Direct numerical simulation of the incompressible temporally developing turbulent boundary layer

2016 ◽  
Vol 796 ◽  
pp. 437-472 ◽  
Author(s):  
M. Kozul ◽  
D. Chung ◽  
J. P. Monty
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Initial Conditions ◽  
Reynolds Numbers ◽  
Momentum Thickness ◽  
Temporal Boundary ◽  
Set Up

We perform a direct numerical simulation (DNS) investigation of the incompressible temporally developing turbulent boundary layer. The approach is inspired by temporal simulations of flows which are generally thought of as developing in space, such as wakes and mixing layers. Compressible boundary layers have previously been studied in this manner yet the temporal approach appears to be under-exploited in the literature concerning incompressible boundary layers. The flow is the turbulent counterpart to the laminar Rayleigh problem or Stokes’ first problem, in which a fluid at rest is set into motion by a wall moving at constant velocity. An initial profile that models the effect of a wall-mounted trip wire is implemented and allows the characterisation of initial conditions by a trip Reynolds number. For the current set-up, a trip Reynolds number of 500 based on the trip-wire diameter successfully triggers transition yet only mildly perturbs the flow so it assumes a natural development at the lowest possible Reynolds number based on momentum thickness. A systematic trip study reveals that as the ratio of momentum thickness to trip-wire diameter approaches unity, our flow approaches a state free from the effects of its starting trip Reynolds number. The transport of a passive scalar by this flow is also simulated. The role played by domain size is investigated with two boxes, sized to accommodate two chosen final Reynolds numbers. Comparisons of the skin friction coefficient, velocity and scalar statistics demonstrate that the temporally developing boundary layer is a good model for the spatially developing boundary layer once initial conditions can be neglected. Analysis of similarity solutions suggests such a rapprochement of the spatial and temporal boundary layers may be expected at high Reynolds numbers given that the only terms that asymptotically persist are those common to both cases. If one seeks statistics for the turbulent boundary layer, the temporal boundary layer is therefore a viable method if modest convergence is sufficient. We suggest that such a temporal set-up could prove useful in the study of turbulence dynamics.

Evolution of zero-pressure-gradient boundary layers from different tripping conditions

2015 ◽  
Vol 783 ◽  
pp. 379-411 ◽  
Author(s):  
I. Marusic ◽  
K. A. Chauhan ◽  
V. Kulandaivelu ◽  
N. Hutchins
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Initial Conditions ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Mean Flow ◽  
Flow Parameters ◽  
The Mean ◽  
Inflow Conditions

In this paper we study the spatial evolution of zero-pressure-gradient (ZPG) turbulent boundary layers from their origin to a canonical high-Reynolds-number state. A prime motivation is to better understand under what conditions reliable scaling behaviour comparisons can be made between different experimental studies at matched local Reynolds numbers. This is achieved here through detailed streamwise velocity measurements using hot wires in the large University of Melbourne wind tunnel. By keeping the unit Reynolds number constant, the flow conditioning, contraction and trip can be considered unaltered for a given boundary layer’s development and hence its evolution can be studied in isolation from the influence of inflow conditions by moving to different streamwise locations. Careful attention was given to the experimental design in order to make comparisons between flows with three different trips while keeping all other parameters nominally constant, including keeping the measurement sensor size nominally fixed in viscous wall units. The three trips consist of a standard trip and two deliberately ‘over-tripped’ cases, where the initial boundary layers are over-stimulated with additional large-scale energy. Comparisons of the mean flow, normal Reynolds stress, spectra and higher-order turbulence statistics reveal that the effects of the trip are seen to be significant, with the remnants of the ‘over-tripped’ conditions persisting at least until streamwise stations corresponding to $Re_{x}=1.7\times 10^{7}$ and $x=O(2000)$ trip heights are reached (which is specific to the trips used here), at which position the non-canonical boundary layers exhibit a weak memory of their initial conditions at the largest scales $O(10{\it\delta})$, where ${\it\delta}$ is the boundary layer thickness. At closer streamwise stations, no one-to-one correspondence is observed between the local Reynolds numbers ($Re_{{\it\tau}}$, $Re_{{\it\theta}}$ or $Re_{x}$ etc.), and these differences are likely to be the cause of disparities between previous studies where a given Reynolds number is matched but without account of the trip conditions and the actual evolution of the boundary layer. In previous literature such variations have commonly been referred to as low-Reynolds-number effects, while here we show that it is more likely that these differences are due to an evolution effect resulting from the initial conditions set up by the trip and/or the initial inflow conditions. Generally, the mean velocity profiles were found to approach a constant wake parameter ${\it\Pi}$ as the three boundary layers developed along the test section, and agreement of the mean flow parameters was found to coincide with the location where other statistics also converged, including higher-order moments up to tenth order. This result therefore implies that it may be sufficient to document the mean flow parameters alone in order to ascertain whether the ZPG flow, as described by the streamwise velocity statistics, has reached a canonical state, and a computational approach is outlined to do this. The computational scheme is shown to agree well with available experimental data.

Momentum Thickness Measurements for Thick Axisymmetric Turbulent Boundary Layers

2003 ◽  
Vol 125 (3) ◽  
pp. 569-575 ◽  
Author(s):  
Kimberly M. Cipolla ◽  
William L. Keith
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Boundary Layers ◽  
Control Volume ◽  
Scaling Law ◽  
Reynolds Numbers ◽  
Momentum Thickness ◽  
Spatial Growth ◽  
Thickness Measurements

Experimental measurements of the mean wall shear stress and boundary layer momentum thickness on long, thin cylindrical bodies are presented. To date, the spatial growth of the boundary layer and the related boundary layer parameters have not been measured for cases where δ/a (a=cylinder radius) is much greater than one. Moderate Reynolds numbers 104<Reθ<105 encountered in hydrodynamic applications are considered. Tow tests of cylinders with diameters of 0.61, 0.89, and 2.5 mm and lengths ranging from approximately 30 meters to 150 meters were performed. The total drag (axial force) was measured at tow speeds up to 17.4 m/sec. These data were used to determine the tangential drag coefficients on each test specimen, which were found to be two to three times greater than the values for the corresponding hypothetical flat-plate cases. Using the drag measurements, the turbulent boundary layer momentum thickness at the downstream end of the cylindrical bodies is determined, using a control volume analysis. The results show that for the smallest diameter cylinders, there is no indication of relaminarization, and a fully developed turbulent boundary layer exists. A scaling law for the momentum thickness versus length Reynolds number is determined from the data. The results indicate that the spatial growth of the boundary layers over the entire length is less than for a comparable flat-plate case.

Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects

2012 ◽  
Vol 710 ◽  
pp. 5-34 ◽  
Author(s):  
Philipp Schlatter ◽  
Ramis Örlü
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Reynolds Numbers ◽  
Normal Velocity ◽  
Low Reynolds ◽  
Inflow Conditions

AbstractA recent assessment of available direct numerical simulation (DNS) data from turbulent boundary layer flows (Schlatter & Örlü,J. Fluid Mech., vol. 659, 2010, pp. 116–126) showed surprisingly large differences not only in the skin friction coefficient or shape factor, but also in their predictions of mean and fluctuation profiles far into the sublayer. While such differences are expected at very low Reynolds numbers and/or the immediate vicinity of the inflow or tripping region, it remains unclear whether inflow and tripping effects explain the differences observed even at moderate Reynolds numbers. This question is systematically addressed by re-simulating the DNS of a zero-pressure-gradient turbulent boundary layer flow by Schlatteret al. (Phys. Fluids, vol. 21, 2009, art. 051702). The previous DNS serves as the baseline simulation, and the new DNS with a range of physically different inflow conditions and tripping effects are carefully compared. The downstream evolution of integral quantities as well as mean and fluctuation profiles is analysed, and the results show that different inflow conditions and tripping effects do indeed explain most of the differences observed when comparing available DNS at low Reynolds number. It is further found that, if transition is initiated inside the boundary layer at a low enough Reynolds number (based on the momentum-loss thickness)${\mathit{Re}}_{\theta } \lt 300$, all quantities agree well for both inner and outer layer for${\mathit{Re}}_{\theta } \gt 2000$. This result gives a lower limit for meaningful comparisons between numerical and/or wind tunnel experiments, assuming that the flow was not severely over- or understimulated. It is further shown that even profiles of the wall-normal velocity fluctuations and Reynolds shear stress collapse for higher${\mathit{Re}}_{\theta } $irrespective of the upstream conditions. In addition, the overshoot in the total shear stress within the sublayer observed in the DNS of Wu & Moin (Phys. Fluids, vol. 22, 2010, art. 085105) has been identified as a feature of transitional boundary layers.

Pressure statistics and their scaling in high-Reynolds-number turbulent boundary layers

2007 ◽  
Vol 585 ◽  
pp. 1-40 ◽  
Author(s):  
Y. TSUJI ◽  
J. H. M. FRANSSON ◽  
P. H. ALFREDSSON ◽  
A. V. JOHANSSON
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Pressure Fluctuations ◽  
Reynolds Numbers ◽  
Turbulent Boundary Layers ◽  
Local Pressure ◽  
Fluctuating Pressure ◽  
High Reynolds

Pressure fluctuations are an important ingredient in turbulence, e.g. in the pressure strain terms which redistribute turbulence among the different fluctuating velocity components. The variation of the pressure fluctuations inside a turbulent boundary layer has hitherto been out of reach of experimental determination. The mechanisms of non-local pressure-related coupling between the different regions of the boundary layer have therefore remained poorly understood. One reason for this is the difficulty inherent in measuring the fluctuating pressure. We have developed a new technique to measure pressure fluctuations. In the present study, both mean and fluctuating pressure, wall pressure, and streamwise velocity have been measured simultaneously in turbulent boundary layers up to Reynolds numbers based on the momentum thickness Rθ ≃ 20000. Results on mean and fluctuation distributions, spectra, Reynolds number dependence, and correlation functions are reported. Also, an attempt is made to test, for the first time, the existence of Kolmogorov's -7/3 power-law scaling of the pressure spectrum in the limit of high Reynolds numbers in a turbulent boundary layer.

A Comparison of Turbulent Boundary Layer Wall-Pressure Spectra

1992 ◽  
Vol 114 (3) ◽  
pp. 338-347 ◽  
Author(s):  
W. L. Keith ◽  
D. A. Hurdis ◽  
B. M. Abraham
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Scaling Laws ◽  
Wall Pressure ◽  
Experimental Investigations ◽  
Length Scale ◽  
Momentum Thickness ◽  
Insight Into

Turbulent boundary layer wall-pressure spectra from various experimental investigations and a recent numerical simulation are presented. The spectra are compared in nondimensional form with three commonly used scaling laws. Attenuations resulting from inadequate sensor spatial resolution are shown to be of primary importance at the higher frequencies. The dependence of the scaling laws on momentum thickness Reynolds number is discussed. The ratio of the outer to the inner boundary layer length scale is shown to provide insight into the observed trends in the spectra.

Prediction of Turbulent Boundary Layer Development in Conical Diffusers

1966 ◽  
Vol 8 (4) ◽  
pp. 426-436 ◽  
Author(s):  
A. D. Carmichael ◽  
G. N. Pustintsev
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Turbulent Boundary Layers ◽  
Energy Deficit ◽  
Momentum Thickness ◽  
Boundary Layer Development ◽  
Layer Development

Methods of predicting the growth of turbulent boundary layers in conical diffusers using the kinetic-energy deficit equation were developed. Three different forms of auxiliary equations were used. Comparison between the measured and predicted results showed that there was fair agreement although there was a tendency to underestimate the predicted momentum thickness and over-estimate the predicted shape factor.

scholarly journals Assessment of inner–outer interactions in the urban boundary layer using a predictive model

2019 ◽  
Vol 875 ◽  
pp. 44-70 ◽  
Author(s):  
Karin Blackman ◽  
Laurent Perret ◽  
Romain Mathis
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Predictive Model ◽  
Boundary Layers ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Limited Range ◽  
Rough Wall ◽  
Wall Boundary ◽  
Layer Flow

Urban-type rough-wall boundary layers developing over staggered cube arrays with plan area packing density, $\unicode[STIX]{x1D706}_{p}$, of 6.25 %, 25 % or 44.4 % have been studied at two Reynolds numbers within a wind tunnel using hot-wire anemometry (HWA). A fixed HWA probe is used to capture the outer-layer flow while a second moving probe is used to capture the inner-layer flow at 13 wall-normal positions between $1.25h$ and $4h$ where $h$ is the height of the roughness elements. The synchronized two-point HWA measurements are used to extract the near-canopy large-scale signal using spectral linear stochastic estimation and a predictive model is calibrated in each of the six measurement configurations. Analysis of the predictive model coefficients demonstrates that the canopy geometry has a significant influence on both the superposition and amplitude modulation. The universal signal, the signal that exists in the absence of any large-scale influence, is also modified as a result of local canopy geometry suggesting that although the nonlinear interactions within urban-type rough-wall boundary layers can be modelled using the predictive model as proposed by Mathis et al. (J. Fluid Mech., vol. 681, 2011, pp. 537–566), the model must be however calibrated for each type of canopy flow regime. The Reynolds number does not significantly affect any of the model coefficients, at least over the limited range of Reynolds numbers studied here. Finally, the predictive model is validated using a prediction of the near-canopy signal at a higher Reynolds number and a prediction using reference signals measured in different canopy geometries to run the model. Statistics up to the fourth order and spectra are accurately reproduced demonstrating the capability of the predictive model in an urban-type rough-wall boundary layer.

A Simplified Form of the Auxiliary Equation for Use in the Calculation of Turbulent Boundary Layers

1958 ◽  
Vol 62 (567) ◽  
pp. 215-219
Author(s):  
T. J. Black
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Auxiliary Equation ◽  
Pressure Gradients ◽  
Momentum Thickness ◽  
Form Parameter ◽  
New Type ◽  
Simple Quadrature

A New type of auxiliary equation is given for calculating the development of the form-parameter H in turbulent boundary layers with adverse pressure gradients. The chief advantage of this new method lies in the rapidity and ease of calculation which has been achieved, without apparent sacrifice of accuracy.Whereas the growth of momentum thickness in the turbulent boundary layer can now be rapidly calculated by methods involving only simple quadrature, the prediction of the form parameter development remains a laborious task, while the results obtained do not always appear to justify the complexity of the calculations.

Hydroacoustics of Transitional Boundary-Layer Flow

1991 ◽  
Vol 44 (12) ◽  
pp. 517-531 ◽  
Author(s):  
Gerald C. Lauchle
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Boundary Layer Flow ◽  
Pressure Fluctuations ◽  
Local Pressure ◽  
Turbulent Spots ◽  
Layer Flow

Transitional boundary layers exist on surfaces and bodies operating in viscous fluids at speeds such that the critical Reynolds number based on the distance from the leading edge is exceeded. The transition region is composed of a simultaneous mixture of both laminar and turbulent regimes occurring randomly in space and time. The turbulent regimes are known as turbulent spots, they grow rapidly with downstream distance, and they ultimately coalesce to form the beginning of fully-developed turbulent boundary-layer flow. It has been long suspected that such a region of unsteadiness may give rise to local pressure fluctuations and radiated sound that are different from those created by the fully-developed turbulent boundary layer at equivalent Reynolds number. This article reviews the available literature on this subject. The emphasis of this literature is on natural and artificially created transitional boundary layers under mostly incompressible conditions; hence, the word hydroacoustics in the title. The topics covered include the dynamics and local wall pressure fluctuations due to the passage of turbulent spots created in a deterministic way, the pressure fluctuations under transitioning boundary layers where the formation and location of spots are random, and the acoustic radiation from transition and its pre-cursor, the Tollmien-Schlichting waves. The majority of this review is for zero-pressure gradient flat plate flows, but the limited literature on axisymmetric body and plate flows with pressure gradient is included.

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