Reynolds Number Dependence Research Articles

Spatio-temporal characteristics of temperature fluctuations in turbulent non-premixed jet flames

We report new results from high-repetition-rate (10kHz) 2D temperature imaging to characterize the temporally-fluctuating nature of the well-known DLR series of turbulent non-premixed jet flames. Specifically, we present temporally-based statistics of temperature fluctuations at multiple simultaneous spatial positions with a specific focus on characterizing the effects of Reynolds number. DLR B (Re=22,800) was found to exhibit a much higher probability of large temporal gradients as compared to DLR A (Re=15,200). While the higher Reynolds number should promote higher fluctuations, the levels were commensurate with an increased effect due to high levels of local flame extinction and re-ignition in DLR B as compared to DLR A. The joint probability density function between the temperature fluctuation and the natural logarithm of the square of the temporal gradient was examined across flame conditions. At an axial position of forty nozzle diameters downstream (x/d=40), DLR A exhibited statistical independence, while DLR B exhibited a negative correlation between the two quantities. These results suggest a Reynolds number-dependence on the spatial development of statistical independence. Integral time scales also are reported for both flames as a function of axial and radial position. The integral time scales are seen to increase with increasing axial and radial position and decrease with increasing Reynolds number as expected from theory.

Reynolds number dependence of flow past a shallow open cavity

Measurements were carried out in a shallow open cavity with particle image velocimetry technique. The cavity has a length- to-depth ratio of 4:1, and the upstream inflow conditions include laminar, transient, and turbulent regimes at seven different Reynolds numbers. The measured instantaneous velocities were analyzed through ensemble average, vortex extraction, and proper orthogonal decomposition (POD) to investigate overall flow circulations, Reynolds stress distribution, spanwise vortex population, and the characteristics of the POD modes. The results reveal distinctive Reynolds number dependence of the cavity flow, e.g. an increase in Reynolds number results in constant migration of the overall circulation, enhancement of Reynolds stress, reduction of correlation between vortex and Reynolds stress, and decrease of fractional energy of the characteristic POD modes. Finally, a phenomenological model was proposed to describe various features of cavity flow.

Reynolds number effects on aerodynamic characteristics and vortex-induced vibration of a twin-box girder

An experimental investigation of Reynolds number effects on aerodynamic characteristics and vortex-induced vibration (VIV) of a twin-box girder was performed. The Reynolds number is in the range of 5.85×103≤Re≤1.12×105 when using the central height of the twin-box girder as the characteristic length. The pressure distributions, aerodynamic force and vortex-shedding frequency at various Reynolds numbers were investigated. The results indicate that all the aerodynamic characteristics have obvious Reynolds number sensitivity. According to the mean and fluctuating pressure distributions, the leading separated bubble length on the lower surface was obtained. With increases in Reynolds number, the transition point from laminar flow to turbulence flow and the reattachment point of the separated shear layer gradually move upstream, and the bubble size shrinks. Simultaneously, the drag force coefficient decreases, whereas the Strouhal number increases. In addition, the bubble length has a good linear relationship with the drag force coefficient and with the Strouhal number. The Reynolds number effects on the VIV of a twin-box girder were investigated at three Reynolds number levels: Re=[6.47×103–7.93×103], [1.17×104–1.62×104] and [1.87×104–2.90×104]. The results indicate that the VIV of a twin-box girder has significant Reynolds number dependence. The peak amplitude of the VIV increases with increase in the Reynolds number. The relationship between the peak amplitude of the VIV of the twin-box girder and the Skop–Griffin number at various Reynolds numbers was obtained, which can be employed to predict the peak amplitude of VIV.

Large eddy simulation of smooth–rough–smooth transitions in turbulent channel flows

We describe a high Reynolds number large-eddy-simulation (LES) study of turbulent flow in a long channel of length 128 channel half heights, δ, with the walls consisting of roughness strips where the long stream-wise extent invites a full relaxation of the mean velocities within each strip. The channel is stream-wise periodic and strips are oriented transverse to the flow resulting in repeated transitions between smooth and rough surfaces along the stream-wise direction. The present LES uses a wall model that contains Colebrook’s empirical formula as a roughness correction to both the local and dynamic calculation of the friction velocity and also the LES wall boundary condition. This operates point-wise across wall surfaces, and hence changes in the outer flow can be viewed as a response to the temporally and/or spatially variant roughness distribution. At the wall surface, dynamically calculated levels of time- and span-wise-averaged friction velocity uτ‾(x) over/undershoot and then fully recover towards their smooth or rough state over a stream-wise distance of order 10–30δ depending on both roughness and Reynolds number. Also, the initial response rate in uτ‾ shows Reynolds number and roughness dependence over both transitions. The growth rate of the internal boundary layer (IBL), defined by the abrupt change in stream-wise turbulent intensity, is found to grow as x0.70 on average over multiple simulation conditions for the case of a smooth-to-rough transition, which agrees with the experimental results of Antonia and Luxton (1971) [1] and Efros and Krogstad (2011) [2]. IBL profiles demonstrate a good collapse on δ/log(Reτ∗), where Reτ∗ is the local Reynolds number based on uτ‾ at the point of full recovery.

Görtler instability of the axisymmetric boundary layer along a cone

Exact partial differential equations are derived to describe Görtler instability, caused by a weakly concave wall, of axisymmetric boundary layers with similar velocity profiles that are decomposed into a sequence of ordinary differential systems on the assumption that the solution can be expanded into inverse powers of local Reynolds number. The leading terms of the series solution are determined by solving a non-parallel version of Görtler’s eigenvalue problem and lead to a neutral stability curve and finite values of critical Görtler number and wave number for stationary and longitudinal vortices. Higher-order terms of the series solution indicate Reynolds-number dependence of Görtler instability and a limited validity of Görtler’s approximation based on the leading terms only. The present formulation is simply applicable to two-dimensional boundary layers of similar profiles, and critical Görtler number and wave number of the Blasius boundary layer on a flat plate are given by G2c = 1.23 and β2c = 0.288, respectively, if the momentum thickness is chosen as the reference length.

Utilization of I–Q signals of ultrasound Doppler velocimeter to obtain 1-D turbulence quantities in pipe flow

A new method based on using inphase–quadrature (I–Q) ultrasound (US) signals was developed in order to overcome time resolution limitations encountered in turbulent flow measurements by ultrasound Doppler velocimetry (UDV). First, mathematical relations to be used in obtaining probability density function (PDF) and auto correlation function (ACF) of randomly fluctuating velocity (u) in the probe direction were derived in the form of the experimental I–Q signals. The results were evaluated with respect to those obtained by UDV or other conventional techniques whenever possible. In terms of general trend, velocity PDFs obtained from analytical relation along with the I–Q signals and from UDV compare well with each other for Reynolds numbers (NRe) of 16730 and 26300 at the pipe center. Smaller standard deviation of velocity PDF from spectrum of I–Q US signals than that of UDV measurements was the only major difference that could be attributed to the enhanced time resolution of the former technique. Effect of increased time resolution was also observed in the measurement of velocity auto correlation coefficients (ACC). Time correlations of the velocity fluctuations could be captured by using I–Q signals as opposed to UDV that resulted in correlations going to zero in one or two time steps.ACC from I–Q signals was used to get turbulence spectrum at the pipe center. In addition Reynolds number and radial position dependency of integral and Taylor microlength scales, Kolmogorov length scale, rate of energy dissipation and eddy diffusion coefficient were also established.

Scale effects on a single-element inverted wing in ground effect

AbstractA study was conducted on a GA(W)-1 wing in order to investigate the effect of testing inverted wings in ground effect at low Reynolds numbers. The wing was tested at a range of ground clearances and Reynolds numbers and results showed that the wing’s performance was dependent on both these parameters. Surface flow-visualisation and numerical simulation results highlighted the existence of a laminar separation bubble on the wing’s suction surface. The results also indicated that both the bubble’s length and the onset of separation were sensitive to ground clearance and Reynolds number. Attempts were made to minimise the wing’s Reynolds number dependency by using transition strips on the suction surface. The transition strip results highlighted the influence that a laminar separation bubble has on the overall performance of the wing and how its presence alters the force enhancement and reduction mechanisms on an inverted wing in ground effect.

Swirling-strength based large eddy simulation of turbulent flow around single square cylinder at low Reynolds numbers

In view of the fact that large scale vortices play the substantial role of momentum transport in turbulent flows, large eddy simulation (LES) is considered as a better simulation model. However, the sub-grid scale (SGS) models reported so far have not ascertained under what flow conditions the LES can lapse into the direct numerical simulation. To overcome this discrepancy, this paper develops a swirling strength based the SGS model to properly model the turbulence intermittency, with the primary characteristics that when the local swirling strength is zero, the local sub-grid viscosity will be vanished. In this paper, the model is used to investigate the flow characteristics of zero-incident incompressible turbulent flows around a single square cylinder (SC) at a low Reynolds number range Re ∈ [103, 104]. The flow characteristics investigated include the Reynolds number dependence of lift and drag coefficients, the distributions of time-spanwise averaged variables such as the sub-grid viscosity and the logarithm of Kolmogorov micro-scale to the base of 10 at Re = 2 500 and 104, the contours of spanwise and streamwise vorticity components at t = 170. It is revealed that the peak value of sub-grid viscosity ratio and its root mean square (RMS) values grow with the Reynolds number. The dissipation rate of turbulent kinetic energy is larger near the SC solid walls. The instantaneous factor of swirling strength intermittency (FSI) exhibits some laminated structure involved with vortex shedding.

Investigation of a ten-path ultrasonic flow meter for accurate feedwater measurements

The flow instruments used in thermal power plants cannot be calibrated directly for the actual process conditions, since no traceable calibration facility with known uncertainty is available. A systematic investigation of the relevant influence parameters is therefore needed. It was found in earlier investigations that the dominant influences on the measurement uncertainty are the flow velocity profile and the temperature. In the present work, we report on our experimental study of the temperature and Reynolds number dependence of a new ten-path ultrasonic flow meter prototype. An improved measuring program is developed that allows for a systematic characterization. Special emphasis was placed on producing and validating well defined velocity profiles on a precision calibration flow rig. It was also for the first time intended and validated to generate fully developed Reynolds-similar velocity profiles for different temperatures so that the two main influence parameters, namely temperature and Reynolds number, can be clearly characterized separately. Since such ideal measurement conditions are not found in practical applications, the approach is also tested for a disturbed flow condition. A well defined disturbance is generated with a new flow disturber.

Evaluation of hot-wire spatial filtering corrections for wall turbulence and correction for end-conduction effects

Several recent spatial filtering corrections for Reynolds stress measured by single component hot-wire probes were assessed using turbulent channel flow data measured over a moderate Reynolds number range. Using measurements with a variety of hot-wire lengths and aspect ratios, the current work determines the impact of these corrections on the actual magnitude and Reynolds number dependence of the near-wall turbulent peak in Reynolds stress and compares it to results from prior direct numerical simulations of turbulent channel flow. Comparison of the results following application of previously published correction schemes were found to produce similar results, with some limitations observed for each technique. Comparison to direct numerical simulation results suggested that additional corrections were needed to correct for end conduction effects. An additional modification for these effects was devised which improved agreement between probes of different lengths and aspect ratios and improved agreement between the measured and direct numerical simulation results .

Analysis of the Lagrangian path structures in fluid turbulence

Because in the Lagrangian frame the time scale separation has a stronger Reynolds number dependence than the length scale case in the Eulerian frame, it is more difficult to reveal inertial range scaling laws, as predicted from dimensional arguments. The present work introduces a newly defined trajectory segment structure to tentatively understand Lagrangian statistics. When a fluid particle evolves in space, its Lagrangian trajectory encounters regions of different dynamics, which can be characterized by the magnitude of material acceleration, i.e., \documentclass[12pt]{minimal}\begin{document}$|\vec{a}|$\end{document}|a⃗|, in certain time span. The extrema of \documentclass[12pt]{minimal}\begin{document}$|\vec{a}|$\end{document}|a⃗| are considered as the representative markers along the Lagrangian trajectories. A trajectory segment is defined as the part bounded by two adjacent extrema of \documentclass[12pt]{minimal}\begin{document}$|\vec{a}|$\end{document}|a⃗|. The time difference and magnitude of the velocity difference at the two ends of each segment are chosen as the characteristic parameters. It shows that such structure reveals interesting turbulence physics, such as the scaling of the structure function and the quantitative description of the time scale. The corresponding explanation and analysis of flow physics are provided as well to improve the understanding of some remaining challenging issues.

Collision statistics of inertial particles in two-dimensional homogeneous isotropic turbulence with an inverse cascade

AbstractThis study investigates the collision statistics of inertial particles in inverse-cascading two-dimensional (2D) homogeneous isotropic turbulence by means of a direct numerical simulation (DNS). A collision kernel model for particles with small Stokes number ($\mathit{St}$) in 2D flows is proposed based on the model of Saffman & Turner (J. Fluid Mech., vol. 1, 1956, pp. 16–30) (ST56 model). The DNS results agree with this 2D version of the ST56 model for $\mathit{St}\lesssim 0.1$. It is then confirmed that our DNS results satisfy the 2D version of the spherical formulation of the collision kernel. The fact that the flatness factor stays around 3 in our 2D flow confirms that the present 2D turbulent flow is nearly intermittency-free. Collision statistics for $\mathit{St}= 0.1$, 0.4 and 0.6, i.e. for $\mathit{St}<1$, are obtained from the present 2D DNS and compared with those obtained from the three-dimensional (3D) DNS of Onishi et al. (J. Comput. Phys., vol. 242, 2013, pp. 809–827). We have observed that the 3D radial distribution function at contact ($g(R)$, the so-called clustering effect) decreases for $\mathit{St}= 0.4$ and 0.6 with increasing Reynolds number, while the 2D $g(R)$ does not show a significant dependence on Reynolds number. This observation supports the view that the Reynolds-number dependence of $g(R)$ observed in three dimensions is due to internal intermittency of the 3D turbulence. We have further investigated the local $\mathit{St}$, which is a function of the local flow strain rates, and proposed a plausible mechanism that can explain the Reynolds-number dependence of $g(R)$. Meanwhile, 2D stochastic simulations based on the Smoluchowski equations for $\mathit{St}\ll 1$ show that the collision growth can be predicted by the 2D ST56 model and that rare but strong events do not play a significant role in such a small-$\mathit{St}$ particle system. However, the probability density function of local $\mathit{St}$ at the sites of colliding particle pairs supports the view that powerful rare events can be important for particle growth even in the absence of internal intermittency when $\mathit{St}$ is not much smaller than unity.

Reynolds number sensitivity to aerodynamic forces of twin box bridge girder

This paper presents the experimental results for a streamlined twin box girder of 1545m span suspension bridge in order to investigate the Reynolds number sensitivity to aerodynamic force and pressure coefficients. High speed wind tunnel testing was carried out on a 1:30 scale sectional model at an aeronautical wind tunnel. The drag and lift coefficients revealed significant decreases at a critical Reynolds number that was in the range of ordinary wind tunnel tests. The safety rail reduced the Reynolds number dependency of aerodynamic force coefficients at negative angles of attack. Similarly, the boundary layer trip strip attached at the bottom surface of the girder reduced the Reynolds number dependency by fixing the flow separation. The pressure coefficients near the gap between the twin boxes changed from negative to positive at the critical Reynolds number, which represented smooth ventilation of wind flow through the gap at the supercritical region. The imbalance of the drag and lift forces acting on each box in the subcritical region gradually resolved and both boxes were almost equally loaded by the forces at the supercritical region.

Steady and unsteady pressure measurements on a swept-wing aircraft

AbstractSteady and unsteady pressure measurements are conducted for a tailless aircraft model. The main aim with the presented experimental work is to investigate the difficulties and possibilities involved in using an available pressure sensing system for accurate unsteady pressure measurement. The experimental procedure which is utilised for unsteady pressure measurements is described in detail. In particular, the importance of synchronised timing is recognised. For a harmonically varying pressure a small time delay in the measurement chain can result in a significant phase shift. Also, difficulties and uncertainties that are still present are pointed out. The results from these experiments are compared to numerical results based on unsteady potential flow theory. In general, the experimental and computational results show similar trends. Especially good agreement is found for the steady pressure measurements. For the unsteady pressure measurements a possible Reynolds number dependency is found for the considered test conditions.

Discussion of “Flow-Excited Acoustic Resonance Excitation Mechanism, Design Guidelines and Counter Measures,” (Ziada, S., and Lafon, P., 2014, ASME Appl. Mech. Rev., 66(1), p. 010802)

The authors have done extensive research in gathering historical background on the subject of flow excited acoustic resonance. They have provided extensive discussion to justify creative formulations for predicting the onset of resonance and estimating the associated maximum pressure amplitudes. Their approach makes use of reported experimental studies plus some of their own to make charts that should be useful for some common industrial problems. An independent scaling approach is offered in this review to verify the dominant parameters and variables employed by the authors in their predictive methods. It was found that for low Mach number flows, a specific Reynolds number (Re) dependence was missing. However, since it is known that the Strouhal dependence is very weak on Reynolds numbers up to about 105, the absence of specific Re dependence is probably inconsequential. Another concern was that interaction between the acoustics and vortex shedding or shear layer instabilities could affect the eigenfrequencies. A simple model showed that this is possible, but Quad Cities experience cited by the authors indicated one case where it was not important. The Rolls-Royce Vertical Lift System example with coaxial closed side-branches could have had a significant interaction with the annular liquid mass on eigenmodes. The mass effect resulting from the annular space connecting both branches could act less like an oscillating shear layer and more like a Helmholtz resonator. This could have a significant effect on the natural frequency of either or both branch pipes. Although that effect is not specifically considered here, if it was significant, it would be naturally embraced in a scale model based on the scaling laws presented in this review.

A description of turbulent wall-flow vorticity consistent with mean dynamics

AbstractA depiction of the mean and fluctuating vorticity structure in turbulent wall flows is presented and described within the context of the self-similar properties admitted by the mean dynamical equation. Data from a relatively wide range of numerical and physical experiments are used to explore and clarify the structure postulated. The mean vorticity indicator for the onset of the four-layer regime of the mean dynamics is revealed. With increasing Reynolds number, the mean vorticity is shown to segregate into two increasingly well-defined domains. Half of the mean vorticity concentrates into a near-wall region of width (relative to the overall flow width) that diminishes proportionally to the inverse square root of Reynolds number. The remainder of the mean vorticity is spread, with diminishing amplitude, over an outer domain that approaches the overall flow width at high Reynolds number. Vorticity stretching and reorientation are surmised to be the characteristic mechanisms accounting for the inner domain behaviour of both the mean and fluctuating vorticity. Vorticity dispersion via advective transport is surmised to be the characteristic mechanism in the outer domain. In this domain, the fluctuating enstrophy approaches that of the instantaneous enstrophy with increasing Reynolds number. This underpins an emerging self-similarity between the mean and r.m.s. vorticity in the domain where the mean velocity profile is logarithmic. The Reynolds number dependence of a number of properties associated with the vorticity field is explored and quantified. The study closes with brief account of the combined vortical and mean dynamical structure of turbulent wall flows.

Intermittency in 2D soap film turbulence

The Reynolds number dependency of intermittency for 2D turbulence is studied in a flowing soap film. The Reynolds number used here is the Taylor microscale Reynolds number Rλ, which ranges from 20 to 800. Strong intermittency is found for both the inverse energy and direct enstrophy cascades as measured by (a) the pdf of velocity differences P(δu(r)) at inertial scales r, (b) the kurtosis of P(∂xu), and (c) the scaling of the so-called intermittency exponent μ, which is zero if intermittency is absent. Measures (b) and (c) are quantitative, while (a) is qualitative. These measurements are in disagreement with some previous results but not all. The velocity derivatives are nongaussian at all Rλ but show signs of becoming gaussian as Rλ increases beyond the largest values that could be reached. The kurtosis of P(δu(r)) at various r indicates that the intermittency is scale dependent. The structure function scaling exponents also deviate strongly from the Kraichnan prediction. For the enstrophy cascade, the intermittency decreases as a power law in Rλ. This study suggests the need for a new look at the statistics of 2D turbulence.

Aeroacoustic Measurements of a Scaled Half-Model at High Reynolds Numbers

The measurement of airframe noise on small-scale models is a well-known and common practice in conventional wind tunnels. Because conventional wind tunnels cannot generally achieve full-scale Reynolds numbers, measurements during the development process of modern aircraft are performed in cryogenic and/or pressurized wind tunnels that are capable of higher-Reynolds-number flows. Thus, the characteristics of the moving fluid are better adapted to the scale model. At the Göttingen Institute of Aerodynamics and Flow Technology of DLR, German Aerospace Center, the microphone-array measurement technique was further developed to perform measurements in a cryogenic wind tunnel at temperatures down to 100 K. A microphone array consisting of 144 microphones was designed and constructed for this purpose. In this paper, acoustic-array measurements performed in a cryogenic wind tunnel are described for various Reynolds numbers using a 9.24% Dornier 728 half-model. Our results showed a significant Reynolds-number dependency of the measured equivalent sound power for various sources.

Large-Eddy Simulation of the Flow Over a Circular Cylinder at Reynolds Number 2 × 104

The flow over a circular cylinder at Reynolds number 2 × 104 was predicted numerically using the technique of large-eddy simulation (LES). Both incompressible and compressible flow formulations were used. The present results obtained at a low-Mach number (M = 0.2) revealed significant inaccuracies like spurious oscillations of the compressible flow solution. A detailed investigation of such phenomena was carried out. It was found that application of blended central-difference or linear-upwind schemes could damp artificial waves significantly. However, this type of schemes has a too dissipative nature compared to pure central-differences. The incompressible flow results were found to be consistent with the existing numerical studies as well as with the experimental data. Basic flow features and flow mechanics were found to be in good agreement with existing experimental data and consistent with previously obtained LES. Special emphasis was put on the spectral analysis. Here, the classical Fourier transform as well as the continuous wavelet transform were applied. Based on the latter, the separated shear-layer instability was precisely clarified. It was found that the Reynolds number dependency between vortex shedding and shear-layer instabilities had a power law relation with n = 0.5.

Three-dimensional numerical study of turbulent flow and heat transfer in a wavy-walled duct

The present study focuses on the computation of fully developed flow and heat transfer through a stationary wavy-walled duct using large eddy simulation (LES) in finite volume framework. Shear improved Smagorinsky model (SISM) has been used for the computation of eddy viscosity. The wavy-wall is described by the sine function y=2a sin2(πx/L). The geometrical ratios Hmin/Hmax and L/a are fixed to 0.2 and 8, respectively. The effect of Reynolds numbers (2053–10,000) on the flow field and heat transfer has been presented. Instantaneous, mean and turbulent quantities are reported. It has been observed that the flow is strongly three-dimensional. The friction factor is found to be insensitive to the Reynolds number. Normalized Nusselt number ratio shows significant Reynolds number dependency.