvature and finite-size contributions and that the usual ansatz for the turbulent eddy viscosity as being linear in the wall distance is insufficient, both for small and large wall distances. We analyze the experimental velocity profile in terms of an r-dependent generalized turbulent viscosity [Formula: see text] (with [Formula: see text] being the wall distance, a pipe radius, u * shear stress velocity, and g([Formula: see text]/a) the nondimensionalized viscosity), which reflects the radially strongly varying radial eddy transport of the axial velocity. After the near wall linear viscous sublayer, which soon sees the pipe wall's curvature, a strong transport (eddy) activity steepens the profile considerably, leading to a maximum in g([Formula: see text]/a) at about half radius, then decreasing again towards the pipe center. This reflects the smaller eddy transport effect near the pipe's center, where even in strongly turbulent flow (the so-called "ultimate state") the profile remains parabolic. The turbulent viscous transport is strongest were the deviations of the profile from parabolic are strongest, and this happens in the range around half radius.

Logarithmic Velocity Profile for Turbulent Flow in Straight Rough Pipe and Evaluation of Karman Constant with Boundary Layer Reynolds Number- A Complete Solution

Logarithmic Velocity Profile for Turbulent Flow in Straight Rough Pipe and Evaluation of Karman Constant with Boundary Layer Reynolds Number- A Complete Solution

Feasible domain of Walker's unsteady wall-layer model for the velocity profile in turbulent flows.

The present work studies, in detail, the unsteady wall-layer model of Walker et al. (1989, AIAA J., 27, 140 – 149) for the velocity profile in turbulent flows. Two new terms are included in the transcendental nonlinear system of equations that is used to determine the three main model parameters. The mathematical and physical feasible domains of the model are determined as a function of the non-dimensional pressure gradient parameter (p+). An explicit parameterization is presented for the average period between bursts (T+B), the origin of time (t+0 ) and the integration constant of the time dependent equation (A0) in terms of p+. In the present procedure, all working systems of differential equations are transformed, resulting in a very fast computational procedure that can be used to develop real-time flow simulators.

Flow around individual Taylor bubbles rising in a vertical column with water: Effect of gas expansion

This paper presents an experimental study to evaluate the effect of bubble expansion on the dynamics of an isolated Taylor bubble rising in a vertical column of water by inspection of the liquid flow around the bubble front. An increase in bubble volume results from gas decompression due to hydrostatic pressure drop as the bubble ascends through the liquid. Two reduced pressures (33.3 and 20.0kN/m2) and atmospheric pressure were maintained at the free liquid surface to provide a wide range of expansion rates.PIV coupled with a Shadowgraphy Technique was used to simultaneously obtain the flow field ahead the bubble and a well-defined gas–liquid interface.A very good correlation was found between predicted bubble volume expansion rates considering ideal gas behavior and the upward net volumetric liquid flow rate obtained by integration of the velocity profiles. Above the bubble nose, the liquid velocity at the centerline decreases rapidly from the value of the Taylor bubble velocity at the tip of the bubble. For distances greater than 0.5D, the liquid flow is undisturbed, with a significant axial velocity component for high bubble volume expansion rates due to the displacement of the liquid promoted by gas expansion. The Reynolds number calculated for the liquid flow was less than 2100 for all conditions used. While this suggests a laminar flow regime in the liquid, coefficient C from Nicklin’s equation obtained from data was equal to 1.4. The shapes of the velocity profiles obtained at the undisturbed liquid flow show that for high expansion rates they resemble the power-law velocity profile for turbulent flow. The bubble volume expansion rate modifies continuously during the Taylor bubble rise and a well-defined liquid velocity profile is never attained.

3D Simulation of Velocity Profile of Turbulent Flow in Open Channel with Complex Geometry

Abstract Simulation of open channel flow or river flow presents unique challenge to numerical simulators, which is widely used in the applications of computational fluid dynamics. The prediction is extremely difficult because the flow in open channel is usually transient and turbulent, the geometry is irregular and curved, and the free-surface elevation is varying with time. The results from a 3D non-linear k– ɛ turbulence model are presented to investigate the flow structure, the velocity distribution and mass transport process in a meandering compound open channel and a straight open channel. The 3D numerical model for calculating flow is set up in cylinder coordinates in order to calculate the complex boundary channel. The finite volume method is used to disperse the governing equations and the SIMPLE algorithm is applied to acquire the coupling of velocity and pressure. The non-linear k– ɛ turbulent model has good useful value because of taking into account the anisotropy and not increasing the computational time. The main contributions of this study are developing a numerical method that can be applied to predict the flow in river bends with various bend curvatures and different width-depth ratios. This study demonstrates that the 3D non-linear k– ɛ turbulence model can be used for analyzing flow structures, the velocity distribution and pollutant transport in the complex boundary open channel, this model is applicable for real river and wetland problem.

Power-law velocity profile in turbulent boundary layers: An integral reynolds-number dependent solution

Geophysical flows of practical interest encompass turbulent boundary layer flows. The velocity profile in turbulent flows is generally described by a log- or a power-law applicable to certain zones of the boundary layer, or by wall-wake law for the entire zone of the boundary layer. In this study, a novel theory is proposed from which the power-law velocity profile is obtained for the turbulent boundary layer flow. The new power-law profile is based on the conservation of mass and the skin friction within the boundary layer. From the proposed theory, analytical expressions for the power-law velocity profile are presented, and their Reynolds-number dependency is highlighted. The velocity profile, skin friction coefficient and boundary layer thickness obtained from the proposed theory are validated by the reliable experimental data for zero-pressure gradient turbulent boundary layers. The expressions for Reynolds shear stress and eddy viscosity distributions across the boundary layer are also obtained and validated by the experimental data.

Computation of some characteristics of gas or liquid turbulent flow in a circular pipe

The dependence of the type of velocity profile in turbulent flow of liquids and gases in a circular tube outside the viscous sublayer and buffer area on the Reynolds number was examined. On this basis, the dependence of the ratio of the velocity averaged over a pipe cross section to maximum velocity, as well as parameters in the balance equation of mechanical energy and momentum on the Reynolds number were studied.

Flow properties of cellulose fiber suspensions flocculated by cationic polyacrylamide

Retention aid systems are commonly used in the papermaking process to flocculate the fine matericals in cellulose fiber suspensions. The addition of polymeric flocculants such as cationic polyacrylamide (C-PAM) also increases the fiber flocculation and the shear strength of the fiber flocs. The break-up process of fiber flocs in highly turbulent flow is of great importance to produce paper with an even fiber distribution. In this study, phase flow encoded nuclear magnetic resonance (NMR) imaging was used to study the pipe flow behavior of cellulose fiber suspensions when cationic polyacrylamide had been added. Axial velocity profiles were measured at different mean bulk flow rates. The mean velocity profiles for turbulent flow were analyzed in terms of the power-law. It was demonstrated that at low shear rates the polymeric flocculant induces phase separation in a dilute fiber suspension, while at high shear rates, polymer induced flocculation reduces turbulent intensities of the flow. Flow encoded NMR images were recorded for the fully turbulent flow of a 0.5 wt.% hardwood fiber suspension at different times (0.5–9.0 min) after polymer addition. Immediately after addition a steady plug flow profile was observed. After 9 min the flow is fully turbulent. This indicates that the polymer macromolecules are disrupted quickly in turbulent flow.

Applied fluid mechanics

Applied fluid mechanics

Pipe Flow Measurements of a Transparent Non-Newtonian Slurry

An experimental description of the flow structure of non-Newtonian slurries in the laminar, transitional, and full turbulent pipe flow regimes is the primary objective of this research. Experiments were conducted in a large-scale pipe slurry flow facility with an inside pipe diameter of 51 mm. The transparent slurry formulated for these experiments from silica, mineral oil, and Stoddard solvent exhibited a yield-power-law behavior from concentric-cylinder viscometer measurements. The velocity profile for laminar flow from laser Doppler velocimeter (LDV) measurements had a central plug flow region, and it was in agreement with theory. The range of the transition region was narrower than that for a Newtonian fluid. The mean velocity profile for turbulent flow was close to a 1/7 power-law velocity profile. The rms longitudinal velocity profile was also similar to a classical turbulent pipe flow experiment for a Newtonian fluid; however, the rms tangential velocity profile was significantly different.

Wall-layer model for the velocity profile in turbulent flows

In the calculation of turbulent flows near walls, a substantial amount of mesh points and computational effort is required to adequately resolve the intense velocity profile variations in the near-wall region. In this study, a profile approximation is obtained for the mean velocity that is based upon consideration of the coherent structure of the time-dependent wall-layer flow. The profile approximation is an analytical formula that satisfies all of the required compatibility conditions at the wall and the logarithmic behavior at the edge of the wall layer. A general method for utilizing the present wall-layer profile model in a prediction method is indicated.

Oxygen Stratification in Industrial Boiler Stacks

The DSS/2 software system was used to numerically simulate oxygen stratification effects in a typical industrial boiler stack. The model developed for the simulation involves turbulent mass transfer in a tube with a constant, high mass flux from the walls of the tube. The concentration profile is considered to be developing, but the velocity profile is assumed to be fully developed. The model is for a gaseous system at constant temperature and pressure; the transport properties are shown to be constant. The universal velocity profile for turbulent flow and von Karman’s expressions for the turbulent eddy diffusivity are incorporated in the model. An expression for a wall concentration profile corresponding to conditions of high mass flux at the wall is developed. The model is then expressed as a system of partial differential equations which are solved using the numerical method of lines together with the DSS/2 numerical integration system. The resulting concentration profiles are presented for various flu...

A short flat diffusion channel with a turbulence-removing device

The aerodynamics of a flat diffuser channel with different expansion angles have been studied at GIAP. The use of short diffusers as constructional elements in chemical equipment with the aim of levelling out the asymmetrical velocity profile of turbulent flow provides a compact design and leads to significant metal savings. The profiles of the mean local velocities and the pulsation components of the velocity were measured during the tests and used to determine the degree of turbulence of the flow. Finds that the parallel insertion of 3 perforated grids and 2 sieves in the flat diffuser levels out the flow and reduces the degree of turbulence from 30 to 1-4% in the range of the expansion angles from 4-90 degrees. Recommends this approach, together with conical diffusers, for inclusion in equipment for chemical technology.

An empirical model of velocity profiles for turbulent flow in smooth pipes

An empirical model of velocity profiles for turbulent flow in smooth pipes

Gas transfer to and across an air-water interface

A treatment based on Reichardt's formulation of the velocity profile in turbulent flow over a smooth plane surface is shown to give good agreement with published data on the boundary layer transfer of heat and mass over a wide range of Prandtl (or Schmidt) number, si. Applied to transfer to a water surface, agreement with published laboratory results is also good for low air speeds (smooth water). Comparison with observations for the sea shows there is little difference between the calculated evaporation coefficient and those reported for the sea with winds of ~7 m s-1. This is consistent with sea trials having so far detected little increase of evaporation and heat transfer coefficients with wind speed over the range 4–10 m s-1.The air/water transfer of non-reactive gas is governed by the resistance of the viscous sublayer of water, and the smooth surface treatment gives the transfer velocity (VL) on a liquid phase basis as VL = 0.082 (ρa/ρw)½σ-⅔u* where ρaρw is the density ratio, air/water, and u* = friction velocity of the surface air flow. The agreement between this formula and published wind tunnel results is good for the smooth water condition. At higher wind speeds transfer exceeds the calculated value and appears then to increase roughly in proportion to the square of the wind speed.

Laminar flow stability in a mass force field

A study is made of the stability of a certain class of velocity profiles in a two-dimensional channel on the basis of a new numerical algorithm for the solution of the Orr-Sommerfeld equation. A profile is found which has (in a certain sense) the property of maximum stability. In form this profile is very similar to the averaged velocity profile of turbulent flow in a two-dimensional pipe.

Laminar and Turbulent Incompressible Boundary Layers on Slender Bodies of Revolution in Axial Flow

The boundary-layer equations for both laminar and turbulent incompressible flows over slender bodies of revolution in axial flow are solved by an implicit finite-difference method. The Reynolds shear-stress term is eliminated by means of an eddy-viscosity concept. Velocity profiles and values of local skin-friction coefficient are obtained for various slender circular cylinders in both laminar and turbulent flows. The deviation of the cylinder skin friction from that of a flat plate is studied. The calculated velocity profiles for turbulent flow are compared with those of both Richmond’s and Yasuhara’s experimental data and with Rao’s proposed formulation of the law of the wall in thick, axisymmetric turbulent boundary layers. In both cases excellent agreement is obtained.

On the velocity profile for turbulent flow in a straight pipe

Nikuradse's velocity profiles for the core of turbulent pipe flow for high Re ( Re>6000) are analysed by taking into account not only the dimensionless distance from the wall (y +) but also an equivalent radial position. An improved equation is introduced for the wall region, and both expressions lead to an improved correlation for the complete tube section. For low turbulent Re ( Re<6000) an empirical equation is proposed incorporating suitably modified dimensionless velocity and wall distance parameters.