It is hypothesized that butterfly wing scale geometry and surface patterning may function to improve aerodynamic efficiency. In order to investigate this hypothesis, a method to measure butterfly flapping kinematics optically over long uninhibited flapping sequences was developed. Statistical results for the climbing flight flapping kinematics of 11 butterflies, based on a total of 236 individual flights, both with and without their wing scales, are presented. Results show, that for each of the 11 butterflies, the mean climbing efficiency decreased after scales were removed. Data was reduced to a single set of differences of climbing efficiency using are paired t-test. Results show a mean decrease in climbing efficiency of 32.2% occurred with a 95% confidence interval of 45.6%-18.8%. Similar analysis showed that the flapping amplitude decreased by 7% while the flapping frequency did not show a significant difference. Results provide strong evidence that butterfly wing scale geometry and surface patterning improve butterfly climbing efficiency. The authors hypothesize that the wing scale's effect in measured climbing efficiency may be due to an improved aerodynamic efficiency of the butterfly and could similarly be used on flapping wing micro air vehicles to potentially achieve similar gains in efficiency.
This research investigation encompasses expanded testing of a high frequency combustion instability suppression technique, in which an instability is able to be controlled by acoustically modulating the incoming oxidizer flow. To test this concept, a single element model rocket combustor (dinner = 10.16 cm and l = 16.51 cm) which burned gaseous oxygen and methane was implemented. The single injector incorporated was of a 45 o impinging pentad style with a JBL 2446J compression driver at the base of the oxidizer supply line. Using this test facility, two acoustic modulation approaches were investigated to determine their effectiveness at damping a spontaneously excited f ≈ 2,400 Hz longitudinal instability. The first approach saw varying 500 Hz bands of white noise applied from f = 0-500 Hz to 2,000-2,500 Hz, while the second approach implemented single frequency signals with arbitrary phase swept from f = 500 Hz -2,500 Hz. It was found that above a certain signal amplitude threshold, 95+ % suppression of the spontaneous combustion oscillation was achieved using these two acoustic modulation approaches. Also, the frequency ranges associated with instability suppression were shown to expand with increased amplitude of the applied acoustic signal in both the band-limited white noise and single frequency sweep studies. Thus from these results, further evidence is provided to support the strategic application of acoustic modulation within an injector as a potential method to control high frequency combustion instabilities for liquid rocket engine applications.
A novel experimental technique is presented for gathering data on the kinematics and trajectories of flapping animals and vehicles. An optical tracking facility was used to record the free flight of the Monarch Butterfly (Danaus plexippus). The 5.7m×9.1m×3.0m capture volume allowed enough space to capture large numbers of sequential flaps. The system automatically tracked reflective markers, which we modified to reduce the effects of additional mass to the flight characteristics. This technique was used to record 2,000 flights of 86 different butterflies. A data analysis method is also presented which calculates information on the flapping as well as motion of the body. A sample of data analyzed over 75 flights spanning 9 butterflies in a climbing trajectory is presented. It was found that the flapping frequency of the butterfly remained fairly constant at approximately 9.89 Hz for all tests spanning a large range of climbing rates. The flapping amplitude was found to vary more significantly across the tests, with an average value of 243 o and a standard deviation of 23 o . The body of the butterfly was also recorded oscillating with the same frequency as the flapping. A phase offset between the flapping and body oscillations was recorded with an average of 90 o and a relatively small standard deviation of 7 o . The amplitude of this oscillation averaged 9.87 mm with a standard deviation of 1.43 mm. We believe the presented experimental technique can help improving our understanding of biological flight and development of micro flapping robots. Nomenclature f = frequency of flapping motion k = reduced frequency ref = reference length, defined as the length of one forewing left = position vector from head to left wing rear = position vector from head to rear wing right = position vector from head to right wing Re = Reynolds number St = Strouhal number ref = reference velocity, defined as the magnitude of the velocity of the butterfly γ = instantaneous flapping angle ϕ = phase angle between flapping and body motions = kinematic viscosity of air = complex frequency
A linear modal analysis is undertaken to investigate the effects of acoustic modulation at the inlet boundary on the longitudinal instability modes of a dump combustor. This study complements an accompanying experimental investigation that demonstrates combustion instability control through single-frequency acoustic modulation at the inlet [Bennewitz, J. W., Frederick, R. A., Jr., Cranford, J. T., Lineberry, D. M., "Combustion Instability Control Through Acoustic Modulation at the Inlet Boundary: Experiments," Journal of Propulsion and Power (to be published)]. The modal analysis employs acoustically consistent matching conditions instead of the conventional mass, momentum, and energy balances. A specific impedance boundary condition at the inlet is derived through a mass-spring-damper model of a speaker diaphragm that provides the acoustic modulation. The speaker model constants are obtained from an apparatus consisting of a speaker attached to a short hard-wall-terminated duct. At first, the modal analysis is shown to predict a naturally unstable first longitudinal mode in the absence of acoustic modulation, consistent with the spontaneously excited combustion instability mode observed experimentally. Subsequently, a detailed investigation involving variation of the modulation frequency from 0 to 2500 Hz and a mean combustor temperature from 1248 to 1685 K demonstrates the unstable to stable transition of a 2300-2500 Hz first longitudinal mode. The model-predicted mode stability transition is consistent with experimental observations, thereby supporting the premise that inlet acoustic modulation is a means to control high-frequency combustion instabilities. From the modal analysis, it may be deduced that the inlet impedance provides a damping mechanism for instability suppression. Nomenclature A = speaker diaphragm area, m 2 A = amplitudes of the longitudinal mode propagating in the positive and negative x directions, Pa B = electromagnetic speaker B field, T b = speaker diaphragm damping coefficient, N · s∕m c = mean sound speed, m∕s d dphgm = diaphragm diameter, cm F = force, N f acous;sys = acoustic system resonant frequency of the speaker constant determination test facility, Hz f mech;spk = mechanical resonance of the speaker, Hz G amp = amplifier gain Hf = speaker model frequency response function, m∕s · A I = current, A k = axial wave numbers of the longitudinal mode propagating in the positive and negative x directions, 1∕m L const;sys = length of the speaker constant determination test facility, cm M = mean flow Mach number m = speaker diaphragm mass, kg N = number of speaker diaphragm voice coil turns p 0 spk = acoustic pressure at the speaker diaphragm, Pa p 0 = acoustic pressure fluctuations, Pa p= mean pressure, Pa T comb = average combustor temperature measured from the four thermocouples located within the chamber, K u 0 spk = acoustic velocity at the speaker diaphragm, m∕s u 0 = acoustic velocity fluctuations, m∕s u = mean velocity, m∕s Z = impedance, Pa · m∕s β = region index κ = speaker diaphr...
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