Behavior Of Turbulent Boundary Layers Research Articles

On the evolution of turbulent boundary layers during flame–wall interaction investigated by highly resolved laser diagnostics

The turbulent boundary layer behavior in the presence of flame–wall interactions (FWI) has an important role on the mass and energy transfer at the gas/solid interface. Detailed experiments resolving the turbulent boundary layer evolution in the presence of FWI are lacking, which impedes knowledge. This work presents a combination of particle image velocimetry (flow field), dual-pump coherent anti-Stokes Raman spectroscopy (gas temperature), and OH laser induced fluorescence (flame topology) measurements to study the evolution of the boundary layer structure in the presence of FWI. Experiments are conducted in a side-wall quenching (SWQ) burner. Findings reveal that the reacting boundary layer flow adheres to the linear scaling law u+=y+ in the viscous sublayer until y+ = 5. Beyond y+ = 5, the flame modifies the velocity and temperature field such that the uz+ streamwise velocity deviates from the viscous sublayer and the law-of-the-wall scaling in the log-layer with uz+ being smaller than that of the non-reacting flow (the subscript z refers to the streamwise coordinate and is used throughout this manuscript). As the fluid approaches the flame impingement location at the wall, the gas temperature increases significantly, causing a threefold increase in kinematic viscosity, ν. Although the near-wall streamwise velocity gradient d〈Uz〉/dy|y=0mm decreases, the larger increase in ν reduces uz+ and leads to the deviation from the law-of-the-wall. Downstream the flame impingement location, ν is relatively constant and uz+ values begin to approach those of the law-of-the-wall. Trends are presented for SWQ and head-on quenching flame topologies, and are intended to help development of more accurate wall models.

The mean wall-normal velocity in turbulent boundary layer flows under pressure gradient

Using a combination of proper variable transformation and integral methods, we rigorously derive an analytical formulation for the mean wall-normal velocity in turbulent boundary layers (TBLs) subjected to arbitrary pressure gradients. The accuracy and robustness of this novel formulation are validated extensively through comparisons with two independent sets of numerical simulation data, demonstrating excellent agreement in both near-equilibrium and non-equilibrium TBLs. In addition, the robustness of the analytical formulations to various choices of boundary-layer edge definition is further confirmed in non-equilibrium TBLs. Our formulation includes a streamwise derivative term, which has minimal significance in near-equilibrium TBLs but plays a crucial role in determining the mean wall-normal velocity in non-equilibrium TBLs. Moreover, we investigate the physical significance of the pre-factors associated with the mean wall-normal velocity components, and unveil a close connection between a previously defined pressure gradient parameter and the ratio of these pre-factors in the analytical equation governing the mean wall-normal velocity. The insights gained from the examination of the pre-factors and their connection to the pressure gradient parameter offer valuable knowledge for interpreting and predicting the behaviour of turbulent boundary layers in various practical applications.

An experimental study on the effects of wall heating on coherent structures in a turbulent boundary layer

An experimental investigation was conducted for a better understanding of the turbulence behavior and the coherent structure in a turbulent boundary layer over a heated plate, which is horizontal facing upwards. To explore the effects of wall temperature on the turbulent boundary layer behavior, the boundary layer flow was observed at four different temperatures between the plate and inlet flow (δT=0, 15, 30, and 50 K), with the momentum Reynolds number of the inlet flow set to Reθ=1196. We show that based on the comparison of turbulent kinetic energy (TKE) distribution between unheated- and heated-wall cases, the wall-heated turbulent boundary layer can be divided into three regions, namely, the near-wall region, the intermediate region, and the outer region. The relationship between the TKE distribution and the coherent structures in each region is explored by comparing the detailed flow-field measurement results for the unheated- and heated-wall cases. In the near-wall region, the decrease in fluid viscosity caused by wall heating has stabilization effects on the turbulent fluctuation. With the increase in wall temperature, the streaky structures display a continuous decrease in their spanwise meandering and an increase in their streamwise coherency. The intermediate region ranges from the logarithmic region to the thermal boundary layer edge. The buoyant force caused by wall heating has a significant effect on the turbulence behavior in this region. Under the influence of buoyant force, the large-scale coherent structures for the wall-heating case were found to contain more kinetic energy and incline away from the wall with a larger angle, which leads to the increased TKE in the intermediate region for the wall-heating case. In the outer region, the occurrence of separated turbulent structures is measurably more common for the wall-heating case. Owing to the shedding of the turbulent structures from the turbulent production source (i.e., large-scale coherent structures originating from the near-wall region), the TKE in the outer region for the wall-heating case is less than that of the unheated case.

The effect of spanwise wavelength of surface heterogeneity on turbulent secondary flows

We examine the behaviour of turbulent boundary layers over surfaces composed of spanwise-alternating smooth and rough strips, where the width of the strips $S$ varies such that $0.32\leqslant S/\overline{\unicode[STIX]{x1D6FF}}\leqslant 6.81$ , where $\overline{\unicode[STIX]{x1D6FF}}$ is the boundary-layer thickness averaged over one spanwise wavelength of the heterogeneity. The experiments are configured to examine the influences of spanwise variation in wall shear stress over a large $S/\overline{\unicode[STIX]{x1D6FF}}$ range. Hot-wire anemometry and particle image velocimetry (PIV) reveal that the half-wavelength $S/\overline{\unicode[STIX]{x1D6FF}}$ governs the diameter and strength of the resulting mean secondary flows and hence the observed isovels of the mean streamwise velocity. Three possible cases are observed: limiting cases (either $S/\overline{\unicode[STIX]{x1D6FF}}\ll 1$ or $S/\overline{\unicode[STIX]{x1D6FF}}\gg 1$ ), where the secondary flows are confined near the wall or near the roughness change, and intermediate cases ( $S/\overline{\unicode[STIX]{x1D6FF}}\approx 1$ ), where the secondary flows are space filling and at their strongest. These secondary flows, however, exhibit a time-dependent behaviour which might be masked by time averaging. Further analysis of the energy spectrogram and fluctuating flow fields obtained from PIV show that the secondary flows meander in a similar manner to that of large-scale structures occurring naturally in turbulence over smooth walls. The meandering of the secondary flows is a function of $S/\overline{\unicode[STIX]{x1D6FF}}$ and is most prominent when $S/\overline{\unicode[STIX]{x1D6FF}}\approx 1$ .

Modeling of In-Line Tube Banks Inside Advanced Gas-Cooled Reactor Boilers

The objective of this research is the prediction of forced convection across confined in-line tube banks found in Advanced Gas-Cooled Reactor (AGR) boiler systems. The focus of this work is periodic flow about a 2 × 2 array. A number of Reynolds-Averaged Navier–Stokes (RANS) turbulence modeling closures have been applied to the challenging case of 1.6 pitch-to-diameter spacing at which flow undergoes transition from straight to diagonal. In contrast to Large Eddy Simulation (LES) predictions, those of RANS models fail to predict transition to diagonal flow. As LES computations are not anticipated to become routine enough for the purpose of flow diagnostics in industrial contexts for many years, further refinement to the RANS methodology in the form of an analytical wall function is one of the main objectives. Its eventual inclusion is not only expected to improve the representation of turbulent boundary layer behavior, but also has scope to account for augmented surface roughness effects experienced by AGR technologies nearing their end-of-life. This work is ultimately in aid of EDF Energy’s policy of AGR lifetime extensions, to allow the UK Government sufficient time to formulate a credible Nuclear New Build scheme to secure our energy requirements in the coming decades. It was found that all but dynamic LES adequately reproduces flow behavior across all criteria considered, and that standard wall functions left much to be desired in the case of flow and thermal predictions, while introducing the analytical wall function generates improvements for flow and heat transfer predictions that are not universally shared between high-Re models utilized.

Experimental Investigation of the Flow Over Single and Successive Hills on Smooth and Rough Walls

This paper describes a laboratory study of the behavior of turbulent boundary layers in the presence of two-dimensional hills. Flow measurements of the developing turbulent boundary layer on a single hill and on two successive hills are performed in a wind tunnel. The mean and turbulent velocities are measured by PIV anemometry. The results provide a detailed description of the inner layers upstream and above the hills in the separation recirculation zones. The deduced mean and fluctuating velocity fields are compared for the flow in the presence of a single hill and two successive hills located on smooth and rough walls.

Understanding Tow Tank Measurements of Total Drag for Long Thin Circular Cylinders

Both the experimental measurements and numerical computations tell us that thin circular cylinders own turbulent boundary layer (TBL) characteristics which are dissimilar from planar geometries once the TBL thickness (δ) exceeds the cylinder radius. But the exceedingly long cylinders that serve as acoustic array systems have resorted to tow tank measurements due to the experimental complexities of axial sag or the required simplifications for efficient predictions. One key measurement in the tow tank experiments is the total drag, where the respective average tangential coefficients have been assessed relative to various scaled cylinder lengths, such as the length-based Reynolds number. We now know that the skin friction whose axial summation provides the total drag is governed by the radius-based Reynolds number as well. Herein, we revisit the many tow tank experiments to isolate the measurement discrepancies attributed to these two distinct Reynolds numbers. Once separated, these measurements provide a vital answer to the transformation of the TBL spatial growth to a temporal one (no additional net δ growth). This final stage is readily identifiable by a streamwise constant skin friction as given by near-wall flow homogeneity. This understanding lends subsequent evaluation of the TBL momentum thickness at the cylinder trailing edge. The present process involves applying several semiempirical expressions formed from the experimental and numerical evidence that supply the spatially evolving TBL characteristics along thin cylinders. Besides gaining an enhanced understanding of the TBL behavior, these semiempirical expressions are further clarified to form a final set that are helpful for design engineers of tow array devices in the military and oceanographic communities.

Effects of Simple Wall-Mounted Cylinder Arrangements on a Turbulent Boundary Layer

Effects of Simple Wall-Mounted Cylinder Arrangements on a Turbulent Boundary Layer

A parametric study of adverse pressure gradient turbulent boundary layers

There are many open questions regarding the behaviour of turbulent boundary layers subjected to pressure gradients and this is confounded by the large parameter space that may affect these flows. While there have been many valuable investigations conducted within this parameter space, there are still insufficient data to attempt to reduce this parameter space. Here, we consider a parametric study of adverse pressure gradient turbulent boundary layers where we restrict our attention to the pressure gradient parameter, β, the Reynolds number and the acceleration parameter, K. The statistics analyzed are limited to the streamwise fluctuating velocity. The data show that the mean velocity profile in strong pressure gradient boundary layers does not conform to the classical logarithmic law. Moreover, there appears to be no measurable logarithmic region in these cases. It is also found that the large-scale motions scaling with outer variables are energised by the pressure gradient. These increasingly strong large-scale motions are found to be the dominant contributor to the increase in turbulence intensity (scaled with friction velocity) with increasing pressure gradient across the boundary layer.

Experimental investigation of turbulent boundary layers over steep two-dimensional elevations

This work presents a laboratory study on the behavior of turbulent boundary layers over steep topographic elevations. Two main topics of interest are addressed here: (i) to investigate and characterize the separated flow region that is formed on the leeside of a steep elevation, and (ii) to evaluate the effects of flow stability conditions on the properties of boundary layers also subject to surface changes in elevation. To carry out this task, water channel and wind-tunnel investigations were conducted. For the former research topic, a neutrally stratified boundary layer was simulated in the water-channel of the Hydraulics Laboratory of FEUP. Mean and turbulent velocities were measured through laser-Doppler anemometry. Results provided a thorough description of the inner layers along the hill and inside the recirculation region. The refined near-wall data has contributed to the calculation of the friction velocity along the hill through different methods. For the latter topic, neutral, stable and unstable boundary layers were simulated in a wind-tunnel in the Laboratory of Turbulence Mechanics of COPPE/UFRJ. Simultaneous velocity and temperature fields were measured with the aid of thermal anemometry. These results allowed the characterization of the effects of the stratification on the speed-up factor, i.e. the maximum acceleration of the flow on hilltop. The present paper has introduced the concept of the heat up/down factor, in order to study the behaviour of the temperature field on the crest of the elevation.

A note on the overlap region in turbulent boundary layers

Two independent experimental investigations of the behavior of turbulent boundary layers with increasing Reynolds number were recently completed. The experiments were performed in two facilities, the Minimum Turbulence Level (MTL) wind tunnel at Royal Institute of Technology (KTH) and the National Diagnostic Facility (NDF) wind tunnel at Illinois Institute of Technology (IIT). Both experiments utilized oil-film interferometry to obtain an independent measure of the wall-shear stress. A collaborative study by the principals of the two experiments, aimed at understanding the characteristics of the overlap region between the inner and outer parts of the boundary layer, has just been completed. The results are summarized here, utilizing the profiles of the mean velocity, for Reynolds numbers based on the momentum thickness ranging from 2500 to 27 000. Contrary to the conclusions of some earlier publications, careful analysis of the data reveals no significant Reynolds number dependence for the parameters describing the overlap region using the classical logarithmic relation. However, the data analysis demonstrates that the viscous influence extends within the buffer region to y+≈200, compared to the previously assumed limit of y+≈50. Therefore, the lowest Reθ value where a significant logarithmic overlap region exists is about 6000. This probably explains why a Reynolds number dependence had been found from the data analysis of many previous experiments. The parameters of the logarithmic overlap region are found to be constant and are estimated to be κ=0.38, B=4.1 and B1=3.6 (δ=δ95).

On the Shear-Stress Integral of Turbulent Boundary Layers

The paper presents an integral method to predict turbulent boundary layer behavior in two-dimensional, incompressible flow. The method is based on the momentum and moment-of-momentum integral equations and a friction law. By means of the compiled data of the 1968 Stanford Conference, the results show that the integral of the turbulent shear stress across the boundary layer, which appears in the moment-of-momentum integral equation, can be described using only two basic assumptions for all cases of flow.

Boundary layer in compressible flow of wet water vapour

In this paper the influence of small droplets, with radius 10 −8 m < r < 10 −6 m , on laminar and turbulent boundary layer behavior is considered. It is found that the laminar boundary layer in a two-phase flow with strongly dispersed liquid retains dissipation energy and that the recovery factor of enthalpy is greater than unity. In turbulent boundary layers small droplets are transported by turbulent diffusion and this leads to the recovery factor being less than unity. Its value in both cases depends mainly on the nondimensional number Ds = C LeL/(U e 2/2) . The laminar boundary layer solution for non-equilibrium two-phase flow is obtained. Profiles of the droplet mass fraction, vapour and droplets temperatures and droplet radius are computed for the case of a steady two-dimensional flow. The turbulent boundary layer is treated using a semi-empirical theory assuming thermodynamic equilibrium.

The Turbulent Boundary Layer Near a Corner

Turbulent boundary-layer behavior in the vicinity of a right-angle corner formed by intersecting flat plates is considered. Due to interference effects a secondary flow is induced. Numerical solutions are obtained for the main stream and secondary motion. Models with and without intermittency factors are considered. It is shown that the secondary motion is significantly different for laminar and turbulent conditions. Similar behavior has previously been observed experimentally.

On the Behavior of Turbulent Boundary Layers near Separation

Theme O NE of the most important problems in aerodynamics is the phenomenon of separation that defines the initiation of the wake. The location of separation can be determined analytically by virtue of the boundary-layer theory, even though this theory is not valid in the immediate neighborhood of separation. In most practical applications the boundary layers are turbulent along the largest portion of the solid boundaries and most often, in the vicinity of separation. A large number of methods have been developed to solve the turbulent boundary-layer equations with an appropriate closure assumption, but a straightforward numerical integration in their differential form was attempted only in the late sixties. A number of such investigations is referenced in the accompanying engineering report of this paper.{ For steady laminar and turbulent boundary-layer flow the location of separation is signaled by the vanishing of the wall shear. This criterion has been extensively used in laminar flows for both experimental and analytical investigations.2 However, for turbulent flow the use of simplified theoretical models has forced investigators to develop heuristic criteria based on approximate expressions that approach certain values in the neighborhood of separation. The present report reconsiders the problem of turbulent separation. The classical closure assumptions are restated and their applicability in the neighborhood of separation is discussed. Some typical features of the flow are checked against available experimental data and previous theoretical predictions. Further, the location of separation is calculated and the response of the boundary-layer equations in the neighborhood of separation is carefully investigated. The present effort is intended to be a step towards the generalization of the method to unsteady flow.

Effect of free stream turbulence on the turbulent boundary layer

It is pointed out in the present study that by allowing the entrainment of free stream turbulence into the turbulent boundary layer and performing an overall turbulent energy balance, very satisfactory quantitative predictions of the effect of free stream turbulence upon the turbulent boundary layer behavior can be made. Furthermore, both theory and experiment indicate a 30 per cent increase in wall friction arising from a free stream turbulence level of only 5 per cent. Since it is felt that some sort of Reynolds analogy would hold, it is suggested that the frequently quoted result of little direct effect of free stream turbulence level on the heat transfer other than a movement of the transition point may be valid only at low Reynolds numbers.

A Wake and an Eddy in a Rotating, Radial-Flow Passage—Part 2: Flow Model

Rotational and three-dimensional terms are added to a strip-integral method for predicting the behavior of turbulent boundary layers. The secondary flow in the boundary layers is analyzed, and a theory for the momentum transport in the corner regions is used to couple the development of all the boundary layers. Simple assumptions for the potential flow and wake regions complete a model which allows the calculation of the whole channel flow, with only the specification of the inlet boundary layers.

Turbulent Boundary Layers

In this lecture I hope to bring together the two branches of turbulence studies, (1) the fundamental study of the physics and mathematics of turbulent flow and (2) the methods of calculating turbulent flow development which are used by aircraft designers and other fluid dynamicists. While it is entirely reasonable that aircraft designers should wish to predict the behaviour of turbulent boundary layers without going deeply into the physical processes which govern their development, it is by no means reasonable that those who develop calculation methods in the first place should ignore the physics of the flow, or represent it by simple-minded formulae chosen for mathematical convenience rather than physical plausibility. Turbulence is not a simple phenomenon! The more naive integral methods that were in vogue until a few years ago have been disposed of once and for all by Thompson. The only method that emerged from Thompson’s review with any credit was Head’s entrainment method, which was distinguished from most of the other integral methods by being based on a clear physical hypothesis about turbulent flow. Head himself regarded this hypothesis as a very crude attempt to represent the entrainment properties of the turbulence, and indeed it is easy to see that this sort of hypothesis must fail in some of the more difficult situations.

A Contribution to the Theory of Turbulence

S of the problem of Wind-Tunnel Turbulence have recently been published by Taylor, von Karman, and Dryden. These studies are concerned with the decay of homogeneous isotropic turbulence. The scale and intensity of the turbulence is assumed to be known at a given instant throughout the fluid and the decay with respect to time is asked for. In this note the authors investigate the turbulence produced at a constant rate in the boundary, and decaying in a direction normal to the surface of generation. This problem, so far as the authors are aware, has not been treated before. The problem becomes especially simple if one considers a fluid in a semiinfinite space bounded by a plane along which the turbulence is produced. The mean motion is assumed to be constant throughout and parallel to the plane. This investigation is not only of theoretical interest but should be useful in the study of the behavior of turbulent boundary layers, and might be of help in the study of the influence of surface roughness. The stated problem can be treated by means of the equation of the statistical theory of turbulence recently proposed by von Karman. It furthermore might serve as the basis for an experiment in which the consequences of the theory can be tested. The considered turbulent motion has statistically an isotropic character due to the absence of mean shear stresses, i.e., the correlations of the velocity components at a certain point in the space with respect to a set of orthogonal axes are independent of the rotation of this system. The turbulence, however, is not homogeneous, since the correlations are functions of the distance from the boundary. Consider a space with the orthogonal axes xiy x2} x3, in which the fluid is bounded by a (xix3) plane and has a, constant mean velocity U in the X direction. The

On the Separation of Turbulent Boundary Layers

S T U D E N T S of fluid mechanics agree now rather generally that the separation of the boundary layer from a wing surface is the cause of burbling and is responsible, therefore, for the complicated phenomena near the stall. There is consequently a great practical as well as scientific interest in obtaining an analytical method of predicting such separation. One method of analyzing flow separation in the case of a turbulent boundary layer was proposed by Gruschwitz and seemed to offer a practical solution. The limited experimental evidence in favor of this method, however, was not sufficient to command confidence in its general application. In the present research an attempt was made to verify the Gruschwitz method by an extended experimental examination of the turbulent boundary layer over a typical wing profile at high Reynolds Numbers. The data here presented lead to the conclusion that the Gruschwitz method does not describe the actual phenomena and is, therefore, not the general solution hoped for. The evidence now seems to point to a dependence of flow separation upon several other variables besides the pressure gradient and the thickness of the boundary layer which need further experimental examination. Such investigation is now under way at the Massachusetts Institute of Technology and a further report will be made in a subsequent paper. The mechanics of flow separation depends upon the motion of the air within the boundary layer. The particles within the boundary layer are retarded by the surface friction and are usually carried against a rising pressure by the momentum transferred to them from outside of the boundary. If the pressure rise is sufficient the particles lose energy, come to rest, and separation occurs. If the momentum is transferred from the exterior stream by molecular exchange purely, the motion is defined as laminar, while the motion is defined as turbulent if the exchange is molar. All boundary layers begin at a stagnation point and remain laminar for a certain distance downstream whatever may be the character of the exterior flow or of the surface. If the prevailing velocity is sufficiently high and the surface sufficiently large, however, the layer will become turbulent and continue so throughout the remainder of its length. The chief characteristic which distinguishes the turbulent flow from the laminar is its much greater ability to transport momentum laterally. This gives it a correspondingly greater ability to proceed against a rising pressure. The separation of laminar boundary layers has recently been studied by von Karman and Millikan who explained the variation of the maximum lift coefficient with low Reynolds numbers in the case of certain wing profiles. The separation of the turbulent boundary layer, however, is of greater importance at the higher Reynolds numbers used in engineering since it is responsible for most of the burbling phenomena met in practice. The studies presented here are an outgrowth of a recent investigation by Gruschwitz on the behavior of turbulent boundary layers for various pressure gradients. Since this method is used for comparison with the experimental data here reported, it will be well to review it briefly.