The confidence limit is a standard measure of the accuracy of the result in any statistical analysis. Most of the confidence limits are derived as follows. The data are first divided into subsections and then, under the ergodic assumption, the temporal mean is substituted for the ensemble mean. Next, the confidence limit is defined as a range of standard deviations from this mean. However, such a confidence limit is valid only for linear and stationary processes. Furthermore, in order for the ergodic assumption to be valid, the subsections have to be statistically independent. For non‐stationary and nonlinear processes, such an analysis is no longer valid. The confidence limit of the method here termed EMD/HSA (for empirical mode decomposition/Hilbert spectral analysis) is introduced by using various adjustable stopping criteria in the sifting processes of the EMD step to generate a sample set of intrinsic mode functions (IMFs). The EMD technique acts as a pre‐processor for HSA on the original data, producing a set of components (IMFs) from the original data that equal the original data when added back together. Each IMF represents a scale in the data, from smallest to largest. The ensemble mean and standard deviation of the IMF sample sets obtained with different stopping criteria are calculated, and these form a simple random sample set. The confidence limit for EMD/HSA is then defined as a range of standard deviations from the ensemble mean. Without evoking the ergodic assumption, subdivision of the data stream into short sections is unnecessary; hence, the results and the confidence limit retain the full‐frequency resolution of the full dataset. This new confidence limit can be applied to the analysis of nonlinear and non‐stationary processes by these new techniques. Data from length‐of‐day measurements and a particularly violent recent earthquake are used to demonstrate how the confidence limit is obtained and applied. By providing a confidence limit for this new approach, a stable range of stopping criteria for the decomposition or sifting phase (EMD) has been established, making the results of the final processing with HSA, and the entire EMD/HSA method, more definitive.

/pdf/a-confidence-limit-for-the-empirical-mode-decomposition-and-zpt11bvpzt.pdf

A confidence limit for the empirical mode decomposition and Hilbert spectral analysis

https://purehost.bath.ac.uk/ws/files/508962/Progress%2520in%2520Aerospace%2520Sciences%2520review%2520article%2520final%2520version.pdf

Unsteady aerodynamics of nonslender delta wings

Flow Measurement Handbook is an information-packed reference for engineers on flow measuring techniques and instruments. Striking a balance between laboratory ideal and the realities of field experience, this handy tool provides a wealth of practical advice on the design, operation, and performance of a broad range of flowmeters. The book begins with a brief review of fluid mechanics principles, how to select a flowmeter, and a variety of calibration methods. Each of the following chapters is devoted to a class of flowmeters and includes detailed information on design, applications, installation, calibration, operation, and advantages and disadvantages. Among the flowmeters discussed are orifice plate meters, venturi meters and standard nozzles, critical flow venturi nozzles, positive displacement flowmeters, turbine and related flowmeters, vortex shedding and fluidic flowmeters, electromagnetic flowmeters, ultrasonic flowmeters, and coriolis flowmeters. Also covered are mass flow measurements using multiple sensors, thermal flowmeters, angular momentum devices, probes, and modern control systems. Many chapters conclude with an appendix on the theory behind the techniques discussed.

Flow Measurement Handbook: Industrial Designs, Operating Principles, Performance, and Applications

Nomenclature AR = aspect ratio; amplitude ratio B = probability density function of velocity c = root chord length f = frequency k = reduced frequency; axial wave number n =w ave number in angular direction P = probability p = pressure fluctuation Re =R eynolds number based on chord length S = spectral density s = local semispan T = period t = time U∞ = freestream velocity u = axial velocity v = swirl velocity x = streamwise distance xbd = breakdown location y = spanwise distance z =v ertical distance above wing surface α = angle of attack � = circulation δ = flap angle � = sweep angle ν = kinematic viscosity τ = time constant � =fi nangle ω =v orticity; radial frequency

Review of Unsteady Vortex Flows over Slender Delta Wings

SUMMARY Here we analyse aeroelastic devices in the wings of a steppe eagle
 Aquila nipalensis during manoeuvres. Chaotic deflections of the
upperwing coverts observed using video cameras carried by the bird (50 frames
s –1 ) indicate trailing-edge separation but attached flow near
the leading edge during flapping and gust response, and completely stalled
flows upon landing. The underwing coverts deflect automatically along the
leading edge at high angle of attack. We use high-speed digital video (500
frames s –1 ) to analyse these deflections in greater detail
during perching sequences indoors and outdoors. Outdoor perching sequences
usually follow a stereotyped three-phase sequence comprising a glide, pitch-up
manoeuvre and deep stall. During deep stall, the spread-eagled bird has
aerodynamics reminiscent of a cross-parachute. Deployment of the underwing
coverts is closely phased with wing sweeping during the pitch-up manoeuvre,
and is accompanied by alula protraction. Surprisingly, active alula
protraction is preceded by passive peeling from its tip. Indoor flights follow
a stereotyped flapping perching sequence, with deployment of the underwing
coverts closely phased with alula protraction and the end of the downstroke.
We propose that the underwing coverts operate as an automatic high-lift
device, analogous to a Kruger flap. We suggest that the alula operates as a
strake, promoting formation of a leading-edge vortex on the swept hand-wing
when the arm-wing is completely stalled, and hypothesise that its active
protraction is stimulated by its initial passive deflection. These aeroelastic
devices appear to be used for flow control to enhance unsteady manoeuvres, and
may also provide sensory feedback.

/pdf/automatic-aeroelastic-devices-in-the-wings-of-a-steppe-eagle-3yp84cn9x3.pdf

Automatic aeroelastic devices in the wings of a steppe eagle Aquila nipalensis.

Experiments were performed for individual reali- zations of the vortex shedding process behind a circular disk at Reynolds numbers of 103—105, at which periodic vortex shedding prevails in the wake. The phase differences regarding the individual vortex shedding structures detected at multiple circumferential locations in the wake were obtained by analyzing the hot-wire signals with a conditional-sampling scheme. The phase differences of vortex shedding detected at circumferential positions 90i apart show a wide scatter, but the anti-phase character is largely preserved in the individual vortex shedding process as detected at circumferential loca- tions 180i apart. The randomness of phase differences involved in the vortex shedding process is noted to be essential in order to satisfy the axisymmetric property of the global flow.

On vortex shedding behind a circular disk

The characteristics of flow developments above 50-deg sweep delta wings with different leading-edge profiles are shown by flow visualizations and velocity measurements. The Reynolds number based on freestream velocity and root chord is about 7 x 103. The leading-edge profiles studied include the shapes of square, round, windward surface beveling, leeward surface beveling, and wedge. Based on the velocity data obtained along the leading edges of the delta wings it is noted that the flow angles associated with the separated shear layers vary with the leading-edge profiles studied. This finding infers that varying the leading-edge profile has an impact on the initial development of the separated shear layer, consequently, the formation of leading-edge vortex. Furthermore, it is shown that the leading edge of windward beveling causes the largest leading-edge flow angle and produces the most organized leading-edge vortex.

Flow developments above 50-deg sweep delta wings with different leading-edge profiles

Response of a vortex flowmeter to impulsive vibrations

Flow visualizations and surface pressure measurements are performed to study the branching phenomenon of a horseshoe vortex upstream of a series of rectangular cylinders with aspect ratios ranging from 0 to 17. The Reynolds numbers are 500 for visualization experiments and 1990 to 6650 for wind tunnel surface pressure measurements. The flow visualization results indicate that a horseshoe vortex will first evolve into a wavy structure and for aspect ratios which are equal or larger than 10, the wavy horseshoe vortex will branch itself into smaller regular vortices. The waviness disappears as soon as branching occurs. The number of the branched smaller vortices increases as the aspect ratio increases further.

J. H. Chou

Papers

On vortex shedding behind a circular disk

Flow developments above 50-deg sweep delta wings with different leading-edge profiles

Response of a vortex flowmeter to impulsive vibrations

Branching of a horseshoe vortex around surface-mounted rectangular cylinders

A T-shaped vortex shedder for a vortex flow-meter