Low Reynolds Number Turbulent Flow Research Articles

Pressure spectra in homogeneous low Reynolds number turbulent shear flow subjected to weak rotation

In this paper, pressure spectra have been derived from the authors’ model (Eur. J. Mech., B/Fluids 12 (1) (1993) 31–42) developed by means of rapid distortion theory (RDT) of homogeneous low Reynolds number turbulent shear flow subjected to weak rotation. The combined effects of uniform shear d U 1/d x 2 and weak rotation Ω 3 on the evolution of pressure spectra have been examined in terms of the rotation number 2Ω 3/( dU 1/ dx 2) . It is found that the system rotation exhibits the opposite effect on the pressure field as compared with the influence of rotation on the velocity fluctuations.

Direct numerical simulations of low Reynolds number turbulent channel flow with EMHD control

We present results of numerical simulations of turbulence control in saltwater channel flows using electromagnetic (EM) forces. The control actuators are millimeter-sized micro-tiles flush mounted in the lower channel wall. This arrangement closely models one of the experimental designs proposed and developed by Bandyopadhyay at NUWC. We have studied two main secondary flow patterns which we denote by UV and WV (i.e., predominantly streamwise/normal and spanwise/normal) induced by both static and pulsed EM forcing. We have observed low net drag reduction, with a maximum of approximately 1%. This may be within the uncertainty of our computations. However, we have also found regions of localized reduction/increase in wall shear stress as high as ±11% versus the uncontrolled flow. Also, in every simulation with control we have observed a consistent (albeit small) reduction in skin friction which increases confidence in the results. The method of pulsing the EM force did not result in any observable resonance effects, at the low Reynolds numbers of this study. The mean turbulence intensities appear to be only weakly correlated with the reduction in viscous drag. The change in net drag does not appear to scale linearly on the magnitude of the EM forcing in the cases we have considered. Flow visualizations in the both the UV and WV cases indicate that the mean secondary flow above the actuators consists of a pair of near-wall oppositely oriented streamwise vortices which induce a flow where the normal velocity is wall-ward and is accompanied by strong spanwise wall jets.

A semi-coarsening strategy for unstructured multigrid based on agglomeration

Extending multigrid concepts to the calculation of complex compressible flow is usually not straightforward. This is especially true when non-embedded grid hierarchies or volume agglomeration strategies are used to construct a gradation of unstructured grids. In this work, a multigrid method for solving second-order PDE's on stretched unstructured triangulations is studied. The finite volume agglomeration multigrid technique originally developed for solving the Euler equations is used (M.-H. Lallemand and A. Dervieux, in Multigrid Methods, Theory, Applications and Supercomputing, Marcel Dekker, 337–363 (1988)). First, a directional semi-coarsening strategy based on Poisson's equation is proposed. The second-order derivatives are approximated on each level by introducing a correction factor adapted to the semi-coarsening strategy. Then, this method is applied to solve the Poisson equation. It is extended to the 2D Reynolds-averaged Navier–Stokes equations with appropriate boundary treatment for low-Reynolds number turbulent flows. © 1998 John Wiley & Sons, Ltd.

Passive and active control of near-wall turbulence

Wall skin friction reduction is the primary focus of this paper. Turbulent boundary layer structure and near-wall turbulence structure are considered in particular along with how passive and active modifications to the structure can lead to reductions in drag. Direct numerical simulation of low Reynolds number turbulent flow over streamwise aligned micro-grooved striations or riblets, particularly V-groove riblets and the application of a near-wall viscous model to the flow over more complicated riblet shapes (V and U groove, thin element, compound and spanwise non-continuous V-groove) are assessed. This assessment provides a qualitative basis for identifying features that may limit riblets to skin friction reduction of about 10%. This leads to consideration of three dimensional riblets or “humplets”, use of oscillations (both fluid and structural), selective interference with existing turbulence and selective introduction of new scales of turbulence with the aim always towards reducing skin friction.

Frictional Effects in Unsteady Turbulent Pipe Flows

In the simulation of rapid transient events in fluid-filled pipelines, the method of characteristics is recognized to provide reliable results during the first pressure excursion. However, if a long term oscillatory response of a rapid event is needed, traditional methods of evaluating viscous losses are inadequate in low Reynolds number turbulent flow events. This paper looks at a method to implement frequency-dependent viscous losses in the method of characteristics for turbulent flow and provides comparisons with experimental records.

Application of neural networks to turbulence control for drag reduction

A new adaptive controller based on a neural network was constructed and applied to turbulent channel flow for drag reduction. A simple control network, which employs blowing and suction at the wall based only on the wall-shear stresses in the spanwise direction, was shown to reduce the skin friction by as much as 20% in direct numerical simulations of a low-Reynolds number turbulent channel flow. Also, a stable pattern was observed in the distribution of weights associated with the neural network. This allowed us to derive a simple control scheme that produced the same amount of drag reduction. This simple control scheme generates optimum wall blowing and suction proportional to a local sum of the wall-shear stress in the spanwise direction. The distribution of corresponding weights is simple and localized, thus making real implementation relatively easy. Turbulence characteristics and relevant practical issues are also discussed.

Flow and thermal structures in a transitional boundary layer

A three-wire probe was specifically designed and fabricated to measure the flow structure and the thermal field in transitional and low Reynolds number turbulent flow. In addition to the skin friction coefficient and Stanton number on the surface, detailed measurements were made of the mean and fluctuation quantities of the flow and temperature fields in the boundary layer. The evolution of the uv profiles indicates that turbulent shear is generated near Y + = 70–100 and imposes itself on the wall within the boundary layer, ut, vt, ϵ H , ϵ M , and Pr t were measured near the end of transition and in the turbulent flow region. Pr t is shown to be greater than the typical value of 0.9 in the near-wall region. The Reynolds analogy factor (2 St/ C f) in the early turbulent flow region is approximately 0.9, which is lower than the typical value of 1.2 for turbulent flow. The data presented in this paper serve as the baseline for a series of consecutive studies related to investigating various parameters that affect laminar-turbulent transition.

Transient, turbulent, smooth pipe friction

Two of the most promising analytical models of unsteady friction in turbulent pipe flows are based on sharply contrasting hypotheses. One uses the history of the flow; the other uses instantaneous conditions. The purposes of this paper are to present an analysis using the former approach and to indicate how to determine which of the two methods is appropriate. A weighting function model of transient friction is developed for flows in smooth pipes by assuming the turbulent viscosity to vary linearly within a thick shear layer surrounding a core of uniform velocity and is thus applicable to flows at high Reynolds number. In the case of low Reynolds number turbulent flows and short time intervals, the predicted skin friction is identical to an earlier model developed by Vardy et al (1993). In the case of laminar flows, it gives results equivalent to those of Zielke (1966, 1968). The predictions are compared with analytical results for the special case of flows with uniform acceleration. It is this case that ...

Free-flight mixing and deposition of aerosols

The mechanism for the deposition of spherical aerosols on a wall is investigated in a high resolution direct numerical simulation of low Reynolds number turbulent flow in a vertical channel. A Stokes drag force is used in the equation of motion for the aerosol and the particles are assumed to have no influence on the flow field. A particle deposits when it is one radius from the wall. This occurs mainly by an inertial-free flight from distances outside the viscous sublayer. Particle concentration profiles are presented as a function of time and as a function of distance from the channel walls. It is shown that particles accumulate in the viscous sublayer by turbophoresis and by free flights that do not carry particles to the wall. A new method for identifying free-flight particles is presented and a prediction of free-flight deposition is made using fluid velocity distributions.

An Expression of Reynolds Stresses in Turbulent Lubrication Theory

This paper proposes an alternative model of Reynolds stresses for turbulent lubrication theory. The approach relies on Prandtl’s mixing length theory which is based on a modified Van Driest mixing formula [1]. However, unlike the previous theories [2, 3] the proposed equation is capable of accounting for the effect of shear stress gradient on the mixing length. Thus it is well suited to turbulent flow analysis in bearings where the presence of shear stress gradient due to the effect of pressure gradient should be considered. A series of velocity measurements in thin channels in the low Reynolds number turbulent flow range are analysed using the theory. The data analysis shows a strong effect of shear stress gradient on the viscous sublayer in the low Reynolds number regime. As a result, a new model of mixing length applicable to the turbulent lubrication analysis in thin film at low or high Reynolds numbers or under low or high shear stress gradient is presented.

Numerical simulation of buoyant, turbulent flow—I. Free convection along a heated, vertical, flat plate

Two models have been developed for predicting free convection low Reynolds number turbulent flows. The models also apply to mixed convection flows. The first, a k-ε model, is based on the notion of eddy diffusivities for momentum and heat. The second, an algebraic stress model, is based on approximations derived for the anisotropic turbulent fluxes by a suitable truncation of their conservation equations. Both formulations apply to variable property flows with high overheat ratios, ΔT T ∞ , and have not required the definition of new model constants. No attempt has been made to modify previously established values of the constants in order to improve agreement between measurements and predictions of the flow investigated. Such an optimization must await the availability of more detailed and reliable experimental measurements of turbulence-related quantities. Fully elliptic forms of the differential transport equations, subject to appropriately specified boundary conditions, have been solved numerically for two flow configurations. Both are two-dimensional. The first corresponds to free convection along a heated vertical flat plate and is the subject of Part I of this study. The second corresponds to free and mixed convection from a heated cavity of arbitrary rectangular cross-section and variable orientation, and is the subject of Part II. For the case of the vertical plate, a comparison between measurements and predictions shows that both models yield fairly accurate results for the mean flow and heat transfer. Near-wall velocity and temperature distributions predicted by both models reveal the 1 3 power-law dependence derived by George and Capp [ Int. J. Heat Mass Transfer 22, 813–826 (1979)] and confirmed for temperature by Siebers et al [ J. Heat Transfer 107, 124–132 (1985)]. Values of the constants in the power-law relations for velocity and temperature have been obtained here numerically for high and low ΔT T ∞ . Predictions of the anisotropic Reynolds stress and turbulent heat flux distributions are in good qualitative agreement with the measurements of Miyamoto et al. [ Proc. 7th Int. Heat Transfer Conference, Vol. 2, pp. 323–328 (1982)]. In particular, regions of negative buoyant and shear production of turbulent kinetic energy observed experimentally are clearly revealed by the calculations.

Numerical simulation of buoyant, turbulent flow—II. Free and mixed convection in a heated cavity

In Part I of this study two models were developed for predicting free and mixed convection low Reynolds number turbulent flows. Detailed comparisons between measurements and predictions for the case of free convection along a heated, vertical, flat plate showed that both models yield accurate results for the mean flow and heat transfer. As a result, the simpler of the two (a k- ε formulation based on the notion of eddy diffusivities for momentum and heat) was extended to predict steady free and mixed convection flows of air in a strongly heated cavity of arbitrary rectangular cross-section and orientation. This is the subject of the present communication. Numerical calculations show that the details of free convection flow in a heated cavity are strongly governed by the characteristics of the local heat transfer. The characteristics depend on the cavity aspect ratio, a b , the inclination angle, α, and the Grashof number, Gr b . For example, stable stratification of heated fluid inside a tilted cavity strongly dampens the turbulent fluctuations, thus reducing convective heat losses from the cavity. Calculations performed for the free convection cases investigated experimentally by Humphrey et al [Sandia Report No. SAND 84–8192 (1985) ; Phil. Trans. R. Soc. A316, 57–84, (1985)] show good qualitative agreement with measurements of the velocity and temperature distributions. Predictions of the Nusselt number, Nu b , display trends which are also in accord with the measurements. For mixed convection, the details of the flow become asymptotically independent of a as the ratio of inertia to buoyant forces, characterized by Re 2 b Gr b , is increased. For a b = 1 and α = 45°, predictions reveal a minimum in Nu b when Re 2 b Gr b ~ 1 . Many of the complex flow patterns revealed experimentally, for both free and mixed convection, are reproduced numerically.

Numerical Calculation of Thermally Stratified Low-Reynolds Number Turbulent Flows

Numerical Calculation of Thermally Stratified Low-Reynolds Number Turbulent Flows

Research Needs in Low Reynolds Number Flow Heat Exchangers

Low Reynolds number flows prevail in some process, power, automotive, aircraft, and other industrial heat exchangers such as shell-and-tube, plate, and compact heat exchangers. Laminar or low Reynolds number turbulent flows are the results of either high viscosity fluids, compact flow passages (i.e., small hydraulic diameter), or low fluid velocities. Significant advancements have been made in the past 100 years in understanding and predicting flow and heat transfer in such internal flows. This paper summarizes the research needs to further advance the science of low Reynolds number flow heat exchangers. Emphasis is primarily given to the thermal design aspects; research needs related to mechanical design, manufacturing, material selection, and other nonthermal design aspects are not covered. Also the coverage is restricted primarily to single-phase applications. The outlined research needs are based on the input from invited lecturers and some participants, experts in the field, at the Fourth NATO Advanced Study Institure in Ankara, Turkey, July 1981.

Turbulence intensity and time-mean velocity distributions in low reynolds number turbulent pipe flows

Measurements of the cross-sectional distributions of axial turbulence intensity and time-mean velocity in hydrodynamically developed pipe flows were made by means of a hot-film anemometer. The investigation was concerned with the low Reynolds number turbulent regime, and experiments were performed for five Reynolds numbers between 3200 and 24 000. Air was the working fluid. The present measurements, taken together with those of Laufer for high Reynolds number pipe flows (up to 500 000). establish that in the near-wall region characterized by y + up to 25, the ratio of turbulence intensity to friction velocity is independent of Reynolds number. This same relative turbulence intensity is also independent of the Reynolds number in the neighborhood of the pipe centerline. The measured time-mean velocity distributions deviate more and more from the universal u +, y + profile with decreasing Reynolds number below 10000. which corroborates the findings of previous investigations.

Low Reynolds Number Turbulent Flow in Large Aspect Ratio Rectangular Ducts

Experiments are reported on fully developed turbulent flows at low Reynolds numbers in rectangular ducts of large aspect ratio. Six ducts, with aspect ratios between 15.5:1 and 35.0:1, were employed for the investigation, covering a Reynolds number range from 5,000 to 27,000. A friction factor, Reynolds number relation expressed as f = 0.507 R−0.30 was found to be an excellent representation of the experimental data when the equivalent diameter was used as the characteristic length dimension. The Blasius and Prandtl circular tube friction factor relations, generalized by use of the equivalent diameter, gave results within 5 percent or better of the aforementioned correlation over the Reynolds number range of this investigation.

Amplification of heat transfer by local injection of fluid into a turbulent tube flow

It is demonstrated experimentally that local fluid injection into a turbulent tube flow gives rise to substantial increases in the heat transfer coefficients in the region downstream of the injection station. In the experiments, fluid was injected into a mainstream flow through a ring of discrete holes situated just upstream of an electrically heated test section. Water was the working fluid. The augmentation of the heat transfer coefficients due to injection is found to increase as the ratio of the injected flow to the test section flow increases. The extent of the augmentation is greater for low Reynolds number turbulent flows than for high Reynolds number turbulent flows.

On three-dimensional bodies of minimum drag at high supersonic speed

Wall skin friction reduction is the primary focus of this paper. Turbulent boundary layer structure and near-wall turbulence structure are considered in particular along with how passive and active modifications to the structure can lead to reductions in drag. Direct numerical simulation of low Reynolds number turbulent flow over streamwise aligned micro-grooved striations or riblets, particularly V-groove riblets and the application of a near-wall viscous model to the flow over more complicated riblet shapes (V and U groove, thin element, compound and spanwise non-continuous V-groove) are assessed. This assessment provides a qualitative basis for identifying features that may limit riblets to skin friction reduction of about 10%. This leads to consideration of three dimensional riblets or “humplets”, use of oscillations (both fluid and structural), selective interference with existing turbulence and selective introduction of new scales of turbulence with the aim always towards reducing skin friction.