Spectra Of Pressure Fluctuations Research Articles

Numerical prediction of turbulent boundary layer noise from a sharp‐edged flat plate

SummaryAn efficient hybrid uncorrelated wall plane waves–boundary element method (UWPW‐BEM) technique is proposed to predict the flow‐induced noise from a structure in low Mach number turbulent flow. Reynolds‐averaged Navier‐Stokes equations are used to estimate the turbulent boundary layer parameters such as convective velocity, boundary layer thickness, and wall shear stress over the surface of the structure. The spectrum of the wall pressure fluctuations is evaluated from the turbulent boundary layer parameters and by using semi‐empirical models from literature. The wall pressure field underneath the turbulent boundary layer is synthesized by realizations of uncorrelated wall plane waves (UWPW). An acoustic BEM solver is then employed to compute the acoustic pressure scattered by the structure from the synthesized wall pressure field. Finally, the acoustic response of the structure in turbulent flow is obtained as an ensemble average of the acoustic pressures due to all realizations of uncorrelated plane waves. To demonstrate the hybrid UWPW‐BEM approach, the self‐noise generated by a flat plate in turbulent flow with Reynolds number based on chord Rec = 4.9 × 105 is predicted. The results are compared with those obtained from a large eddy simulation (LES)‐BEM technique as well as with experimental data from literature.

Wake dynamics and surface pressure variations on two-dimensional normal flat plates

The relationship between vortex dynamics and surface pressure fluctuations on the leeward face of a two-dimensional normal thin flat plate was studied using Direct Numerical Simulations for incompressible flow at a Reynolds number of 1200. The vortex shedding frequency was observed in the spectra of pressure fluctuations on both faces of the plate, while a lower frequency spectral peak was only evident on the leeward pressure fluctuations. Local sharp peaks of low pressure in the separated shear layers coincide with increases in the leeward face pressure fluctuations. These observations are tied to the vortex dynamics using the invariant Q, commonly used for vortex identification. Q is also proportional to the source term for the Poisson equation for the instantaneous pressure. The pressure, which is the only contributor to the plate drag, varies significantly in response to alterations to the vortex shedding, which can be observed in differences of vortex trajectories. At minimum drag, the pressure fluctuations are small, which is attributed to lower values of Q associated with weaker vortices.

Instability of precession driven Kelvin modes: Evidence of a detuning effect

We report an experimental study of the instability of a nearly-resonant Kelvin mode forced by precession in a cylindrical vessel. The instability is detected above a critical precession ratio via the appearance of peaks in the temporal power spectrum of pressure fluctuations measured at the end-walls of the cylinder. The corresponding frequencies can be grouped into frequency sets satisfying resonance conditions with the forced Kelvin mode. We show that one triad is associated with a parametric resonance of Kelvin modes. For the first time, we observe a significant frequency variation of the unstable modes with the precession ratio. We explain this frequency modification by considering a detuning mechanism due to the slowdown of the background flow. By introducing a semi-analytical model, we show that the departure of the flow from the solid body rotation leads to a modification of the dispersion relation of Kelvin modes and to a detuning of the resonance condition. Our calculations reproduce the features of experimental measurements. We also show that a second frequency set, including one very low frequency as observed in the experiment, does not exhibit the properties of a parametric resonance between Kelvin modes. Our observations suggest that it may correspond to the instability of a geostrophic mode.

Porous domes as wind noise filters for infrasound sensing on Mars

The ability to detect infrasonic waves on Mars will enable further understanding of its environment. For example, infrasound arrivals from large storm systems, dust devils, and bolides can be used to understand source mechanisms and constrain impact statistics. The InSight microbarometer will measure the effect of ambient pressure fluctuations on seismometer data. It may also be able to detect infrasonic signals from distant sources, which, however, will be contaminated by wind noise. On Earth, infrasound stations use large-area spatial filters to reduce wind-noise contamination. These filters consist of long drilled pipes arranged radially around the sensor. Since this arrangement may not be easily deployable on Mars, we investigate the feasibility of tent-like porous domes, erected around the sensor, as wind-noise filters. Through theoretical modeling, we predict the power spectrum of wind pressure fluctuations at the center of the dome under Martian conditions. The results show that, as the porosity of the dome wall is lowered from 80% to 40%, a secondary wind-noise PSD peak is formed, moving from approximately 0.4 Hz–3 Hz, while the high-frequency “tail” (∼ 20 Hz) becomes stronger; low frequencies (f<0.1 Hz) show the typical characteristics of the energy-containing range. The porosity dependence shows promise in the potential to “adapt” the filter characteristics to various wind conditions. The research was supported by the Louisiana Space Grant Consortium (LaSPACE).

Thermodynamic analysis of energy dissipation and unsteady flow characteristic in a centrifugal dredge pump under over-load conditions

The present paper aims to investigate the energy dissipation related to unsteady flow phenomena inside a three-bladed impeller of a centrifugal dredge pump under over-load operating conditions. Three-dimensional unsteady numerical simulations of the centrifugal pump are performed by adopting the SAS SST-curvature correction turbulence model with the total energy equation. The simulating results are verified by comparing the performance results and pressure fluctuation with available experimental data. The unsteady flow patterns and energy dissipation in the rotating impeller are analysed by entropy distribution and pressure fluctuation spectra. A high-entropy area appears in the impeller flow passage when the discharge increases. It is indicated in the unsteady simulation results that a vortex flow with high entropy generates and detaches periodically, which causes the hydraulic energy loss under over-load operating conditions. In numerical simulations, a frequency as 3.3 times of rotating frequency is found in the pressure spectral analysis at 1.45 Q0 operating condition, which is related to the unsteady flow structure. The secondary flow near the volute tongue is found at 1.45 Q0 operating condition due to the large angle of attack when discharge increases.

Aeroacoustic simulation of the high-lift airfoil using hybrid reynolds averaged Navier-Stokes/high-order implicit large eddy simulation method

A hybrid RANS/HILES method (HRILES) is developed by combining the RANS-SST model and high order implicit large eddy simulation method (HILES) and employed with the Ffowcs Williams-Hawkings (FW-H) equation to predict the slat noise of 30P30N high-lift airfoil. Comparison has been made between the HRILES method and the traditional DDES based on the full-turbulence model SST by simulating the single cylinder case with &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$Re_{{d}}=4.3\times10^4$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20190777_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20190777_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;. The HRILES method is able to predict the transition phenomenon and the small-scale separation bubble in the sub-critical wake region while the DDES can't and get a better mean wall pressure distribution than DDES. The amplitude and frequency spectrum of the far-field sound pressure level are in good agreement with the experimental data. In the simulation of 30P30N high-lift airfoil, the famous IDDES model is also used for comparison, both results are compared with experimental measurements. The computational mesh is provided by Japan Aerospace Exploration Agency (JAXA) in the Workshop on Benchmark problems for Airframe Noise Computations (BANC). The HRILES method obtains quantitative agreement with experimental data in terms of mean wall pressure coefficient, frequency spectrum of pressure fluctuations on the slat surface, and the mean flow statistics in the slat cusp shear layer. The IDDES model slightly underestimate the suction effect on the upper surface of the slat, and delays the instabilities in the slat cusp shear layer. The near-field noise spectra are compared with measurements obtained in JAXA low-speed Wind Tunnel. Narrow band peaks present are well recovered by both methods, while IDDES model overestimate the broadband noise. Far-field noise directivity results of every components, filtered in the band [256Hz–10KHz], are compared with each other, and the slat cove is confirmed to dominate the sound noise levels. The slat and flap noises show a typical dipole distribution, while the main wing noise's directivity is not apparent. Computational results show that the HRILES method, as one kind of generalized Hybrid RANS/LES method, HRILES can smoothly switch between the SST model and the HILES method. HRILES has the high-resolution simulation capability of the HILES in the LES region, and can reduce the requirements of the HILES method on the near-wall grid distribution by using the SST model in the inner boundary layer. As a result, the HRILES method has advantages in simulations at high reynolds numbers and aeroacoustic problems. Further research will be carried out in the applications at higher reynolds number flows with complex geometry in the future.

Wall-pressure spectra models for supersonic and hypersonic turbulent boundary layers

This paper presents an investigation of pressure fluctuations spectra beneath supersonic and hypersonic turbulent boundary layers at zero pressure gradient. High-order implicit Large Eddy Simulations have been used to provide numerical data for assessing existing models and further improving their qualitative accuracy in predicting wall-pressure spectra. Several different models have been investigated and it is shown that existing models fail to capture the correct behaviour of pressure fluctuations in supersonic and hypersonic boundary layers across a broad range of frequencies. The models have been modified by introducing compressibility corrections. The modified models are validated against implicit Large Eddy Simulations, Direct Numerical Simulations, and experimental data. The qualitative accuracy of the models is discussed and the most promising model is identified.

Simultaneous effects of mesh refinement, grid configuration and wall boundary condition on prediction of pressure gradients and velocity profiles of microparticles in a conical fluidized bed

The reliability and accuracy of numerical results of microparticle fluidization in a conical bed, affected simultaneously by mesh refinement, the grid configuration and the wall boundary condition (BC), are analyzed. Specifically, pressure gradients and velocity profiles of titania powder are studied for a conical bed. The Gidaspow drag correlation and different wall BCs are considered using a Eulerian–Eulerian two-fluid model. Predictions of the pressure fluctuation, power spectra of the corresponding pressure fluctuations, bed pressure drop, minimum fluidization velocity, axial solid velocity, bed expansion ratio, and particle size distribution are compared with experimental data. Mesh sensitivity analysis using hexahedral and tetrahedral cells with a uniform mesh and near-wall mesh refinement is conducted to investigate the effects of mesh configurations in estimating particle flow patterns. Simulations show that significant savings in terms of computational time are realized by choosing a uniform mesh while the hexahedral structure, the near-wall mesh refinement, and the free-slip BC give the closest fit to the experimental data.

Blood hammer phenomenon in human aorta: Theory and modeling

This paper contains the results of computing of a blood pressure and a flow speed in a human aorta in a diastolic phase of a heart cycle. The model is based on the one-dimensional flow approach. The blood hammer effect means abrupt increasing of pressure in a blood vessels due to the sharp changes in flow speed. The closing of aortic valve at the proto-diastole phase causes such blood hammer.We consider an aorta as a simple cylindrical conduit with elastic walls. The aortic valve and the bifurcation were located in the opposite ends of the conduit. The analysis of possible types of blood hammer effect in the “conduit-blood” system was performed. The lifelike initial and boundary conditions for the problem were proposed.We found a strong peak of pressure during the first third of diastole at the normal closure of the aortic valve. We observed the minor fluctuations of pressure in the later part of diastole too. Blood flow speed also has minor oscillations during the diastole. Such results are typical under the complete blood hammer effect condition.An abnormal long valve closure causes an incomplete blood hammer effect. In that case the calculated oscillations of the flow speed had higher intensity without strong pressure peak.The Fourier spectra of pressure fluctuations are located in the range of 16–87 Hz, that is nearby to known frequencies of the second heart sound produced by aortic valve.

Investigation of Spectral Characteristics by Passive Control Methods Past a Supersonic Cavity

Numerical investigations of the leading-edge sawtooth spoiler and slanted aft wall were performed to explore the mechanisms of the suppression of pressure fluctuations in an open-type cavity flow, focusing on the pressure fluctuation spectra and their spatial distributions. The rectangular cavity has a length-to-depth ratio of six, and the freestream Mach number is 1.5. Improved delayed detached-eddy simulation was used to predict the unsteady cavity flows and pressure fluctuations. Both control methods exhibited effectiveness in pressure fluctuation suppression, but their respective mechanisms are quite different. It was observed that the leading-edge sawtooth spoiler lifts the shear layer and reduces its interaction with the aft wall. The energy distribution of Rossiter modes changes significantly, which indicates that the pressure fluctuation feedback loop inside the cavity has changed. However, the slanted aft wall merely alters the cavity flowfield. Unlike the leading-edge method, the Rossiter mode distribution and the feedback mechanism remain unchanged. The slanted aft wall mainly suppresses the upstream-traveling perturbation generated by the cavity trailing edge but has little influence on the downstream-traveling perturbation.

Effect of the Density of a Microspherical Catalyst on the Operating Regimes of a Fluidized Bed

An experimental study is performed of a circulating fluidized bed of two types of finely dispersed Geldart A particles with different bulk densities. The first type of particles have bulk density ρb = 1200 kg/m3, while the bulk density of the second type of particles is ρb = 1300 kg/m3. The studies are performed on a test bench 0.7 m in diameter and 5.75 m tall at room temperature with air used as the fluidizing gas. The velocity of fluidization ranges from 0.1 to 0.75 m/s. The bed is sectioned along its height with a set of horizontal diffuser grids. The results from measuring the fluctuations, the average drops in pressure, and the pressure distribution along the height of the fluidized bed are used to estimate the effect produced by the density of particles on its operational regimes. Velocity of transition Uc, determined from the mean-square deviations of pressure drop fluctuations, is 0.40 m/s for lighter particles and 0.35 m/s for heavier particles. Velocity of transition Uc determined from the power of the energy spectrum of pressure fluctuations Е is 0.45 and 0.40 m/s for lighter and heavier particles, respectively. The results from pressure measurements along the bed height show a linear drop with increasing bed height, and this drop is faster for heavier particles than for lighter particles.

External flow velocity and synthetic jets parameters influence on cavity flow structure and acoustics characteristics using RANS/ILES

An influence of synthetic jets on the flow in a three-dimensional cavity M219 was studied using RANS/ILES method. Calculations were performed for Mach numbers M0 = 0.85 and M0 = 1.5. Synthetic jets’ operating parameters such as their position, number, frequency, and amplitude were varied. An impact of these parameters and M0 on flow in the cavity, distributions, and levels of pressure fluctuations on the cavity walls as well as the narrowband spectra of pressure fluctuations were obtained. Synthetic jets located in front of a cavity may reduce peak pressure pulsations on the cavity back wall by 37% for a subsonic external flow. Moreover, it was found that synthetic jets may decrease the second and the third modes of pressure fluctuations on the back wall both for subsonic flow and supersonic case.

Generation of interior cavity noise due to window vibration excited by turbulent flows past a generic side-view mirror

We investigate the interior noise caused by turbulent flows past a generic side-view mirror. A rectangular glass window is placed downstream of the mirror. The window vibration is excited by the surface pressure fluctuations and emits the interior noise in a cuboid cavity. The turbulent flows are simulated using a compressible large eddy simulation method. The window vibration and interior noise are predicted with a finite element method. The wavenumber-frequency spectra of the surface pressure fluctuations are analyzed. The spectra are identified with some new features that cannot be explained by the Chase model for turbulent boundary layers. The spectra contain a minor hydrodynamic domain in addition to the hydrodynamic domain caused by the main convection of the turbulent boundary layer. The minor domain results from the local convection of the recirculating flow. These domains are formed in bent elliptic shapes. The spanwise expansion of the wake is found causing the bending. Based on the wavenumber-frequency relationships in the spectra, the surface pressure fluctuations are decomposed into hydrodynamic and acoustic components. The acoustic component is more efficient in the generation of the interior noise than the hydrodynamic component. However, the hydrodynamic component is still dominant at low frequencies below approximately 250 Hz since it has low transmission losses near the hydrodynamic critical frequency of the window. The structural modes of the window determine the low-frequency interior tonal noise. The combination of the mode shapes of the window and cavity greatly affects the magnitude distribution of the interior noise.

Investigation of peak wind loads on tandem heliostats in stow position

Abstract This paper investigates the effects of turbulence in the atmospheric boundary layer (ABL) on the peak wind loads on heliostats in stow position in isolation and in tandem configurations with respect to the critical scaling parameters of the heliostats. The heliostats were exposed to a part-depth ABL in a wind tunnel using two configurations of spires and roughness elements to generate a range of turbulence intensities and integral length scales. Force measurements on different-sized heliostat mirrors at a range of heights found that both peak lift and hinge moments were reduced by up to 30% on the second tandem heliostat when the spacing between the heliostat mirrors was close to the mirror chord length and converged to the isolated heliostat values when the spacing was greater than 5 times the chord length. Peak wind loads on the tandem heliostat were above those on an isolated heliostat for an integral-length-scale-to-chord-length ratio L u x / c of less than 5, whereas tandem loads were 30% lower than an isolated heliostat at L u x / c of 10. The reduced loads on the tandem heliostat corresponded to a shift to higher frequencies of the fluctuating pressure spectra, due to the break-up of large eddies by the upstream heliostat.

Unsteady pressure fluctuations measured on a hammerhead space vehicle and comparison with Coe and Nute's 1962 data

A detailed survey of pressure fluctuations was conducted on a replica of the generic, “hammerhead” shaped space vehicle tested more than half century ago by Coe and Nute (1962). A large number of current and past space vehicles follow this general hammerhead configuration. The present test was conducted in the 11-by-11 ft Transonic Wind Tunnel of NASA Ames Research Center over the critical transonic Mach number range of 0.6 ≤ M ≤ 1.2 where typical vehicles encounter very high levels of surface pressure fluctuations during ascent through the atmosphere. Out of the many different types of instrumentations used for this test, data from the dynamic pressure sensors are presented in this paper. In addition, shadowgraph flow visualizations, and a qualitative measure of turbulent fluctuations, estimated from high-speed photography, are also presented. The data set provided a clear insight into the local high level of fluctuations from the formation of the transonic shocks on the payload fairing and also from the impingement of the separated shear layer on the second stage. Space–time correlation showed interesting physics of upstream propagation of pressure fluctuations on the payload fairing when local shock waves were present. A comparison of the magnitude of pressure fluctuations between the present test and that done earlier by Coe and Nute showed good agreement when the limited frequency bandwidth of equipment used in the latter was accounted for. Similarly, when accounting for the differences in the free-stream dynamic pressure, the spectra of surface pressure fluctuations were in reasonable agreement between the present and Coe–Nute tests. The present test provides a far more complete picture of pressure fluctuations due to the usage of a large number of pressure transducers (216 versus 30), wider frequency bandwidth (50 kHz versus 1 kHz), and unsteady pressure-sensitive paint.

Aeroacoustic Prediction of a Multi-Element Airfoil Using Wall-Modeled Large-Eddy Simulation

Wall-modeled large-eddy simulation is employed in combination with the Ffowcs Williams–Hawkings equation to predict and analyze the aeroacoustics of a 30P30N three-element airfoil. The results are compared with experimental measurements, and quantitative agreement is obtained in terms of flow statistics, frequency spectra of pressure fluctuations on the slat surface, and the far-field noise spectra, thus demonstrating the feasibility and accuracy of the wall-modeled large-eddy simulation approach. The slat cove is confirmed to be the primary sound source and emits narrowband tonal noise at several resonance frequencies in addition to broadband noise. The main element is the largest contributor to low-frequency noise, and the flap is a negligible noise source at all frequencies. Computational results for different freestream Mach numbers indicate that the resonance frequencies are well predicted by the semi-empirical models of Block (“Noise Response of Cavities of Varying Dimensions at Subsonic Speeds,” NASA Technical Note D-8351, 1976) and Terracol et al. (“Investigation of the Unsteady Flow and Noise Generation in a Slat Cove,” AIAA Journal, Vol. 54, No. 2, 2016). The intensity of flyover noise is shown to largely scale with the fifth-power of Mach number, as suggested by Guo and Joshi (“Noise Characteristics of Aircraft High Lift Systems,” AIAA Journal, Vol. 41, No. 7, 2003), but in most other directions, the Mach number scaling of sound intensity is higher than the fifth power.

Numerical evaluation of transient flow characteristics in a transonic centrifugal compressor with vaned diffuser

Three-dimensional, compressible, unsteady Navier–Stokes equations are solved to investigate the flow field of a transonic centrifugal compressor with high compression ratio. The computational domain is consisted of an inlet bell mouth and an impeller with splitter blades, followed by a two-dimensional wedge vaned diffuser. The numerical method was validated by comparing the results with those of experiments in terms of aerodynamic compressor performance and flow field within the compressor passages. A detailed analysis of instantaneous and time-averaged flow field was conducted in the impeller and diffuser passages. The present study focuses on the pressure fluctuations and entropy production within the impeller and diffuser passages at the compressor design point. It is shown that the interaction between the impeller and diffuser blades leads to unsteadiness at the interface region and a pulsating behavior within the diffuser passages. Pressure waves with different convective velocities, generated by the impeller–diffuser interaction and pseudo-periodic unsteady separation bubbles, are captured in the time/space domain along the diffuser blade surfaces. The pressure fluctuation spectra were evaluated to analyze the noise characteristics of the centrifugal compressor as the main source of blade passing frequency noise. It is expected that the current unsteady Reynolds-Averaged Navier–Stokes (URANS) approach can be used as a tool for the prediction of unsteady flow and compressor noise characteristics with a proper turbulence model and well-resolved grids.

Detached-Eddy Simulation of a Supersonic Reattaching Shear Layer

A numerical investigation of low-frequency unsteadiness in a Mach 2.9 turbulent, reattaching shear layer was carried out with delayed detached-eddy simulation. The results were compared to data from a series of experiments performed at Princeton University. The true experimental conditions were matched, and calculations were run for 0.5 s of physical time, capturing a frequency range of about 10 Hz to 1 MHz and about 65 cycles of the Strouhal number 0.03 scale. Because of the approximations used to reduce computational cost, the computations predicted a greater flow turning angle at separation than was measured experimentally. Accounting for the consequent shift in reattachment location, the mean flow properties were predicted fairly accurately. The computations overpredicted the intensity of pressure fluctuation near reattachment, but they captured the form of the pressure fluctuation spectrum accurately. The discrepancies between the computational results and the experimental data may be the result of mean flow three-dimensionality and large-scale fluctuations in the incoming boundary layer that were not accounted for in the numerical model. Few computational studies have captured such long timescales for a high-Reynolds-number flow, and the results indicate the feasibility of studying very low-frequency unsteadiness in reattaching flows with a detached-eddy simulation. The results may also provide guidance for the total simulated time required to fully capture flows with large, slow recirculation zones.

WALL PRESSURE FLUCTUATIONS BEHIND A PIPE NARROWING

Wall pressure fluctuations behind a pipe narrowing of the abrupt, trapezium-like and streamlined axisymmetric shapes are studied experimentally. A sharp increase in their rms level in a finite region immediately downstream of the narrowing, leading up to a pronounced maximum upstream of the point of jet re-attachment, is found. Approximate estimates for the upper limits of the lengths of that region and its typical domains, as well as quantitative relationships both for the distance from the narrowing to the point of maximum rms pressure and for the rms magnitude at this point are obtained for all the shapes. Inspection of the wall pressure power spectrum reveals the presence of a few pronounced low-frequency maxima for all the narrowing shapes. The maxima are found to be associated with the large-scale eddies in the domains of separated and reattached flow, and their frequencies are close to the characteristic frequencies of the eddies’ formation. These maxima are the main distinguishing features of the spectrum under investigation compared to the power spectrum of the wall pressure fluctuations in a fully-developed turbulent flow in a pipe without narrowing. Study of the narrowing shape effects reveals the appropriate changes in the investigated statistical characteristics of the pressure, the power spectrum being more sensitive to the changes in the shape parameters compared to the rms pressure. Recommendations about possible practical application of the obtained results are given.

Aerofoil trailing‐edge noise prediction models for wind turbine applications

AbstractThis paper proposes a modified TNO model for the prediction of aerofoil trailing‐edge noise for wind turbine applications. The capabilities of the current modified model and four variants of the TNO model are analysed through a comprehensive study which includes 10 aerofoils and involves two different wind tunnels. The Reynolds numbers considered are between 1.13 and 3.41 million, and the effective angles of attack are between −2.20° and 13.58°. The merit of a model is assessed by comparing two aspects of the numerically predicted and the experimentally measured sound pressure level spectra: the sound pressure level difference between two different aerofoils at similar lift coefficients within a certain frequency range (referred to as the delta noise); and the closeness in terms of spectral magnitude and shape of the predicted and measured sound pressure level spectra. The current modified model is developed by deriving new formulations for the computation of the wall pressure fluctuation spectrum. This is achieved by using the approximate ratio of the normal Reynolds stress components for an anisotropic flow over a flat plate to estimate the vertical Reynolds stress component, and by introducing new stretching factors to take the effects of turbulent flow anisotropy into account. Compared with the four TNO model variants tested, the current modified model has strong delta noise prediction ability, and is able to predict sound pressure level spectra that are more consistent and closer to measurements for the vast majority of aerofoils and flow conditions tested in the two wind tunnels. Copyright © 2017 John Wiley &amp; Sons, Ltd.