This paper presents systematic and comprehensive experimental investigations into the use of circular dimples to reduce broadband noise on airfoils. The dimples are introduced on the suction surface of symmetric NACA airfoils with different thickness ratios for the control of broadband noise over a wide range of frequencies. The effects of dimple arrangements (inline and staggered) and their locations (1/3rd and 1/5th of the chord from the leading edge) on the noise characteristics are studied in detail to determine the best dimple arrangement, location, and airfoil geometry for low noise. Results indicate that the inline arrangement of dimples positioned at 1/3rd of the chord from the leading edge provides significant noise reductions of about 6-8 dB, particularly from mid to high frequencies. When the dimples are shifted to 1/5th of the chord from the leading edge, the degree of noise reduction decreases, which indicates that the noise reduction performance of airfoils decreases when the dimples are introduced near the leading edge. Further, it reveals that the inline arrangement of dimples on thicker airfoils provides superior noise reductions (6-8 dB) as compared to thinner airfoils (4-6 dB). Flow visualization reveals that the flow field is inconsistent throughout the span of the dimpled surface due to the evolution of small vortices from the dimple corner. It enhances mixing and accelerates flow structures passing over the dimpled surface, which is indicated by the presence of a high degree of spanwise decoherence/phase lag in the hotwire measurements. The presence of higher spanwise decoherence/phase lag due to the presence of the inconsistent flow field leads to significant reductions of far-field noise in dimpled airfoils. Further, the inline arrangement of dimples exhibits much higher levels of noise reduction as compared to staggered ones, due to the presence of a greater degree of spanwise decoherence/phase lag resulting from the substantial disruption of the flow field in the spanwise direction.

The present study experimentally and numerically investigates the flow past flat plates and NACA0012 airfoils with the different trailing edge (i.e., blunt, sharp, and rounded) and both end-rounded configurations on the far-field acoustic emissions and complex flow phenomena to determine the best edge geometry for low noise. The studies are conducted for various jet speeds of 20, 30, and 40 m/s (chordwise Reynolds numbers of 1.812 × 10 5 , 2.72 ×10 5 , and 3.62 ×10 5 ). It is observed that all the edge-modified flat plates show the highest directivity at an emission angle of 60° for all jet velocities studied. The comparison of power directivities between realistic and flat plate airfoils reveals that the realistic airfoils radiate lower acoustic emissions as compared to flat plate airfoils, albeit they show a common feature of downstream directivity. In general, the far-field acoustic emissions of both end-rounded plates are observed to be lower as compared to blunt, sharp, and rounded trailing edge geometries. The leading edge modification is also observed to reduce airfoil self-noise. The likely reason for the lower far-field acoustic emissions provided by both end-rounded trailing edged foils is due to the modification in the boundary layer characteristics owing to the presence of smooth flow around the rounded leading edge as well as reduced vortex strength as compared to the other foil geometries. Thus, the present study demonstrates that passive modifications of leading edge profiles are essential along with trailing edge for achieving lower acoustic emissions and higher noise reductions.

The study investigates how an acoustic field influences evaporation and internal circulation of twin drops when their in-between horizontal spacing varies. The acoustic source is a simple sine wave (i) with and (ii) without white noise at various frequencies. The circulation and outer flow are visualized. Maximum evaporation rate and circulation are found for the lowest frequency and highest spacing. The rate rises with the spacing for a given frequency up to a critical distance. The evaporation becomes almost identical beyond the critical spacing. A correlation among the spacing, evaporation rate, and outer flow velocity is demonstrated. The rate becomes lowest for a given frequency at the least spacing since the vapors accumulated in the surrounding are not swept out by the acoustic-induced flow. The visualization shows a horizontal outer flow, which becomes vertical with the rise in spacing because the acoustic wave can sweep the vapor out. The horizontal flow for the least spacing transforms itself to vertical when the wave amplitude is raised. The evaporation thus rises because the wave now sweeps the vapors out. We show that the perception that any acoustic wave enhances the evaporation of multiple nearby drops is incorrect. The evaporation and circulation decline faster with the rise in frequency since the surrounding flow becomes weak. Thus, we show how the spacing influences the evaporation when acoustic is incident and how the evaporation can be raised by sweeping the accumulated vapor out using higher amplitude acoustics for the closer drops.

Purpose In this paper, probabilistic response and performance analysis of a nonlinear tri-stable energy harvesting with piezoelectric coupling driven by exponentially correlated Gaussian colored noise are investigated. The effects of the system parameters, depth of potential well function, noise intensity and its correlation time on the mean square voltage are studied. Methods The joint probability density function (PDF) as well as the voltage generated are obtained by numerically solving the four dimensional Fokker-Plank (FP) equation for the coupled electromechanical system. The results as obtained using the FP solution are verified using the Monte Carlo simulations (MCS). Results A relative comparison of single, double and triple well potential functions on energy harvesting is presented. It is observed that the electromechanical coupling coefficient, damping ratio, intensity of noise and time constant and the shape of the potential wells have significant effects on the harvested energy. Under random excitation, for lower intensity of noise the energy harvester with single potential well outperforms the harvester with multiple deep potential wells. Beyond a threshold value of noise intensity, energy harvester with multiple well potentials outperforms as the jump from one potential well to another becomes more frequent with inter-well dynamics functioning. It is found that the probability of jumps between potential wells is enhanced with increase in the noise intensity and corresponding increase in the mean power generation. Nevertheless, this enhancement is weakened with increase in correlation time of noise. Conclusion The study has shown that, the energy harvested can be optimized by suitable choice of the potential function, coupling parameters, the noise intensity and its correlation time.

Moulded elastomeric vibration isolators used in aerospace applications are studied for predicting transient vibration response to typical excitations. Vibration isolators used in the present study undergo non-linear static deformations followed by transient dynamic loads. Static deformation is imposed by the specified displacement during assembly of metallic steel parts of isolator, and a static inertial load is applied as the load rating of the isolators. Statically deformed state is obtained using total Lagrangian approach assuming Hookean material model for metallic parts and Yeoh material model for elastomers. Steel properties are used from the literature, and Yeoh material constants are obtained from uni-axial tension test data of elastomer specimen. For transient response study, dynamic elastomeric constants are obtained from test in a Dynamic Mechanical Analyzer as a frequency–dependant complex function. To account for the pre-deformed state of elastomers, the Yeoh material constants are modified which includes frequency–dependant material characteristics and damping in the range of interest using multiplicative non-separable variable law based on the methodology provided for Mooney–Rivlin model. The Finite Element formulation and experimental validation provided for frequency domain response in the previous work is modified to study the isolators for rectangular and trapezium pulse loads and sinusoidally varying loads. Numerical results are validated with experimental observations for rectangular pulse load.

The present study numerically investigates the effect of Mach 5.8 flow past different stepped taper spikes on the aerodynamic drag and heating of a blunted nose cone. The effect of different spike taper angles (2.5°, 5°, 6.25°, 7.5° and 10°) and step depths (0.15, 0.2, 0.25, 0.5 and 1.0 mm) provided at the root of the spike, on the drag and heating of a blunted cone are compared with a straight one having the same spike length and step width to ascertain the best taper spike which provides the lowest drag coefficient and heat flux. The heat flux decreases with the increase of spike taper from 0 to 7.5°, while it remains almost constant beyond 7.5° taper. Further, the decrease in the drag coefficient is almost negligible beyond a spike taper of 7.5°. It shows that the best spike taper for minimum drag and heat flux is 7.5°. The effect of step depths on a 7.5° spike taper reveals that the best spike depth for minimum drag and heat flux is 0.15 mm. Mach contours show shock structures such as leading shock, separation shock, and re-attachment shock, while the velocity vectors show flow features around the spike/nose.

The present study numerically, investigates the aerodynamic characteristics of low speed flow past symmetric NACA airfoils, for various t/c values of 0.10, 0.15, 0.18, 0.21 and 0.24 at chordwise Reynolds numbers of 2 × 105 and 4 × 105, where t is the airfoil thickness and c is the airfoil chord. The presence of laminar separation bubble is indicated by oscillatory behaviour of pressure coefficient on the suction surface beyond peak pressure. The fluctuations in lift/drag are seen at smaller t/c values of 0.10 and 0.15, whereas no fluctuations are seen at a higher t/c value of 0.21. An empirical expression is developed to predict the mean lift, viscous as well as total drag coefficients for symmetric airfoils as a function of t/c only, which varies linearly for both the Reynolds numbers studied. The velocity vectors show the flow separations phenomenon only at smaller t/c values of 0.10 and 0.15, while at a higher t/c value of 0.21, well behaved and steady flow field is seen, which might be the reason for the absence of lift/drag fluctuations. The far-field acoustic measurements of symmetric NACA airfoils for various thickness ratios reveal that thicker airfoil (NACA0021, t/c = 0.21) radiates lower acoustic emissions (i.e., about 2 dB) as compared to the thinner (NACA0010, t/c = 0.10) ones.

The dynamics of a nonlinear single degree freedom oscillator on a moving belt subjected to combined harmonic and random excitations is numerically investigated. The dynamics is described by differential equations with discontinuities due to dry friction between the mass and the belt. The discontinuous oscillator is modelled as a Filippov system. Discontinuity induced bifurcations such as the adding sliding bifurcations due to harmonic excitation and stochastic bifurcations like the P and D bifurcations are investigated by numerically integrating the equations of motion using an adaptive time stepping method. A bisection approach is used to accurately determine the discontinuity point, and a Brownian tree approach is used to follow the correct Brownian path. The associated Fokker–Planck (FP) equation is solved by the finite element method. The largest Lyapunov exponent is computed by using the Müller jump matrix and the Wedig algorithm. The effects of the system parameters on the dynamics of the system are investigated.

Dynamics of nonlinear oscillators with discontinuous nonlinearities subjected to harmonic and random excitations is investigated. Impact, dry friction and Hertzian type compliant contact nonlinearities are considered. Stochastic bifurcations like the P-bifurcation and D-bifurcation are discussed. P and D bifurcations are characterized respectively by the joint probability density functions (jpdf) of the response and the largest Lyapunov exponent. The jpdf is obtained by the solution of the corresponding Fokker–Planck equation by the finite element and path integral methods. The results are verified by Monte Carlo simulation methods. Adaptive time step integration procedure (ATSP) is adopted which accurately determines the point of discontinuity. A bisection method and a Brownian tree approach are used in this process and direct the solution along the correct Brownian path. Numerical results are also obtained using non-smooth coordinate transformations like the Zhuvarlev and Ivanov transformations converting the discontinuous systems to equivalent smooth systems and compared with the results of the ATSP. The Filippov convex transformation is used in the case of the dry friction nonlinearity in the integration near the discontinuity. The results are discussed with respect to some examples like the Duffing and Van der Pol oscillators with impact and dry friction.

This paper provides an experimental study into the use of multi-wavelength sinusoidal leading edge ( LE) serrations for enhancing the aerofoil-broadband noise reductions. The noise reduction performances of multi-wavelength serration profiles introduced on a flat plate are compared against those generated by single-wavelength profiles when applied separately. The multi-wavelength leading edge serration is made in such a way that its maximum amplitude is kept same as that of each single-wavelength ones to be compared. The present study reveals that the dual-wavelength serrations provide higher noise reductions over a narrow band of frequencies as compared to single and triple wavelength ones. Further, it reveals that the noise reduction characteristics of dual-wavelength serrated airfoils are similar to the flat plates. It shows that the baseline plate generate higher noise radiations for all emission angles as compared to leading edge serrated plates, but the common feature among them is the downstream directivity. For the range of frequencies 0.9 to 5 kHz, the highest directivity is seen at an emission angle of 55° for the baseline, while it occurs at 75° for the serrated plates. The dual wavelength serrations generate lowest acoustic radiations as compared to single and triple ones for all the emission angles. Also, it is noticed that the radiation levels of the dual serrations decrease with increase in amplitude of the serration, which shows that the longer dual serrations generate lowest acoustic radiations. Thus, the present study illustrates that the dual wavelength leading edge serrations act as the best passively modified serration profiles for achieving the highest noise reductions over a wide range of frequencies as compared to single and triple wavelength ones.

The dynamics of a discontinuous nonlinear oscillator with compliant Hertzian contacts, subjected to combined harmonic and stochastic excitations, is investigated. Adaptive time stepping procedure combined with a bisection method and Brownian tree approach is used for accurately determining the discontinuity point and to direct the solution along the correct Brownian path. A stochastic bifurcation analysis is carried out and is quantified in terms of the expected largest Lyapunov exponent and the joint probability density function (pdf) of the response.

In the present study, the flow and aerodynamic features of a sharp trailing edged flat plate airfoil are systematically compared with NACA0012 airfoil. The studies are conducted for three different Reynolds numbers 1.89 × 105, 2.83 × 105 and 3.78 × 105 and angles of attack 20°, 25° and 30°. The present study shows that the occurrence of vortex shedding phenomena for the flat plate is substantially different from NACA0012 airfoil. Further, the re-attachment location of the shed vortices is closer to the trailing edge for the flat plate, whereas for NACA0012 airfoil it occurs at a certain distance upstream of the trailing edge. The NACA0012 airfoil generates higher lift coefficients at a higher Reynolds numbers of 2.83 × 105 and 3.78 × 105, whereas for the flat plate it occurs at a lower Reynolds number of 1.89 × 105. The spectra of lift coefficient reveal that the amplitude of the primary shedding frequency dominates for the flat plate and NACA0012 airfoil at lower and higher Reynolds numbers of 1.89 × 105 and 3.78 × 105, respectively, while it becomes almost same for an intermediate Reynolds number of 2.83 × 105. The present study reveals that the drag coefficient at high Reynolds number (3.78 × 105) is directly proportional to the initial merging point of the two shed vortices for both the flat plate and NACA0012 airfoil.

This paper deals with the development of an empirical expression to determine the lower cut-off frequency of an anechoic chamber when the source volume, chamber volume, wedge height as well as the major dimensions (i.e., total distance between the source and the chamber wall) are known. The frequency obtained from the empirical expression compares well within ±3% of the lower cut-off frequency obtained from the experiments. The paper also addresses the construction details and calibration procedure of the anechoic chamber. The chamber is calibrated by verifying the inverse square law for different directions from the sound source, and the lower cut-off frequency of the chamber is found to be 315 Hz within ±0.5 dB. Further, the fan broadband noise measurements are made, inside and outside, of the anechoic chamber in order to demonstrate the echo-free nature of the chamber and the spectra clearly shows that the chamber is anechoic for a broad range of frequencies.

This paper addresses the problem of determining the optimal parameters of a sky-hook damper type suspension in the control of the stationary response of half car vehicle models traversing a rough road. The optimal values of the sky-hook damper suspension parameters are obtained by equating the active suspension control force using linear quadratic regulator (LQR) with that of the sky-hook damper suspension force. Results show that the performance of half car model with optimal sky-hook damper suspension is almost close to the performance of half car model with LQR control.

This paper presents a procedure for determination of dynamic properties of rolling element bearing by using the vibration signals picked up at the bearing caps. The rotor-bearing assembly is idealized as Duffing oscillator and random vibration signals modelled as exponentially correlated (Ornstein-Uhlenbeck) colored noise. Expressing the excitation as a first order filtered white noise enables the direct formulation of the 3D-Fokker Planck (FP) equation for system response through the Markov vector approach. Closed form solution of the stationary FP equation is derived. Subsequently the response statistics of experimentally obtained random vibration signal are processed through the closed form solution of the FP equation as the inverse process of parameters estimation from the measured response. Further, the dynamic behavior of rigid rotor-bearing system is investigated under combined excitation of white noise and harmonic forces arising due to rotor unbalance force. The effect of system nonlinearities, stiffness, damping and unbalanced excitation force on the dynamic response are investigated using the bifurcation plot. For assessment of structural degradation of bearings, a novel entropy based approach is developed. Experimental studies on roller bearing are carried out to demonstrate the effectiveness of the proposed approach.

Dynamics of discontinuous nonlinear systems subjected to random excitation is studied. Such systems occur in many mechanical and aerospace applications involving impact, friction, clearance, backlash, freeplay etc. These systems are characterized by sharp switches in dynamical behaviour described by discontinuous stochastic differential equations. An adaptive time stepping approach is developed in combination with a bisection algorithm to locate precisely the discontinuity point in the numerical integration advanced by the Milstein method. The Brownian tree approach is used to direct the integration along the correct Brownian path. The examples of a Duffing oscillator with one- and two-sided impacts and a linear oscillator with a nonlinear discontinuous dry friction-type damper (Coulomb damping) subjected to combined harmonic and white noise excitations are considered. Stable periodic motion, D-bifurcation and chaotic dynamics are exhibited in different parametric regimes. The path-wise numerical integration procedure demonstrates the accuracy and efficiency of the proposed scheme in the dynamic analysis of the noisy vibro-impact oscillator and the friction oscillator.

This paper addresses the problem of determining the optimal parameters of a sky-hook damper type suspension in the control of the stationary random response of half car vehicle models traversing a rough road with constant velocity. The feedback control scheme is realized by approximating the sky-hook damper strategy, and the optimal parameters of the sky-hook damper are obtained by equating the sky-hook damper suspension force with that of a fully active suspension force using linear quadratic regulator with preview control (LQR with preview control). Results show that the overall performance of the sky-hook damper approximately 99% matches with performance of LQR with preview control (look ahead preview control) over a specified vehicle velocity range.

The present study investigates the aerodynamic characteristics of spherically blunted nose cone at a hypersonic Mach number of 5.8, numerically. The studies are conducted for different combinations of bluntness ratios and semi-cone angles, at zero angle of attack, in order to ascertain the nose cone parameters which provide minimum aerodynamic drag coefficient. The velocity vector shows the flow deceleration near the nose, re-acceleration through the sides as well the formation of recirculation zones. The structure of bow shock formed ahead of the nose as well as shock detachment distance is depicted by the Mach number contours. It is observed that the shock detachment distance follows linearly increasing behaviour with increase in bluntness ratios for all semi-cone angles studied. An empirical expression is developed for the shock detachment distance using the regression analysis, which reveals that it is mainly a function of bluntness ratio. It is observed that the aerodynamics drag coefficient attains a minimum value for smaller, bluntness ratios and semi-angle. Further, the aerodynamic drag coefficient is observed to be a strong function of bluntness ratios for smaller semi-cone angles.

The present work numerically and experimentally investigates Mach 5.8 flow past passively modified nose cone configurations such as taper/stepped taper spiked, spherically blunted, and parabolic nose cones at a fineness ratio of 3.6 and zero angle of attack in order to determine the best passively modified geometry that provides the control of both the aerodynamic drag coefficient and surface heat flux. The velocity vectors show the flow directions/recirculation zones and so on at the root of the taper as well as stepped taper spikes, whereas the Mach number contours show the features of shock in front of the taper/stepped taper spikes as well as the nose tip of the taper/stepped taper spiked blunted and parabolic nose cones. The present study reveals that the "stepped taper spiked parabolic nose cone" configuration provides lowest aerodynamic drag coefficient and surface heat flux as compared with all the other nose cone configurations investigated. The modifications in the flow/shock features such as the conversion of strong curved shock into weaker oblique shock waves, flow deceleration, and so on, at the root of the spike due to backward-facing steps in "stepped taper spiked parabolic nose cone" may be the reason for achieving lower aerodynamic drag/heating.

The present study investigates the effect of circular trailing edge on the complex flow phenomena occurring in the near-wake, nearer far-wake and far-wake zones for different Reynolds numbers and angles of attack. The velocity vector depicts that the maximum lift is obtained when the leading-edge vortex attains maximum size, whereas the minimum lift is achieved when the trailing-edge vortex attains maximum size. The near-wake zone extends up to an x/c value of 1.2; thereafter, it undergoes transition for the range of x/c values from 1.2 to 7 and beyond an x/c value of 7, the far-wake zone begins where the complex nonlinear flow phenomena occur, (x is the streamwise distance from the circular trailing edge, and c is the chord length). The spectra reveals the formation of primary vortex shedding with single dominant frequency in the near wake, whereas two dominant frequencies correspond to the primary vortex shedding as well as secondary large-scale oscillations, in the far wake. In the near-wake vortices convect alternately while in the far-wake vortices of opposite sign move in pairs and undulates at low frequency without remaining fixed at the centerline of the circular trailing edge.