Incident Turbulence Research Articles

Introduction of generalized Bessel–Laguerre–Gaussian beams and its central intensity travelling a turbulent atmosphere

The so-called Generalized Bessel–Laguerre–Gaussian (GBLG) beam is introduced, in this paper, and an approximate formula of the average axial intensity of its propagation through a turbulent atmosphere is investigated using the extended Huygens–Fresnel diffraction integral in the paraxial approximation and on the Rytov theory. The analytical expression elaborated is regarded as the main result of this work. Several above studies are derived here as special cases from our research. The impact of some parameters, including incident beam parameters and turbulence strength, on the distribution of the axial intensity of the GBLG beam and on the profiles of some particular beams through a turbulent atmosphere are carried out numerically in the paper. From our numerical results-, the propagation of Gaussian beams, Laguerre–Gaussian beams and Bessel–Gaussian beams through the considered medium are deduced as particular cases.

A remote microphone technique for aeroacoustic measurements in large wind tunnels

The present study was devoted to the development and application of a remote microphone technique for aeroacoustic measurements in large aerodynamic wind tunnels. In this technique, the microphone and its connecting line to the sensing port are fitted within an aerodynamically streamlined fairing. A model-based calibration method was applied to account for the phase lag and dissipation within the microphone connecting line. The proposed system permits to carry out acoustic measurements when the wind tunnel surface cannot be altered, since the fairing can be simply glued on the wall. The fairing is streamlined to minimize flow disturbances as well as the risk of separation which would otherwise contaminate the wind tunnel flow quality and acoustic measurements. It was furthermore hoped that the acceleration of the flow over the fairing surface might reduce the turbulence fluctuations and thereby increase the signal-to-noise ratio of the acoustic measurements. Those aerodynamic effects were investigated with a set of hot-wire measurements performed in the subsonic L2B small wind tunnel of von Karman Institute (VKI). The mean velocity and the turbulence intensity profile were analyzed in the presence of different inflow turbulence characteristics at 5, 10 and 15m/s freestream velocity. The effect of incident turbulence on the acoustic measurement was investigated applying the calibration procedure and comparing the measurements with a wall-mounted reference microphone signal in similar flow conditions. The results indicate that the wished beneficial effects of the flow acceleration are not significant. As an application, this technique is used to measure the noise emitted from the contra-rotating fans of the large L1 subsonic wind tunnel of the von Karman Institute, where the microphone fairing is placed inside the diffuser and thus subjected to a thick turbulent boundary layer. The results indicate that in spite of the mitigated turbulence-reduction performance of the fairing, it provides a measurement solution that is suitable for large wind tunnels provided the signals are compensated using the measured dynamic calibration. While it should be stressed that the calibration procedure itself is not new, the originality of the present paper stands in the proposed fairing design, and in the aerodynamic/acoustic investigation of its effect on the flow.

Experimental investigation of the turbulence induced by a bubble swarm rising within incident turbulence

This work reports an experimental characterisation of the flow properties in a homogeneous bubble swarm rising at high Reynolds numbers within a homogeneous and isotropic turbulent flow. Both the gas volume fraction $\unicode[STIX]{x1D6FC}$ and the velocity fluctuations $u_{0}^{\prime }$ of the carrier flow before bubble injection are varied, respectively, in the ranges $0\,\%<\unicode[STIX]{x1D6FC}<0.93\,\%$ and $2.3~\text{cm}~\text{s}^{-1}<u_{0}^{\prime }<5.5~\text{cm}~\text{s}^{-1}$. The so-called bubblance parameter ($b=V_{r}^{2}\unicode[STIX]{x1D6FC}/u_{0}^{\prime 2}$, where $V_{r}$ is the bubble relative rise velocity) is used to compare the ratio of the kinetic energy generated by the bubbles to the one produced by the incident turbulence, and is varied from 0 to 1.3. Conditional measurements of the velocity field downstream of the bubbles in the vertical direction allow us to disentangle three regions that have specific statistical properties, namely the primary wake, the secondary wake and the far field. While the fluctuations in the primary wake are similar to that of a single bubble rising in a liquid at rest, the statistics of the velocity fluctuations in the far field follow a Gaussian distribution, similar to that produced by the homogenous and isotropic turbulence at the largest scales. In the secondary wake region, the conditional probability density function of the velocity fluctuations is asymmetric and shows an exponential tail for the positive fluctuations and a Gaussian one for the negative fluctuations. The overall agitation thus results from the combination of these three contributions and depends mainly on the bubblance parameter. For $0<b<0.7$, the overall velocity fluctuations in the vertical direction evolve as $b^{0.4}$ and are mostly driven by the far-field agitation, whereas the fluctuations increase as $b^{1.3}$ for larger values of the bubblance parameter ($b>0.7$), in which the significant contributions come both from the secondary wake and the far field. Thus, the bubblance parameter is a suitable parameter to characterise the evolution of liquid agitation in bubbly turbulent flows.

Effect of turbulent atmosphere on the on-axis average intensity of Pearcey–Gaussian beam

The propagation characteristics of the Pearcey–Gaussian (PG) beam in turbulent atmosphere are investigated in this paper. The Pearcey beam is a new kind of paraxial beam, based on the Pearcey function of catastrophe theory, which describes diffraction about a cusp caustic. By using the extended Huygens–Fresnel integral formula in the paraxial approximation and the Rytov theory, an analytical expression of axial intensity for the considered beam family is derived. Some numerical results for PG beam propagating in atmospheric turbulence are given by studying the influences of some factors, including incident beam parameters and turbulence strengths.

Inflow broadband noise from an isolated symmetric airfoil interacting with incident turbulence

Inflow noise from a symmetric airfoil interacting with homogeneous and isotropic turbulence is investigated focusing on the effects of airfoil geometry. The numerical method employed is based on computational aeroacoustic techniques using the high-order dispersion-relation-preserving finite-difference schemes for solving two-dimensional linearized Euler equations. Effects on inflow noise of the airfoil thickness, leading-edge radius, and freestream Mach number are examined by comparing the acoustic power spectrum of the airfoils and their flow field characteristics. Acoustic power levels of airfoils are found to exponentially decrease in the high-frequency range as airfoil thickness increases because incident turbulent velocities are more distorted in the larger stagnation region near the leading edge. This distortion is shown to be related to the slope angle of the streamline of steady mean flow near the leading edge. However, this high-frequency reduction weakens as the Mach number increases due to the decreasing slope angle. In addition, the chordwise velocity component in the incident turbulence contributes more to the radiating acoustic pressure level as the freestream Mach number increases, which also results in less high-frequency reduction at higher freestream Mach number. At fixed airfoil thickness, increasing the leading-edge radius leads to decreases in the acoustic power level, which may also be explained by size variation of the stagnation region around the leading edge. An approximate algebraic formula for acoustic power spectra is derived on the basis of these observations. Acoustic power spectra predicted using this formula are shown to closely follow the numerical results. Finally, the applicability of the algebraic formula and the current numerical methods to more realistic problems are confirmed by comparing their predictions with the measured data.

The lift on an aerofoil in grid-generated turbulence

The three-dimensional effects of turbulence cannot be neglected when the spanwise wavelength of the incident turbulence is not effectively infinite with respect to the chord, which may invalidate the strip assumption. Based on three-dimensional theory, a general approach, expressed in terms of a two-dimensional Fourier transform of the correlation of the buffeting force, is proposed to identify the two-wavenumber spectrum and aerodynamic admittance of the lift force on an aerofoil. It is essential that the approach presented can be validated in wind tunnel experiments. The coherence of the lift force on an aerofoil in grid-generated turbulence is obtained by simultaneous measurements of unsteady surface pressures around several chordwise strips on a stiff sectional model, which controls the accuracy of results. For the purpose of the Fourier transform, three empirical coherence models of the lift force are presented to fit the experimental results. Compared with the linearized theory, the two-wavenumber aerodynamic admittance can describe well the pressure distribution and the pattern of energy transition in an isotropic turbulence field. Thus, the failure mechanism of the traditional strip assumption can be demonstrated explicitly. In addition, the results obtained also validate the theory proposed by Graham (Aeronaut. Q., vol. 21, 1970, pp. 182–198;Aeronaut. Q., vol. 22, 1971, pp. 83–100). The present approach can be extended to study the three-dimensionality of the buffeting force on line-like structures with arbitrary cross-configurations, such as long-span bridges and high-rise buildings.

On-sky demonstration of optimal control for adaptive optics at Palomar Observatory.

High-order adaptive optics systems often suffer from significant computational latency, which ultimately limits the temporal error rejection bandwidth when classical controllers are employed. This Letter presents results from an on-sky, real-time implementation of an optimal controller on the PALM-3000 adaptive optics system at Palomar Observatory. The optimal controller is computed directly from open-loop wavefront measurements using a multichannel subspace system identification algorithm, and mitigates latency by explicitly predicting incident turbulence. Experimental results show a significant reduction in the residual wavefront error over the controlled spatial modes, illustrating the superior performance of the optimal control approach versus the nominal integral control architecture.

Time-domain inflow boundary condition for turbulence–airfoil interaction noise prediction using synthetic turbulence modeling

The present paper deals with development of the synthetic turbulence inflow boundary condition (STIBC) to predict inflow broadband noise generated by interaction between turbulence and an airfoil/a cascade of airfoils in the time-domain. The STIBC is derived by combining inflow boundary conditions that have been successfully applied in external and internal computational aeroacoustics (CAA) simulations with a synthetic turbulence model. The random particle mesh (RPM) method based on a digital filter is used as the synthetic turbulence model. Gaussian and Liepmann spectra are used to define the filters for turbulence energy spectra. The linearized Euler equations are used as governing equations to evaluate the suitability of the STIBC in time-domain CAA simulations. First, the velocity correlations and energy spectra of the synthesized turbulent velocities are compared with analytic ones. The comparison results reveal that the STIBC can reproduce a turbulent velocity field satisfying the required statistical characteristics of turbulence. Particularly, the Liepmann filter representing a non-Gaussian filter is shown to be effectively described by superposing the Gaussian filters. Each Gaussian filter has a different turbulent kinetic energy and integral length scale. Second, two inflow noise problems are numerically solved using the STIBC: the turbulence–airfoil interaction and the turbulence-a cascade of airfoils interaction problems. The power spectrum of noise due to an isolated flat plate airfoil interacting with incident turbulence is predicted, and its result is successfully validated against Amiet׳s analytic model (Amiet, 1975) [4]. The prediction results of the upstream and downstream acoustic power spectra from a cascade of flat plates are then compared with Cheong׳s analytic model (Cheong et al., 2006) [30]. These comparisons are also in excellent agreement. On the basis of these illustrative computation results, the STIBC is expected to be applied to investigate more complicated inflow noise problems including the effects of non-uniform mean flow, nonlinear interaction, and real airfoil shapes.

Characteristics of distributed aerodynamic forces on a twin-box bridge deck

To facilitate an effective assessment of stress-related bridge performance and safety, stress-level buffeting analysis of a long-span cable-supported bridge is necessary. A stress-level buffeting analysis requires knowledge of characteristics of distributed aerodynamic forces on the surfaces of a bridge deck. This paper first presents a formulation for distributed aerodynamic forces on the surfaces of a bridge deck based on the quasi-steady theory. The characteristics of distributed aerodynamic forces, such as pressure coefficients, pressure admittances and span-wise pressure coherences, are introduced in the formulation. In consideration of different characteristics of incident and signature turbulences, the empirical mode decomposition is then adopted to separate their effects on the distributed aerodynamic forces. Wind tunnel pressure tests of a sectional motionless bridge deck model were conducted to identify the characteristics of distributed aerodynamic forces on the surfaces of the Stonecutters cable-stayed bridge with a twin-box bridge deck as a case study. The results indicate that the separation of incident and signature turbulence effects is necessary and that the proposed framework is feasible although more works need to be done towards a complete stress-level buffeting analysis.

Energy modeling of photovoltaic thermal systems with corrugated unglazed transpired solar collectors – Part 2: Performance analysis

This paper is the second of two companion papers focused on energy modeling and performance analysis of building-integrated photovoltaic thermal (PV/T) systems with corrugated unglazed transpired solar collectors (UTCs). In Part 1, energy models are presented for two configurations: UTC only and UTC with PV panels. The models predict the energy output of the system for different weather and system design conditions and are validated using measured data from an outdoor test facility. In this paper (Part 2), the system performance is evaluated based on data drawn from the literature and simulations with Computational Fluid Dynamics (CFD) and energy models. The analysis includes parameters that are unique for this system, such as the corrugation geometry and the collector orientation. Validated, high resolution CFD simulations are used to study the impact of plate orientation and incident turbulence intensity, based on the comparison of exterior and interior Nusselt (Nu) number and the cavity exit air temperature, as well as the PV surface temperature when UTCs are integrated with PV panels. It is found that for configurations with UTC only, both exterior and interior convective heat transfer is enhanced in the ‘vertical’ installation, while similar results were obtained for increased incident turbulence intensity levels. However, only minor influences from these two parameters are observed for UTCs with PV panels. The energy model is used to investigate the optimal geometry for both configurations. It is found that parameters such as slope length and corrugation wavelength have the most significant impact on UTC performance while the wavelength and PV panel height have the largest effect for UTCs with PV panels.

Airflow and thermal analysis of flat and corrugated unglazed transpired solar collectors

The flow structure and convective heat transfer mechanisms in Unglazed Transpired solar Collectors (UTCs) are crucial to their performance. High-resolution, 3-dimensional, steady, Reynolds-Averaged Navier–Stokes (RANS), Computational Fluid Dynamics (CFD) simulations have been used to analyze the convective heat transfer processes for both flat and corrugated UTCs. The performance of five potentially suitable turbulence closure models: Standard k–ε, Renormalization Normal Group k–ε (RNG k–ε), Realizable k–ε, Shear Stress Transport k–ω (SST k–ω) and Reynolds Stress Model (RSM), has been evaluated. Two scenarios have been considered: a flat UTC under free stream approaching flow and a corrugated UTC subjected to a plane wall jet flow. The results were compared against experimental data from the literature and those obtained using a full-scale experimental set-up in a solar simulator, in terms of the velocity and turbulent kinetic energy of the airflow as well as the plate surface and air temperature. The validation study showed that the RNG k–ε model has the best overall performance for both UTC geometries at reasonable accuracy and computing cost. A parametric analysis has been conducted using the RNG k–ε model at 3m/s approaching flow velocity, for different suction flow rates (0.01 and 0.06m/s) and free stream turbulence intensities (0.1% and 20%). The results showed that in UTCs, it is the suction velocity, rather than the suction ratio of Vs/U∞, that has the most profound impact on the boundary layer development and thermal efficiency. For flat UTCs, the presence of perforations is more significant than the level of turbulence intensity in the approach flow. However, for corrugated UTCs, the incident turbulence intensity plays a more important role in the system performance than the perforation dimensions due to the turbulent interaction between the corrugated geometry and the incoming flow. Although a high suction rate can help maintain the asymptotic boundary layer profiles and, hence simplify the energy analysis of UTCs, it is not applicable in practice due to the requirement of large fan power. These outcomes will not only further advance the development of UTCs and optimize their performance but also provide insights for the development of simplified thermal analysis models for use in building energy simulation.

Measurement of the Noise Resulting from the Interaction of Turbulence with a Lifting Surface

An experimental study of the noise resulting from the interaction of an airfoil with incident turbulence is presented. The test models include NACA0015 airfoils of different chord lengths, a flat plate with a sharp leading edge, and an airfoil of same section as a reference Fowler flap. The airfoils are immersed in nearly isotropic turbulence. Two approaches for performing the noise measurements are used and compared. The effects that turbulence intensity and integral length scales, airfoil geometry, velocity and angle of attack have on the incident turbulence interaction noise are examined. Detailed directivity measurements are presented. It is found that noise spectral levels beyond the peak frequency decrease at a slower rate for the sharper airfoil leading edges, and that spectral peak level (at 0° angle of attack) appears to be mostly controlled by the airfoil's thickness and chord. Increase in turbulence integral scale and intensity are observed to lead to a uniform increase of the noise spectral levels with an LI2 dependence (where L is the turbulence longitudinal integral scale and I is the turbulence intensity). Noise levels are found to scale with the 6th power of velocity and the 2nd power of the airfoil chord. Sensitivity to changes in angle of attack appears to have a turbulence longitudinal integral scale to chord (C) ratio dependence, with large effects on noise for L/C ≥ 1 and decreased effects as L/C becomes smaller than 1. For all L/C values, the directivity pattern of the noise resulting from the incident turbulence is seen to remain symmetric with respect to the direction of the mean flow until stall, at which point, the directivity becomes symmetric with respect to the airfoil chord. It is also observed that sensitivity to angle of attack changes is more pronounced on the model suction side than on the model pressure side, and in the higher frequency range of the spectra for the largest airfoils tested (L/C < 0.24).

Time- and frequency-domain computations of broadband noise due to interaction between incident turbulence and rectilinear cascade of flat plates

Time-domain computational aeroacoustic (CAA) techniques are developed to investigate the broadband noise resulting from the interaction of a rectilinear cascade of flat plates with incident homogeneous, isotropic turbulence. The investigation is carried out by comparing the prediction results obtained by employing the time-domain CAA method with those using existing frequency-domain methods. A semi-analytic model (Wei & Cheong, 2010) and a full three-dimensional rectilinear cascade model (Lloyd & Peake, 2008; Lloyd, 2009) are adopted for the frequency-domain computations. By comparing these computation results, the three-dimensional characteristics of inflow turbulence noise are investigated; in particular, the effects of the wavenumber components of ingested turbulence in the spanwise direction are taken into consideration in the investigation. First, CAA results are compared with those from the semi-analytic model. The results for the acoustic modes of relatively low spanwise wavenumbers obtained using both methods show good agreement, but as the spanwise wavenumber increases, the results obtained by the two methods become increasingly different. To investigate in detail the reason for these differences, mode-decomposition analysis is performed by adopting a hybrid method as well as by employing the CAA and the semi-analytic method. The hybrid method involves the following two sequential computations: (i) the upwash velocities on the flat plate airfoils of the rectilinear cascade are first predicted using the frequency-domain method, and (ii) the acoustic wave propagation is subsequently analyzed using time-domain CAA techniques, with these upwash velocities applied as the boundary conditions on the flat plate. It is seen that the results of the time-domain CAA technique and the hybrid method show good agreement, irrespective of the wavenumber and frequency. However, comparisons of the acoustic solutions from three computations reveal that the prediction results of the semi-analytic model deviate more from the other two predictions as the spanwise wavenumber of the acoustic wave increases and the frequency decreases. On a basis of this observation, a formulation is derived for the error in the pressure jump across the flat-plate predicted by using the semi-analytic method. This formulation shows that the error is approximately inversely proportional to the sound speed in the spanwise direction of the concerned acoustic modes. This result quantitatively clarifies the limitations of applying the frequency-domain method of Wei & Cheong (2010) to the three-dimensional turbulence-cascade interaction problems. Secondly, the prediction results using the time-domain CAA method are compared with those from the full three-dimensional rectilinear model that is believed to be exact model for the cascade geometry considered in this paper. This comparison shows the good agreements between two predictions, which support the above arguments for the error and the successful application of the time-domain CAA methods. It is expected that these methods can be extended to the broadband noise problem in an annular cascade, including the nonlinear interaction of the real-airfoil cascade with the incident nonhomogeneous gust.

Effect of incident flow conditions on convective heat transfer from the inclined windward roof of a low-rise building with application to photovoltaic-thermal systems

Steady RANS CFD simulations were used to evaluate convective heat transfer from the roof of a low-rise building immersed in an atmospheric boundary layer for different terrain, with relevance to photovoltaic-thermal (PV/T) systems. Dimensionless correlations for the exterior convective heat transfer coefficient (CHTC), expressed as Nusselt number (Nu), were developed for the windward roof, based on Reynolds number and incident turbulence intensity at eaves height, thereby quantifying the strong influence of incident turbulence on the CHTC. Simulations were also performed for a generic flat plate of the same streamwise length so as to provide further insight into the effects of incident turbulence on the windward roof boundary layer. The CHTC values for the windward roof and, hence, the correlations presented here, for a given terrain, are largely insensitive (less than 5% change) to variations in roof slope (from 20 to 45°) or small changes in wind direction (up to 20° from the normal to the eaves). Mixed convection simulations for conditions with significant buoyancy forces (Richardson numbers from 0.9 to 7) show that the CHTC values can be up to 14% higher than those based on forced convection only.

Application of a Beamforming Technique to the Measurement of Airfoil Leading Edge Noise

The present paper describes the use of microphone array technology and beamforming algorithms for the measurement and analysis of noise generated by the interaction of a turbulent flow with the leading edge of an airfoil. Experiments were performed using a setup in an aeroacoustic wind tunnel, where the turbulent inflow is provided by different grids. In order to exactly localize the aeroacoustic noise sources and, moreover, to separate airfoil leading edge noise from grid-generated noise, the selected deconvolution beamforming algorithm is extended to be used on a fully three-dimensional source region. The result of this extended beamforming are three-dimensional mappings of noise source locations. Besides acoustic measurements, the investigation of airfoil leading edge noise requires the measurement of parameters describing the incident turbulence, such as the intensity and a characteristic length scale or time scale. The method used for the determination of these parameters in the present study is explained in detail. To demonstrate the applicability of the extended beamforming algorithm and the experimental setup as a whole, the noise generated at the leading edge of airfoils made of porous materials was measured and compared to that generated at the leading edge of a common nonporous airfoil.

Propagation of wrinkled turbulent flames in the context of hydrodynamic theory

We study the propagation of premixed flames in two-dimensional homogeneous isotropic turbulence using a Navier–Stokes/front-capturing methodology within the context of hydrodynamic theory. The flame is treated as a thin layer separating burnt and unburnt gases, of vanishingly small thickness, smaller than the smallest fluid scales. The method is thus suitable to investigate the flame propagation in the wrinkled flamelet regime of turbulent combustion. A flow-control system regulates the mean position of the flame and the incident turbulence intensity. In this context we study the individual effects of turbulence intensity, turbulence scale, thermal expansion, hydrodynamic strain and hydrodynamic instability on the propagation characteristics of the flame. Results are obtained assuming positive Markstein length, corresponding to lean hydrocarbon–air or rich hydrogen–air mixtures. For stable planar flames we find a quadratic dependence of turbulent speed on turbulence intensity. Upon onset of hydrodynamic instability, corrugated structures replace the planar conformation and we observe a greater resilience to turbulence, the quadratic scaling being replaced by scaling exponents less than one. Such resilience is also confirmed by the observation of a threshold turbulence intensity below which the propagation speed of corrugated flames is indistinguishable from the laminar speed. Turbulent speed is found to increase and later plateau with increasing thermal expansion, this affecting the average flame displacement but not the mean flame curvature. In addition, turbulence integral scale is also observed to affect the propagation of the flame with the existence of an intermediate scale maximizing the turbulent speed. This maximizing scale is smaller for corrugated flames than it is for planar flames, implying that small eddies that will be unable to significantly perturb a planar front could be rather effective in perturbing a corrugated flame. Turbulent planar flames, and more so corrugated flames, were observed to experience a positive mean hydrodynamic strain, which was explained in terms of the overwhelming mean contribution of the normal component of strain. The positive straining causes a decrease in the mean laminar propagation speed which in turn can decrease the turbulent speed. The effect of the flame on the incident turbulent field was examined in terms of loss of isotropy and vorticity destruction by thermal expansion. The latter can be mitigated by a baroclinic vorticity generation which is enhanced for corrugated flames.

Numerical modelling of forced convective heat transfer from the inclined windward roof of an isolated low-rise building with application to photovoltaic/thermal systems

Abstract The present work evaluates forced convective heat transfer from the inclined windward roof of an isolated low-rise building, with application to building-integrated Photovoltaic/Thermal (PV/T) systems. High resolution, 3-D, steady, Reynolds-Averaged Navier–Stokes (RANS) Computational Fluid Dynamics (CFD) simulations of the wind flow field near the roof of a building with plan dimensions of 4.2 m by 6 m, a 3 m eaves height and a 30° roof slope, are conducted, with the results validated by experimental data from a 1:50 scale model tested in a boundary layer wind tunnel. The heat transfer model is validated using the boundary layer correlation for an isothermal horizontal flat plate in uniform flow. Full-scale simulations, with the same building geometry and numerical model, for Reynolds numbers (Re) from 2.2 × 105 to 7.7 × 105 based on wind speed at eaves height and sloped roof length, are also carried out, for four roughness length (z0) values representing open and suburban terrain. From these, dimensionless correlations for the exterior convective heat transfer coefficient (CHTC), expressed as Nusselt number (Nu), for the windward roof are developed which include the Re and the incident turbulence intensity at eaves height. The windward roof average CHTC is dependent upon the presence and extent of the leading edge separated flow region. This region reduces in size as both Re and eaves height turbulence intensity are increased, such that at high turbulence levels it disappears and the value of the exponent on the Re term in the Nu correlation approaches that for a flat plate turbulent boundary layer.

Heat transfer from the stagnation area of a heated cylinder at ReD = 140,000 affected by free-stream turbulence

The effect of free-stream grid-turbulence on the flow around and heat transfer from the stagnation region of a circular cylinder was studied using direct numerical simulations (DNS). Simulations with and without free-stream fluctuations were carried out at a Reynolds number of Re D = 140,000 (based on the inflow velocity and the cylinder diameter D), which is in the higher subcritical range. A splitter plate was introduced behind the cylinder to counteract the formation of a vortex street. To resolve the flow up to 746.5 million grid points were employed. Compared to the fully laminar simulation, the addition of Tu = 30% grid turbulence at the inflow plane was found to lead to an increase in heat transfer at the stagnation line of the cylinder of 66%. A very good agreement was obtained with the correlations of Dullenkopf and Mayle [K. Dullenkopf, R. Mayle, The effects of incident turbulence and moving wakes on laminar heat transfer in gas turbines, ASME J. Turbomach. 116 (1994) 23–28; K. Dullenkopf, R. Mayle, An account of free-stream-turbulence length scale on laminar heat transfer, ASME J. Turbomach. 117 (1995) 401–406].

Frequency-domain computation of inflow broadband noise due to interaction of a rectilinear cascade of flat plates with incident turbulence

This paper deals with the broadband noise due to the interaction between convected turbulent gusts and a rectilinear cascade of flat plates bounded by two parallel walls. An analytic formulation for the acoustic power spectrum due to this turbulence-cascade interaction is derived, which can be used to assess the effects of the span-wise wavenumber components of ingesting turbulent gust on the overall acoustic power spectrum. This three-dimensional theory is based on the two-dimensional theory of Cheong et al. (2006, 2009). The three-dimensional model is shown to provide a close fit to the measured spectrum of rotor-stator interaction. The predictions using this three-dimensional model are also compared with those using the previous two-dimensional model by Cheong et al. (2006; 2009). Through this comparison, it is found that the contributions to the acoustic power of the span-wise wavenumber components of incident turbulent gust are increased as the frequency is augmented, which is mainly due to three-dimensional dispersion-relation characteristics of acoustic waves. This implies that the number of incident turbulent gust modes directly involved in generating cut-on acoustic waves increases as the frequency increases. Therefore, in the lower frequency range, three-dimensional acoustic power is less than its corresponding two-dimensional one, whereas, as the frequency increases, the three-dimensional acoustic power spectrum closely follows those of two-dimension. The formulation is also used to make a parametric study about the effects on the power spectrum of the blade number, stagger angle, gap-chord ratio, and Mach number.

Attenuation of the wake of a sphere in an intense incident turbulence with large length scales

We report an investigation of the wake of a sphere immersed in a uniform turbulent flow for sphere Reynolds numbers ranging from 100 to 1000. An original experimental setup has been designed to generate a uniform flow convecting an isotropic turbulence. At variance with previous works, the integral length scale of the turbulence is of the same order as the sphere diameter and the turbulence intensity is large. In consequence, the most intense turbulent eddies are capable of influencing the flow in the close vicinity of the sphere. Except in the attached region downstream of the sphere where the perturbation of the mean velocity is larger than the standard deviation of the incident turbulence, the flow is controlled by the incident turbulence. The distortion of the turbulence while the flow goes round the sphere leads to an increase in the longitudinal fluctuation and a decrease in the transversal one. The attenuation of the transversal fluctuations is still significant at 30 radii downstream of the sphere whereas the longitudinal fluctuations relax more rapidly toward the incident value. The more striking result however concerns the evolution of the mean velocity defect with the distance x from the sphere. It decays as x−2 and scales with the standard deviation of the incident turbulence instead of scaling with the mean incident velocity.