Turbulent Wall Flows Research Articles

Study of the heat transfer characteristics in turbulent combined wall and offset jet flows

The heat transfer study of a combined wall jet and offset jet flow with different wall jet and offset jet flow velocities are considered. The flow is considered two-dimensional, steady, incompressible, turbulent at high Reynolds number with negligible body forces. The streamline curvature modification of the standard k– ε model is used to carry out the turbulence modeling. The Reynolds number is varied from 10 4 to 4 × 10 4 and Pr = 0.71 is taken for all computations. Constant wall temperature and constant wall heat flux boundary conditions are considered. The results are presented in the form of local Nusselt number, local heat flux, surface temperature in case of constant heat flux condition, average Nusselt number and total heat transfer.

An interactive bypass transition mechanism in wall-bounded flows

The interaction between two localized disturbances is analysed in a subcritical channel flow through direct numerical simulations. The initial perturbations are in the form of two pairs of counter-rotating vortices. One of them interacts with the wall-normal vorticity layers set up near the wall, by locally compressing or stretching part of them through the straining motion it induces. The breakdown of spanwise symmetry leads to the rapid development of a new wall-normal vorticity patch that is tilted by the shear and rolls up into a new small-scale streamwise vortex. The process results in a localized turbulent spot at later stages of development. A detailed analysis is carried out to determine the role of different parameters entering the physics of the mechanism. Several critical thresholds that trigger the interactive bypass transition process are found and analysed. The similarity parameters resulting from the parametric investigation coincide well with those governing the self-sustaining Reynolds-shear-stress-producing eddies in the buffer layer of a fully developed turbulent wall flow. It is suggested that the mechanism we propose may play a role in the regeneration cycle of the near-wall turbulence-generating structures by bypassing the three-dimensional streak instability mechanism.

On the Lamb vector divergence in Navier–Stokes flows

The mathematical and physical properties of the Lamb vector divergence are explored. Toward this aim, the instantaneous and mean dynamics of the Lamb vector divergence are examined in several analytic and turbulent flow examples relative to its capacity to identify and characterize spatially localized motions having a distinct capacity to effect a time rate of change of momentum. In this context, the transport equation for the Lamb vector divergence is developed and shown to accurately describe the dynamical mechanisms by which adjacent high- and low-momentum fluid parcels interact to effect a time rate of change of momentum and generate forces such as drag. From this, a transport-equation-based framework is developed that captures the self-sustaining spatiotemporal interactions between coherent motions, e.g. ejections and sweeps in turbulent wall flows, as predicted by the binary source–sink distribution of the Lamb vector divergence. New insight into coherent motion development and evolution is found through the analysis of the Lamb vector divergence.

Simulating drag reduction phenomenon in turbulent pipe flows

Drag reduction using polymeric additives is an interesting phenomenon in turbulent pipe flows which was first discovered by Toms [Toms, B.A., 1948. Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proc. First Int. Cong. Rheol. 2, 135–141]. Due to its industrial importance, the phenomenon has been the subject of much study in the past, in both theoretical and experimental domains alike. As to the mechanisms involved, it has been argued that polymeric additives act through affecting the structure of turbulent bursts near the wall by boosting the extensional viscosity of the base fluid (see [Lumley, J.L., Blossey, P., 1998. Control of turbulence. Ann. Rev. Fluid Mech. 30, 311–327]). In practice, drag reduction as large as 90% has been achieved with concentration as low as 20 ppm of certain high-molecular-weight flexible polymers. Prediction of such huge drag reductions obtained using polymeric additives has not been possible in the past partly, because of the limitations of the computational facilities and also because of the inadequacies of the constitutive equations used for the simulations. Recently, Pinho [Pinho, F.T., 2003. A GNF framework for turbulent flow models of drag reducing fluids and proposal for a k– ε type closure. J. Non-Newtonian Fluid Mech. 114, 149–184] modified the generalized Newtonian fluid (GNF) model in such a way that it could take into account the extensional viscosity (a measure of the elastic behavior of a fluid) in addition to the shear viscosity (a measure of the viscous behavior of a fluid). Based on this idea, Pinho (2003) derived the first time-averaged turbulent flow formulations for viscoelastic fluids. These formulations were used by Cruz and Pinho [Cruz, D.O.A., Pinho, F.T., 2003. Turbulent pipe flow predictions with a low-Reynolds number k– ε model for drag reducing fluids. J. Non-Newtonian Fluid Mech. 114, 109–148] and Cruz et al. [Cruz, D.O.A., Pinho, F.T., Resende, P.R., 2004. Modeling the new stress for improved drag reduction predictions of viscoelastic pipe flow. J. Non-Newtonian Fluid Mech. 121, 127–141] by embedding the low-Reynolds turbulence model of Nagano–Hishida [Nagano, Y., Hishida, M., 1987. Improved form of the k– ε model for wall turbulent shear flows. J. Fluid Eng. 109–156]. They performed several simulations using this well-known turbulence model and showed that it can well predict the large drag reduction observed in practice for some polymeric additives. But for certain other polymers the prediction were found not to be so great. In this work, it will be shown that better predictions can be obtained for these polymers if use is made of another low-Reynolds number k– ε turbulence model called Launder–Sharma model [Launder, B.E., Sharma, B.I., 1974. Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transfer 1, 131–138] for the simulations.

Intermediate Scaling of Turbulent Momentum and Heat Transfer in a Transitional Rough Channel

The properties of the mean momentum and thermal balance in fully developed turbulent channel flow on transitional rough surface have been explored by method of matched asymptotic expansions. Available high quality data support a dynamically relevant three-layer description that is a departure from two-layer traditional description of turbulent wall flows. The scaling properties of the intermediate layer are determined. The analysis shows the existence of an intermediate layer, with its own characteristic of mesolayer scaling, between the traditional inner and outer layers. Our predictions of the peak values of the Reynolds shear stress and Reynolds heat flux and their locations in the intermediate layer are well supported by the experimental and direct numerical simulation (DNS) data. The inflectional surface roughness data in a turbulent channel flow provide strong support to our proposed universal log law in the intermediate layer, that is, explicitly independent transitional surface roughness. There is no universality of scalings in traditional variables and different expressions are needed for various types of roughness, as suggested, for example, with inflectional type roughness, Colebrook–Moody monotonic roughness, etc. In traditional variables, the roughness scale for inflectional roughness is supported very well by experimental and DNS data. The higher order effects are also presented, which show the implications of the low Reynolds-number flows, where the intermediate layer provides the uniformly valid solutions in terms of generalized logarithmic laws for the velocity and the temperature distributions.

Optimum length of tubes for heat transfer in turbulent flow at constant wall temperature

Maximum heat transfer per cross-sectional area of a tube with smooth wall in turbulent flow at constant wall temperature is determined for a given pressure loss. The dimensionless tube length is determined dependent on the pressure Reynolds number, Prandtl number and inlet local pressure loss coefficient. Limiting cases for short and long tubes are separately investigated. Semi-empirical equations are derived for both optimum dimensionless tube length and dimensionless maximum heat flow per cross-sectional area using numerically obtained values with a maximum deviation of ±6.6% and with a RMSE of 3.5%. The results can also be applied to the channels with non-circular cross-sectional area.

Influence of PIV interrogation area on turbulent statistics up to 4th order moments in smooth and rough wall turbulent flows

The paper presents measurements performed over a smooth surface, a transitionally rough surface generated by wire mesh and a fully rough surface that comprised transverse square ribs in a channel. The flow was seeded using fluorescent particles and the high quality vectors obtained using particle image velocimetry (PIV) technique were used to compute the mean velocity, turbulent statistics up to the fourth order moments as well as the production and dissipation terms in the transport equation for the turbulent kinetic energy. By using different interrogation areas and overlaps to process the PIV images, the interrogation area sizes in wall units varied from 2.9 to 52.4. In the first part of the paper, these interrogation areas were used to study the spatial resolution effects on the mean and higher order moments over the smooth and rough surfaces. For the second part of the paper, classical scaling and the scaling proposed by George and Castillo [W.K. George, L. Castillo, Zero-pressure-gradient turbulent boundary layer, Appl. Mech. Rev. 50 (12) (1997) 689–729] and Zagarola and Smits [M.V. Zagarola, A.J. Smits, Mean-flow scaling of turbulent pipe flow, J. Fluid Mech. 373 (1998) 33–79] were used to document the salient effects of surface roughness on the flow characteristics. The results show spatial resolution effects on some of the turbulent statistics, and it is evident that these effects are more pronounced over the rough surfaces than on the smooth surface. The smaller interrogation area sizes used in this study are adequate to reasonably evaluate all the statistics and production term but not the dissipation rate. It was observed that the power law proposed by George and Castillo [W.K. George, L. Castillo, Zero-pressure-gradient turbulent boundary layer, Appl. Mech. Rev. 50 (12) (1997) 689–729] is better than the log law for modeling low Reynolds number turbulent flows over rough surfaces. The results also support the premise that the mechanisms for turbulence production and transport close to the ribs are markedly different from those for a smooth surface.

Effects of pressure gradients on entropy generation in the viscous layers of turbulent wall flows

By employing results of direct numerical simulations, it is possible to examine entropy generation due to friction in the viscous layers of turbulent flows with significant streamwise pressure gradients, both for boundary layers and channels. About two-thirds or more of the entropy generation per unit surface area S″ occurs there. Increasing the pressure gradient increases direct dissipation and decreases turbulent dissipation (in wall coordinates). The integral of the entropy generation rate per unit surface area to the edge of the viscous layer is relatively insensitive to pressure gradients for channels but decreases moderately for boundary layers.

The landscape Reynolds number and other dimensionless measures of Earth surface processes

An analogy between turbulent fluid systems and landscape drainage systems [Parker, G., Haff, P.K., Murray, A.B., 2001, EOS, Transactions of the American Geophysical Union, 82, pp. F564.] is suggested by the observation that transport in both systems can be approximated by diffusion with size-proportional effective diffusivities, with a cross-over at small scales to Fickian diffusion. The “landscape” Reynolds number of a typical fluvial landscape is estimated to be of order Re L ∼ 10 6 to 10 9, these large values reflecting the relative efficiency of fluvial transport compared to creep. Re L is the ratio of the large-scale effective diffusivity of rivers to the small-scale diffusivity of creep processes on hillslopes. The spatial dependence of the effective diffusivity produces rivers with logarithmic long-profiles, similar to the profiles of many rivers in nature, and analogous to the logarithmic dependence of mean fluid velocity on distance from a wall in turbulent flow. The landscape example suggests how other generalized “Reynolds numbers” can be constructed as ratios of large-scale to small-scale diffusivities to measure the efficiencies of complex processes that affect the surface. As an example, the global airline transportation network is estimated to have an efficacy relative to that of direct human mechanisms for transport of similar goods and materials of about 10 8 as measured by a corresponding “technology” Reynolds number. The appearance of such large dimensionless numbers, pertaining to the consequences of human invention and design, reflects the emergence of the technosphere as an increasingly efficient overlay on the historical domain of biology and surficial geology.

Organised structures in wall turbulence as deduced from stability theory-based methods

In earlier work, we have explored the relevance of hydrodynamic stability theory to fully developed turbulent wall flows. Using an extended Orr-Sommerfeld Equation, based on an anisotropic eddy-viscosity model, it was shown that there exists a wide range of unstable wave numbers (wall modes), which mimic some of the key features of turbulent wall flows. Here we present experimental confirmation for the same. There is good qualitative and quantitative agreement between theory and experiment. Once the dominant coherent structure is obtained from stability theory, control of turbulence would be the next logical step. As shown, the use of a compliant wall shows considerable promise.

Surface and Gas Temperature Measurements Along a Film Cooled Wall

Film cooling is widely used to protect critical sections of propulsion devices from extreme heat loads in the internal flowpath. Many studies have been conducted to formulate scaling laws characterizing the effectiveness of film cooling in a variety of configurations for the development of engineering correlations. There is an emerging demand for detailed measurements near film-cooled surfaces to support computational model development of these complex wall-bounded flows. In this study a unique hot wind tunnel facility was used to perform detailed measurements in a canonical two-dimensional thermally stratified wall-jet configuration. Wall temperature, adiabatic effectiveness, and turbulent flow measurements were performed over a range of carefully controlled inlet conditions. Far-field laboratory effectiveness measurements compare well with previously developed scaling laws; however, the effect of the ratio of mainstream to cooling stream temperature is significantly underpredicted. The micro-thermocouple probe used in this study provided mean flow temperatures and detailed turbulent statistics characterizing the nearwall mixing behavior. The mean flow temperature measurements in the far field demonstrate self-similar behavior whereas fluctuating temperatures indicate fully developed turbulence in the wall layer. The turbulent statistics provided in this study are especially useful for development and validation of computational models of film-cooled surfaces.

A coupled boundary element–finite difference model of surface wave motion over a wall turbulent flow

AbstractAn effective numerical technique is presented to model turbulent motion of a standing surface wave in a tank. The equations of motion for turbulent boundary layers at the solid surfaces are coupled with the potential flow in the bulk of the fluid, and a mixed BEM–finite difference technique is used to model the wave motion and the corresponding boundary layer flow. A mixing‐length theory is used for turbulence modelling. The model results are in good agreement with previous physical and numerical experiments. Although the technique is presented for a standing surface wave, it can be easily applied to other free surface problems. Copyright © 2005 John Wiley & Sons, Ltd.

Resistance Reduction in Pulsating Turbulent Pipe Flows

The paper describes the effects of forced harmonic oscillations of fixed frequency and amplitudes in the range Λ=Um/Ub=1-11 on the characteristics of a turbulent pipe flow with a bulk Reynolds number of 5900. The resulting Stokes layer δ is a fraction of the pipe radius χ=R/δ=53 so that the vorticity associated to the oscillating motion is generated in a small near wall region. The analysis is carried out processing a set of statistically independent samples obtained from wall-resolved large eddy simulations (LES); time and space averaged global quantities, extracted for the sake of comparison with recent experimental data, confirm the presence of a non-negligible drag reduction phenomenon. Phase averaged profiles of the Reynolds stress tensor components provide valuable material for the comprehension of the effects of the time varying mean shear upon the near wall turbulent flow structures. The large scales of motion are directly computed through numerical integration of the space filtered three-dimensional Navier-Stokes equations with a spectrally accurate code; the subgrid scale terms are parametrized with a dynamic procedure.

Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows

The properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available highquality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a pre­ dominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular signi­ ficance is attached to the viscous/Reynolds-stress-gradient balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In parti­ cular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds num ber approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds num ber and have the same order of magnitude, there is additional theore­ tical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged momentum balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall.

Relation between the hydrodynamic parameters of two different turbulent wall flows

Relation between the hydrodynamic parameters of two different turbulent wall flows

Determination of the measuring position in laser-Doppler anemometry

The present paper is concerned with the determination of the measuring position of a laser-Doppler anemometer (LDA) relative to a wall. The proposed method is based on the finding that the output of a hot-wire anemometer increases when the wire, which is mounted in quiescent air parallel to the wall, is brought closer than 800 μm to the wall. For given hot-wire anemometer parameters, the hot-wire anemometer output voltage depends on the wall material and the wire distance from the wall. After suitable calibration for the wall material of the test section, the anemometer reading in a test rig can be used to find the wire position. Moving the measuring volume of a LDA-system across the wire yields an output voltage variation of the LDA-photomultiplier showing a Gaussian shape. When the maximum output voltage is reached, the centre of the measuring control volume is located at the centre of the wire and, hence, the location of the LDA-measuring position is known. All position measurements for the LDA-system are then taken relative to this point using the scale of the LDA-traversing system. If optical effects of transparent test section walls are eliminated by employing refractive index matched liquids, there are other ways to find the measuring position of a laser-Doppler anemometer relative to a wall. One such method and its application to the study of the turbulent near wall flow in a pipe is described in this paper.

Turbulent pipe flow predictions with a low Reynolds number k– ε model for drag reducing fluids

A low Reynolds number k– ε turbulence model is developed for predicting turbulent wall flows of viscoelastic fluids. The model uses a non-linear molecular viscosity that is affected by the turbulent fluctuations and a new damping function is introduced to account for near-wall effects. This new function was made equal to the eddy viscosity damping function which was derived taking into account viscometric and elastic effects. Flow predictions compare favourably with results from experiments with several viscoelastic fluids, especially the friction factor and the mean velocity. Comparisons of the turbulence kinetic energy are less good, but the model is able to capture the shift of the peak turbulence kinetic energy and rate of dissipation away from the wall, the decrease in those peak values and of the production of k, and the Reynolds shear stress deficit across the pipe. An advantage of the present single-point turbulence closure relative to previous attempts at modelling polymer drag reduction, is the fact that here the input is only the mean velocity and fluid properties and no other modifications of the turbulence model are required to deal with different fluids. Further developments of the turbulence model are suggested at the end.

Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms

It is well known that the drag in a turbulent flow of a polymer solution is significantly reduced compared to Newtonian flow. Here we consider this phenomenon by means of a direct numerical simulation of a turbulent channel flow. The polymers are modelled as elastic dumbbells using the FENE-P model. In the computations the polymer model is solved simultaneously with the flow equations, i.e. the polymers are deformed by the flow and in their turn influence the flow structures by exerting a polymer stress. We have studied the results of varying the polymer parameters, such as the maximum extension, the elasticity and the concentration. For the case of highly extensible polymers the results of our simulations are very close to the maximum drag reduction or Virk (1975) asymptote. Our simulation results show that at approximately maximum drag reduction the slope of the mean velocity profile is increased compared to the standard logarithmic profile in turbulent wall flows. For the r.m.s. of the streamwise velocity fluctuations we find initially an increase in magnitude which near maximum drag reduction changes to a decrease. For the velocity fluctuations in the spanwise and wall-normal directions we find a continuous decrease as a function of drag reduction. The Reynolds shear stress is strongly reduced, especially near the wall, and this is compensated by a polymer stress, which at maximum drag reduction amounts to about 40% of the total stress. These results have been compared with LDV experiments of Ptasinski et al. (2001) and the agreement, both qualitatively and quantitatively, is in most cases very good. In addition we have performed an analysis of the turbulent kinetic energy budgets. The main result is a reduction of energy transfer from the streamwise direction, where the production of turbulent kinetic energy takes place, to the other directions. A substantial part of the energy production by the mean flow is transferred directly into elastic energy of the polymers. The turbulent velocity fluctuations also contribute energy to the polymers. The elastic energy of the polymers is subsequently dissipated by polymer relaxation. We have also computed the various contributions to the pressure fluctuations and identified how these change as a function of drag reduction. Finally, we discuss some cross-correlations and various length scales. These simulation results are explained here by two mechanisms. First, as suggested by Lumley (1969) the polymers damp the cross-stream or wall-normal velocity fluctuations and suppress the bursting in the buffer layer. Secondly, the ‘shear sheltering’ mechanism acts to amplify the streamwise fluctuations in the thickened buffer layer, while reducing and decoupling the motions within and above this layer. The expression for the substantial reduction in the wall drag derived by considering the long time scales of the nonlinear fluctuations of this damped shear layer, is shown to be consistent with the experimental data of Virk et al. (1967) and Virk (1975).

Integral space–time scales in turbulent wall flows

A direct numerical simulation of the Navier–Stokes equations is used to compute the space–time correlations of velocity fluctuations in a turbulent channel flow. By examining the autocorrelation R(ξ,τ) of the longitudinal wall shear-stress as a function of the streamwise and temporal separations, the effects of the limited extent of the computational domain when (artificial) periodic boundary conditions are used can be described and quantified. A time scale similar to the conventional integral scale but statistically related to the life time of the turbulent structures is computed from spatio-temporal data. The convection velocity, defined as the direction in the ξ,τ plane where the autocorrelations have their maximum at vanishingly small time delay, is computed as a function of the distance from the wall, and compared with the data available in the literature. Based on autocorrelations, the accuracy within which Taylor’s hypothesis is verified is quantitatively assessed. Last, the effect of the spatial discretization on the statistical characterization of wall turbulence is discussed.

Direct Numerical Simulation of Wind-Driven Turbulent Flow.

In this study, Direct numerical simulation (DNS) of wind-driven turbulent flow at the Reynolds number is about 3 300 based on the gas layer height and the free stream velocity, was conducted by the direct numerical solution procedure (MARS method) for a coupled gas-liquid flow. As the results, completely mass conservation was kept during the all calculation time and the capacity of MARS method as the method for DNS of multiphase turbulent flow indicated. In wind-driven turbulent flow, local friction coefficient in gas side was 15% decreased compared with the wall turbulent flow. Near free surface, large horizontal scale shaped the water surface wave motion supplied the velocity fluctuations to the fluid motion. But, vertical component of turbulent intensity was constrained by the water surface existence as well as turbulent open-channel flow at low Froude number. In both gas- and water-side, high and low speed streaky structures were observed and these structures and surface wave motion was interacted each other. It seems that relationships between wave height and turbulent boundary layer thickness was one of the important factors in wind-driven turbulent structure.