Velocity Defect Research Articles

Statistical properties of neutrally and stably stratified boundary layers in response to an abrupt change in surface roughness

We conducted experimental investigations on the effect of stable thermal conditions on rough-wall boundary layers, with a specific focus on their response to abrupt increases in surface roughness. For stably stratified boundary layers, a new analytical relation between the skin-friction coefficient, $C_f$ , and the displacement thickness was proposed. Following the sharp roughness change, the overshoot in $C_f$ is slightly enhanced in stably stratified layers when compared with that of neutral boundary layers. Regarding the velocity defect law, we found that the displacement thickness multiplied by $\sqrt{2/C_f}$ , performs better than the boundary layer thickness alone when describing the similarity within internal boundary layers for both neutral and stable cases. A non-adjusted region located just beneath the upper edge of the internal boundary layer was observed, with large magnitudes of skewness and kurtosis of streamwise and wall-normal velocity fluctuations for both neutral and stable cases. At a fixed wall-normal location, the greater the thermal stratification, the greater the magnitudes of skewness and kurtosis. Quadrant analysis revealed that the non-adjusted region is characterised by an enhancement/reduction of ejection/sweep events, particularly for stably stratified boundary layers. Spatially, these ejections correspond well with peaks of kurtosis, exhibit stronger intensity and occur more frequently following the abrupt change in surface conditions.

Turbulent activity in the near-wall region of adverse pressure gradient turbulent boundary layers

Two direct numerical simulation (DNS) databases are investigated to understand the effect of the outer-layer turbulence on the inner layer’s structures and energy transfer mechanisms. The first DNS database is the non-equilibrium adverse-pressure-gradient (APG) turbulence boundary layer (TBL) of Gungor et al. [1]. Its Reynolds number and the inner-layer pressure gradient parameter reach above 8000 and 10, respectively. The shape factor spans between 1.4 and 3.3, which indicates the flow has various velocity defect situations. The second database is the same flow as the first one but the outer layer turbulence is artificially eliminated in this flow. Turbulence is removed above 0.15 local boundary layer thickness. For the analysis, we chose four streamwise positions with small, moderate, large, and very-large velocity defect. We compare the wall-normal distribution of Reynolds stresses, two-point correlations and spectral distributions of energy, production and pressure strain. The results show that the inner layer turbulence can sustain itself when the outer-layer turbulence does not exist regardless of the velocity defect or the pressure gradient. The two-point correlations of both cases show that outer large-scale structures affect the inner layer structures significantly. The streamwise extent of the correlation contours scales with pressure-viscous units. This shows the importance of the pressure gradient’s effect on the inner-layer structures. The spectral distributions demonstrate that the energy transfer mechanisms are probably the same in the inner layer regardless of the velocity defect, which suggests the near-wall cycle may exist even in very-large defect APG TBLs where the mean shear in the inner layer is considerably lower than small-defect APG TBLs.

Consistent outer scaling and analysis of adverse pressure gradient turbulent boundary layers

Under adverse pressure gradient (APG) conditions, the outer regions of turbulent boundary layers (TBLs) are characterized by an increased velocity defect $U_{e}-U$ , an outwards shift of the peak value of the Reynolds shear stress $-\langle uv\rangle$ and an appearance of the outer peak value of the Reynolds normal stress $\langle uu\rangle$ . Here $U_{e}$ is the TBL edge velocity. Scaling APG TBLs is challenging due to the non-equilibrium effects caused by changes in the APG. To address this, the response distance of TBLs to non-equilibrium conditions is utilized to extend the Zagarola–Smits scaling $U_{zs} = U_{e}({\delta ^{*} }/{\delta })$ and ensure that the original properties of the Zagarola–Smits scaling are maintained as $Re \to \infty$ . Here $\delta ^{*}$ is the displacement thickness and $\delta$ is the boundary layer thickness. Based on the established correlation between $U_{e}-U$ and $-\langle uv\rangle$ , the scaling is extended to $-\langle uv\rangle$ . Furthermore, considering the coupling relationship between Reynolds stress components, the scaling is extended to encompass each Reynolds stress component. The proposed consistent scaling is verified using five non-equilibrium databases and five near-equilibrium databases, successfully collapsing the data of the TBL outer region. The pressure gradient parameter $\beta =({\delta ^{*} }/{\rho u_{\tau }^{2} }) ({\mathrm {d} P_{e} }/{\mathrm {d}\kern0.7pt x})$ of these databases spans two orders of magnitude. Here $P_{e}$ is the boundary layer edge pressure, $u_{\tau }$ is the friction velocity and $\rho$ is the density. Finally, the influence of the APG on the inner and outer regions of TBLs is analysed using the mean momentum balance equation. The analysis suggests that the shift of the $-\langle uv\rangle$ peak to the outer region under APG conditions is due to an insufficient inertia term near the inner region to balance the APG. It is observed that the APG promotes interaction between the inner and outer regions of TBLs, but the inner and outer regions still retain distinctive properties.

Vortex dynamics and boundary layer transition in flow around a rectangular cylinder with different aspect ratios at medium Reynolds number

The numerical investigation focuses on the flow patterns around a rectangular cylinder with three aspect ratios ( $L/D=5$ , $10$ , $15$ ) at a Reynolds number of $1000$ . The study delves into the dynamics of vortices, their associated frequencies, the evolution of the boundary layer and the decay of the wake. Kelvin–Helmholtz (KH) vortices originate from the leading edge (LE) shear layer and transform into hairpin vortices. Specifically, at $L/D=5$ , three KH vortices merge into a single LE vortex. However, at $L/D=10$ and $15$ , two KH vortices combine to form a LE vortex, with the rapid formation of hairpin vortex packets. A fractional harmonic arises due to feedback from the split LE shear layer moving upstream, triggering interaction with the reverse flow. Trailing edge (TE) vortices shed, creating a Kármán-like street in the wake. The intensity of wake oscillation at $L/D=5$ surpasses that in the other two cases. Boundary layer transition occurs after the saturation of disturbance energy for $L/D=10$ and $15$ , but not for $L/D=5$ . The low-frequency disturbances are selected to generate streaks inside the boundary layer. The TE vortex shedding induces the formation of a favourable pressure gradient, accelerating the flow and fostering boundary layer relaminarization. The self-similarity of the velocity defect is observed in all three wakes, accompanied by the decay of disturbance energy. Importantly, the decrease in the shedding frequency of LE (TE) vortices significantly contributes to the overall decay of disturbance energy. This comprehensive exploration provides insights into complex flow phenomena and their underlying dynamics.

Heat transfer and turbulent heat flux budgets in cooling films

Statistics from large-eddy-simulation (LES) of cooling films with different cooling holes are used to evaluate budgets in the transport equation of turbulent heat flux. The capability of LES has been assessed by comparing simulated results with experimental data, while the correctness of the procedure generating turbulent heat flux budgets has been examined on a turbulent boundary layer. The mechanism of heat transfer has been preliminarily studied throughout the three-dimensional flow field at different blowing ratios using a general outer scaling, to recognize specific regions with corresponding heat transfer patterns. A compressible version of budget terms in the transport equation of turbulent heat flux is then explored to show the thermal behavior of flow downstream from the cooling film holes. Characteristics of each budget term are presented in a defect scaling consistent with the scaling suitable for Reynolds stresses and Reynolds stress budgets. Furthermore, these budget terms are compared among an array of different cooling hole shapes combined with different blowing ratios to explore self-similarity. Results show that the dynamic balance of all budget terms is significantly influenced by the cooling hole shape, while each turbulent heat flux budget term may scale with the velocity defect, temperature deficit, and the normalized streamwise distance to the power of an exponent dependent on the hole shape.

Air–Sea Enthalpy and Momentum Exchange Coefficients from GPS Dropsonde Measurements in Hurricane Conditions

The intensity of tropical cyclones is highly dependent on air–sea enthalpy and momentum exchange. At extreme wind speeds, the values of the enthalpy, CK, and momentum, CD, exchange coefficients are characterized by high uncertainty. The present study aims to expand the previously used algorithm for CD retrieval to obtain the values of CK from wind speed measurements and the enthalpy profiles obtained from NOAA GPS dropsondes in hurricane conditions. This algorithm uses concepts from technical hydrodynamics, describing turbulent boundary layers on flat plates and pipes. According to this approach, the velocity (and enthalpy) defect profiles are self-similar in the entire boundary layer, including the layer of constant fluxes and the “wake” part, where the airflow adapts to the undisturbed flow region. By using the self-similarity property, the parameters of the constant flow layer (the roughness parameter, friction velocity, and the enthalpy and exchange coefficients CD and CK) could be obtained from measurements in the “wake” part for wind speeds from 20 m/s to 72 m/s. The estimates of the CK/CD ratio revealed values of 0.7 and 0.96 (depending on the self-similar approximation limits), and the results suggest that there are slight variations with the wind speed.

Over 100 mVVOCImprovement for Rear Passivated ACIGS Ultra‐Thin Solar Cells

AbstractA decentralized energy system requires photovoltaic solutions to meet new aesthetic paradigms, such as lightness, flexibility, and new form factors. Notwithstanding, the materials shortage in the Green Transition is a concern gaining momentum due to their foreseen continuous demand. A fruitful strategy to shrink the absorber thickness, meeting aesthetic and shortage materials consumption targets, arises from interface passivation. However, a deep understanding of passivated systems is required to close the efficiency gap between ultra‐thin and thin film devices, and to mono‐Si. Herein, a (Ag,Cu)(In,Ga)Se2ultra‐thin solar cell, with 92% passivated rear interface area, is compared with a conventional nonpassivated counterpart. A thin MoSe2layer, for a quasi‐ohmic contact, is present in the two architectures at the contacts, despite the passivated device narrow line scheme. The devices present striking differences in charge carrier dynamics. Electrical and optoelectronic analysis combined with SCAPS modelling suggest a lower recombination rate for the passivated device, through a reduction on the rear surface recombination velocity and overall defects, comparing with the reference solar cell. The new architecture allows for a 2% efficiency improvement on a 640 nm ultra‐thin device, from 11% to 13%, stemming from an open circuit voltage increase of 108 mV.

Scaling and similarity laws in three-dimensional wall jets

Wall jets appear in many situations of technological and scientific interest. In gas turbines, flows produced by the film as well as impingement cooling devices are three-dimensional wall jets. High-lift devices produce flows that can easily be represented by two-dimensional wall jets. It has been known for a long time that wall jets in both stagnant and moving environments display a layered structure and only partially obey similarity laws. In this paper, we derive scaling laws and obtain self-similar velocity defect and Reynolds stress profiles for the outer part of three-dimensional wall jets in the high-Reynolds-number limit. The scaling laws are derived from prime principles under realistic assumptions about the behavior of the flow. We show that the leading term in an expansion of the turbulent kinetic energy (TKE) as a series of powers of the distance from the source must scale like the transversal velocity causing the jet to spread laterally. Only the second term in the TKE expansion is shown to scale like the square of the velocity defect. The scaling laws are tested on numerical and experimental data representing two commonly used film cooling devices.

Altering the wake dynamics of a circular cylinder with harmonic forcing

The time-averaged velocity profile in the wake of a circular cylinder resembles a “U” type or a “V” type profile due to a velocity defect. Bhattacharya and J. W. Gregory [“The effect of spatially and temporally modulated plasma actuation on cylinder wake,” AIAA J. 58, 3808–3818 (2020)] showed experimentally that the wake dynamics could be altered with harmonic forcing in such a way that instead of a velocity defect, a “jet-like” profile emerged with a characteristic “W” profile. The harmonic forcing was created by modulating the waveform of a dielectric barrier discharge plasma actuators' supply signal with a frequency twice that of the shedding frequency. However, the reason for the appearance of the “W” profile was not clear in S. Bhattacharya and J. W. Gregory [“The effect of spatially and temporally modulated plasma actuation on cylinder wake,” AIAA J. 58, 3808–3818 (2020).] In this paper, we use numerical simulation to recreate the test conditions implemented by Bhattacharya and J. W. Gregory [“The effect of spatially and temporally modulated plasma actuation on cylinder wake,” AIAA J. 58, 3808–3818 (2020).] We apply large-eddy simulation to study the impact of the pulsed, harmonic forcing on the wake of a circular cylinder at a subcritical Reynolds number of 4700. The plasma actuators are modeled with a body-force approach. The frequency of the driving signal of the plasma actuator is modulated at twice the shedding frequency. The amplitude of the signal is set at 6 kV peak to peak to create a blowing ratio of 0.8. The goal is to understand how the wake changes in three dimensions and the impact on separation on the cylinder surface due to the harmonic forcing. Results show that pulsed forcing causes vortices from one side of the wake to cross the centerline. This crossing creates an effective jet-like velocity along the centerline, resulting in a W velocity profile. Such a W profile is observed at least up to a streamwise distance of five cylinder diameters. Additionally, the pulsed actuation significantly increases the magnitude of primary and secondary frequencies throughout the wake. Forcing caused a 50% increase in the transverse velocity fluctuations at the centerline of the wake at the streamwise location of x/d=5. There was a similar increase in 33% at the centerline in the streamwise velocity fluctuations at the same location.

Post-shock turbulence recovery in oblique-shock/turbulent boundary layer interaction flows

The oblique shock impinging on the supersonic turbulent boundary layer leads to a mixing layer and the emergence of large-scale coherent structures within the interaction zone which leave significant velocity defect and turbulence amplification downstream. In the present study, we investigate the turbulence recovery in the post-shock region by exploiting direct numerical simulation data of the oblique-shock/turbulent boundary layer interaction flow at the incoming Mach number of $2.28$ and the shock angle of $33.2^\circ$ , with special attention paid to the contribution of the mixing layer and large-scale structures to flow dynamics. For that purpose, we propose to split the mean velocity, Reynolds stresses and spanwise spectra into a canonical portion that is constructed according to the statistics of canonical turbulent boundary layers, and a mixing-layer-induced portion. We found that the hidden mixing layer grows with the boundary layer thickness and that the induced mean shear and Reynolds stresses decay at different rates. The mean velocity recovers to the canonical profiles at a distance of 13 boundary layer thicknesses downstream where the mixing-layer-induced mean shear ceases to have strong impacts. The recovery of Reynolds stresses requires 10 boundary layer thicknesses in the near-wall region but a much longer streamwise extent in the outer region due to the slow decay of large-scale motions. These large-scale motions superpose on the near-wall turbulence, intensifying the turbulent fluctuations, yet having a trivial impact on the skin friction, for the contribution of the mixing-layer-induced mean shear and Reynolds shear stress are balanced by the advection term. We further establish a simple physical model capable of approximately predicting the streamwise evolution of mixing-layer-induced mean shear and turbulent kinetic energy. This model suggests that the complete recovery of turbulence in the outer region requires a streamwise extent of approximately 50 boundary layer thicknesses.

Experimental investigation of the effects of the Reynolds number on the performance and near wake of a wind turbine

Wind tunnel experiments provide worthwhile insights for designing efficient micro wind energy harvesters and large-scale wind turbines. As wind tunnel tests with large-scale wind turbines are expensive and not always feasible, most experiments are conducted with geometrically scaled rotors. Furthermore, micro-scale runners used for wind energy harvesting face the issue of lower efficiency than large turbines. A better understanding of Reynolds number effects induced by the downsizing of a turbine would help to design more efficient wind energy harvesters and more faithfully scaled experiments. This paper reports on Reynolds number effects on the performance and wake of micro-scale wind turbines. Wind turbines’ power and torque coefficients are measured in a wind tunnel for a wide range of Reynolds numbers. The wake axial velocity fields and the vortex core locations are collected for three Reynolds numbers using phase-averaged and phase-locked particle image velocimetry technique. The results emphasize that an increase in the Reynolds number leads to larger power coefficients, torque coefficients, and optimum tip-speed ratios. Higher Reynolds numbers induce wider wake expansion and a larger axial velocity defect. This quantitative analysis will contribute to a clearer understanding of the scaling effects and help to design more efficient wind energy harvesters.

MESO-MACRO ENERGY EXCHANGE IN SHOCK-WAVE PROCESSES AND DYNAMIC STRENGTH OF AB2 STEEL

Impact tests of low-alloy martensitic-bainitic steel AB2 showed that the scale of dynamic deformation and the fracture mechanism change in a threshold manner. The change in the mechanism and scale of fracture is triggered by the resonant excitation of large-scale structural elements of the material (grain conglomerates) due to plastic flow oscillations. In this case, the grain-boundary mechanism of dynamic fracture is replaced by a transcrystalline one. Beyond the strain rate threshold, mesoscopic elementary carriers of dynamic deformation are divided into two groups: low-velocity and high-velocity. Accordingly, the velocity distribution of mesoparticles shows two humps. The velocity spread of mesoparticles sharply increases under these conditions, while the mass velocity defect (change in the shock wave amplitude) becomes negative. The latter fact indicates the local acceleration of mesoparticles in discrete regions of the target (the so-called shooting of mesoparticles in the shock wave direction). Transcrystalline cracks are randomly distributed throughout the sample and have a random orientation.

Energy transfer mechanisms in adverse pressure gradient turbulent boundary layers: production and inter-component redistribution

Production and inter-component redistribution of turbulence in adverse pressure gradient (APG) turbulent boundary layers (TBLs) with small and large velocity defects are investigated, along with the structures playing a role in these energy transfer mechanisms. We examine the wall-normal and spectral distributions of energy, production and pressure-strain in APG TBLs, and compare these distributions with those in canonical flows. It is found that the spectral distributions of production and pressure-strain are not affected profoundly by an increase of the velocity defect, although the energy spectra change drastically in the inner layer of the large-defect APG TBL. In the latter, the signature of the inner-layer streaks is absent from the energy spectra. In the outer layer, energetic, production and pressure-strain structures appear to change from wall-attached to wall-detached structures with increasing velocity defect. Despite this, the two-dimensional spectral distributions have similar shapes and wavelength aspect ratios of the peaks in all these flows. Therefore, the conclusion is that the mechanisms responsible for turbulence production and inter-component energy transfer may remain the same within each layer in all these flows. It is the intensity of these mechanisms within one layer that changes with velocity defect, because of the local mean shear variation.

Towards an Algorithm for Retrieval of the Parameters of the Marine Atmospheric Boundary Layer at High Wind Speeds Using Collocated Aircraft and Satellite Remote Sensing

A method has been developed for the retrieval of the atmospheric boundary layer parameters in tropical cyclones, namely the dynamic speed, the wind speed at a 10 m height, and the roughness parameter. For the analysis, the wind speed profiles were obtained from NOAA GPS-dropsondes and collocated with the data from the Stepped-Frequency Microwave Radiometer (SFMR). The parameters of the atmospheric boundary layer from the GPS-dropsonde data were obtained by taking into account the self-similarity of the velocity defect profile. The emissivity, determined from the radiometric measurement data, was calibrated to the field data from the GPS-dropsondes. Empirical relations between the wind speed, dynamic wind speed, and aerodynamic drag coefficient with the surface emissivity have been proposed. Based on a comparison of the measured dynamic parameters and the surface emissivity, empirical formulas have also been proposed. From an analysis of cross-polarized Sentinel-1 SAR images and collocated SFMR measurements for hurricanes Irma (2017/09/07) and Maria (2017/09/21 and 2017/09/23), we have obtained the dependences of the NRCS on the ocean surface emissivity, surface wind speed, and friction velocity. These results could potentially be used to improve the algorithm for the retrieval of boundary layer parameters in tropical cyclones from remote sensing data.

Experimental observations on turbulent boundary layers subjected to a step change in surface roughness

Based on experimental data acquired with particle image velocimetry, we examine turbulent boundary layers that are subjected to an abrupt change in wall roughness in the streamwise direction. Three different sandpapers (P24, P36 and P60) together with a smooth wall are used to form a number of different surface transition cases, including both R $\rightarrow$ S (where upstream surface is rough and second surface is either smooth or smoother compared with the upstream surface) and S $\rightarrow$ R (where upstream surface is smoother compared with the downstream surface; both surfaces are rough). This enables us to investigate the effect of the surface transition strength ( $M = \ln [y_{02}/y_{01}]$ , where $y_{01}$ and $y_{02}$ are the roughness lengths of the upstream and downstream surfaces, respectively) on the growth of the internal boundary layer (IBL) and the corresponding flow structure. The results show that for each surface transition group (i.e. R $\rightarrow$ S and S $\rightarrow$ R), the thickness of the IBLs is proportional to the strength of the surface transition, and that the IBLs are thicker for the S $\rightarrow$ R cases compared with their R $\rightarrow$ S counterparts for similar $|M|$ , when normalised by the initial boundary layer thickness ( $\delta _0$ ). The results also show that the growth rates of the IBLs could be represented by a power law, consistent with the previous studies. However, despite a wide range of scatter in the literature for the power-law exponent, an average value of $0.75$ (varies between $0.71$ and $0.8$ with no clear trend) is obtained in the present study considering all the surface transition cases. The pre-factor for the power-law fit, on the other hand, is found to be related to the strength of the surface transition. In addition to the variations in the velocity defect and diagnostic plots with the growth of the IBLs, sweep and ejection events appear to differ significantly (depending on the type of the step change). Two-point spatial correlations, moreover, show that the structure is more elongated in the wall-normal and streamwise directions, as the flow accelerates over the downstream surface (i.e. R $\rightarrow$ S cases). For the reverse transition cases (i.e. S $\rightarrow$ R, where the flow decelerates over the downstream rougher surface), however, the correlation coefficients shrink in size in both directions.

In-Vivo PIV Measurement Of The Blood Flow In The Heart And Main Vein Of Medaka Embryo

In order to examine the generation mechanism of the vertebrates, including humans, and to explore the diverging point of the genetic abnormalities, it is effective to investigate the growth of the embryo of an artificial mutant. As the embryos of Medaka hatch outside of the body and their egg membrane are transparent, it is quite easy to carry out the in-vivo observation of their organs. Moreover, the development and the structure of their major organs of Medaka are quite similar to those of human. Thus, the observation of the developmental abnormalities of Medaka embryos may serve as a clue to the pathologic investigation of the genetic disease and hopefully give some insight to the future effective treatment. Presently, the intracardiac blood flows of Medaka embryos have been observed by a high-speed camera under microscope. The obtained images are pre-processed and the velocity fields in the heart and in the main vein of Medaka embryo are measured by PIV method. The red blood cells flowing inside the heart and in the main vein of Medaka embryos are used as tracer particles. The image pre-processing was applied to capture the image of red blood cells and then the cross-correlation method can be applied. As a result, it is found that the velocity defect caused by the valve closing is clearly observed in the main vein and the amplitude of the velocity defect is decreasing with the distance to the heart. It is also found that the beating of the heart corresponds to the pulsatio of the flow velocity of the red blood cell in the heart. In conclusion, the authors observed the Medaka embryo under microscope with a high-speed camera and measured the velocities of the red blood cells in the heart and in the main vein by PIV measurement using the pre-processed images.

Exact Solutions to Navier–Stokes Equations Describing a Gradient Nonuniform Unidirectional Vertical Vortex Fluid Flow

The paper announces a family of exact solutions to Navier–Stokes equations describing gradient inhomogeneous unidirectional fluid motions (nonuniform Poiseuille flows). The structure of the fluid motion equations is such that the incompressibility equation enables us to establish the velocity defect law for nonuniform Poiseuille flow. In this case, the velocity field is dependent on two coordinates and time, and it is an arbitrary-degree polynomial relative to the horizontal (longitudinal) coordinate. The polynomial coefficients depend on the vertical (transverse) coordinate and time. The exact solution under consideration was built using the method of indefinite coefficients and the use of such algebraic operations was for addition and multiplication. As a result, to determine the polynomial coefficients, we derived a system of simplest homogeneous and inhomogeneous parabolic partial equations. The order of integration of the resulting system of equations was recurrent. For a special case of steady flows of a viscous fluid, these equations are ordinary differential equations. The article presents an algorithm for their integration. In this case, all components of the velocity field, vorticity vector, and shear stress field are polynomial functions. In addition, it has been noted that even without taking into account the thermohaline convection (creeping current) all these fields have a rather complex structure.

Empirical Model for Low-Speed Rough-Wall Turbulent Boundary Layer Pressure Spectra

An empirical model for estimating surface pressure spectra in high Reynolds number rough-wall turbulent boundary layers in the low-speed regime is presented. The model is based on the low-frequency mean velocity defect scaling [1] and the high-frequency shear friction velocity scaling [2]. This model satisfactorily predicts surface pressure spectra measured over a wide range of roughness configurations in high Reynolds number flows free of transitional effects. These data also provide insights into the characteristics of the turbulent scales which are on the order of the roughness size and comprise the mid-frequency region. The slope of this region is highly dependent on roughness element density and element-relative measurement location. This contradicts the premise of an overlap region with slope . An evanescent pressure decay model provides evidence that the slope changes are due to a roughness-dependent pressure decay within the interstitial flow and suggests that a traditional mid-frequency similarity law may not be possible.

Direct Numerical Simulation of Heat Transfer of Lead–Bismuth Eutectic Flow Over a Circular Cylinder at Re = 500

The flow and heat transfer characteristics of the lead–bismuth eutectic (LBE) (Prandtl number Pr = 0.025) passing over a circular cylinder at Re = 500 are studied by direct numerical simulation and compared with the case of the air (Pr = 0.71). This article makes two major contributions: (1) heat transfer characteristics for the LBE flowing past a circular cylinder. For the case of air, the results show that a similarity exists among the wake structure of instantaneous temperature, fluctuating temperature, and velocity. However, these fields differ severely for the case of LBE. The local time-averaged Nusselt number (Nu¯) and circumferentially averagedNu¯are smaller in the LBE than that in the air. The circumferential and spanwise distributions ofNu¯in the LBE show a greater uniformity. The regions with larger circumferential or spanwise inhomogeneity appear in the flow separation zone. Besides, a resemblance between the distribution of the root mean square of fluctuation temperature and the turbulence kinetic energy can be recognized in the air; however, the similarity disappears for the case of LBE and in which the temperature fluctuation is smaller than that in the air. (2) Study on the temperature and velocity defect laws in the wake. By introducing the defect scales, it is concluded that the velocity field has not entered the self-preserving state yet, while the self-preserving state starts at the location of five times the diameter of the cylinder downstream of the cylinder for the temperature in the LBE and that of 21 times for the temperature in the air. In summary, even if without taking the buoyancy force into consideration, this article provides a fruitful description of the flow and heat transfer characteristics when the LBE flows past a cylinder, which is a typical flow in a helical coil steam generator of lead–bismuth alloy-cooled fast reactors. These highly resolved data on velocity and temperature are valuable for turbulence and heat fluxes modeling in the future and may facilitate the in-depth understanding of such flow and heat transfer characteristics within a limited variation range of operating temperature.

Turbine tonal noise prediction using an improved quasi-3D linear model

This study presented a fast tonal noise prediction method for the turbine. The improved quasi-3D linear model was developed based on Hanson's coupled 2D cascade theory of blade row and Goldstein's duct aeroacoustics equation. The improved model can take into the influence of the radial modes account by applying the strip theory. Furthermore, a two-flat-plates assumption was used for the first time to account for the large turning angle of the turbine blade, and different wake velocity defect models with coefficient correction have been developed for each of the two-flat-plates. Briefly, firstly applying extended Hanson's theory to predict the unsteady load on blade surface and then using Goldstein equation to calculate cut-on modes and sound power level of interested frequencies. The present model was validated by URANS/Goldstein hybrid model by comparing the tonal noise radiation generated by the final stage of the GE E3 low pressure turbine at different rotational speeds and various stator-rotor spacings. The results showed that the present model generally agreed well with the hybrid model and can correctly capture the variations of the sound power level with the operating conditions, which indicated that the present model might be applied as an effective tool for turbine tonal noise prediction with less cost in early design phase of turbine blade.