Unsteady Forces Research Articles

A Study on the Influence of Unsteady Forces on the Roll Characteristics of a Submarine during Free Ascent from Great Depth

The maximum diving depth of modern submarines has always been increasing. Although this has been useful and in some cases necessary, it usually comes with some risks. For instance, when a submarine encounters an emergency situation that requires immediate ascent from great depths, the situation becomes more dangerous, especially due to its rolling characteristics. To investigate the effect of unsteady forces during free ascent motion of submarines at great depths on submarine rolling, in this study, the SST-DDES model combined with the overset grid technique was used for the numerical simulation of a submarine free ascent. Water tank experiments for free ascent were conducted to validate the numerical approach, which confirmed the reliability of the numerical method. Following this, the CFD method was employed to conduct an initial exploratory investigation into the free ascent motion of deep-submergence submarines. The free ascent motion of submarines at great depths under five different degrees of freedom combinations was studied. The computational results indicated that submarines are more prone to roll over during free ascent at great depths. At a depth six times the length of the submarine, the maximum roll angle underwater reaches 22.8°. In addition, unsteady rolling moments, lateral forces, and yawing moments have a significant effect on submarine rolling, intensifying the tendency to roll. Furthermore, it was observed that the vertical hydrodynamic attack angle β is related to the rolling stability of the submarine, such that a moderate decrease in β is beneficial for the rolling stability. The numerical calculation method and preliminary research findings can provide theoretical support for controlling the ascent motion of real submarines.

Research on the mechanism of chlorine corrosion resistance of graphite tailings modified recycled coarse aggregate concrete: Corrosion product transformation and multi-scale mathematical characterization model

This research investigated the impact of substituting sand with graphite tailings (GT) on the chloride ion erosion resistance of recycled aggregate concrete (RAC). The role of GT is to significantly inhibit the penetration of chloride ions into the interior and slow down the corrosion process. However, the durability of graphite tailings recycled aggregate concrete (GTRAC) still depends on the replacement rate of recycled aggregate. At the same time, a multi-scale dynamic model of physical adsorption-chemical binding-free transport and erosion of chloride ions in GTRAC were established based on unsteady viscous fluid force and molecular dynamics.

State augmentation method for non-stationary/non-Gaussian vibrations of multi degree-of-freedom linear systems

The basic assumptions of stationary/Gaussian excitations and temporal independence in linear systems are commonly employed in stochastic dynamic analyses, facilitating various engineering investigations. However, in certain scenarios such as wind-induced vibrations under non-synoptic extreme wind, these assumptions may lead to unreliable predictions. The excitations exhibit significant non-stationary/non-Gaussian features due to the inherent non-synopticity of the flow. Moreover, when accounting for motion-induced forces, the coupled aerodynamic-mechanical system is modeled as a linear time-varying system marked by time-dependent aerodynamic damping and stiffness. This study aims to introduce a state augmentation method for examining the multi-modal vibrations of a long-span bridge excited by non-synoptic winds. Both unsteady motion-induced forces and non-stationary/non-Gaussian turbulence-induced forces are considered to predict the buffeting response. Based on stochastic calculus theory and the stars and bars method, we derive equations governing the statistical moments of all orders for the response of a dynamic system with multiple degrees of freedom. A comprehensive buffeting analysis of the model bridge to all wind segments of Typhoon Hagupit is conducted by using the proposed method, showing potentially greater responses when considering the non-synoptic features of the wind.

The intrinsic rarity of equilibrium response in stratigraphic processes

Conventional sequence stratigraphy is based, explicitly or implicitly, on the hypothesis that steady external forcing results in a steady stratigraphic configuration (equilibrium response), so that an unsteady stratigraphic configuration is usually believed to result from unsteady external forcing. Recent advances in autostratigraphy, on the other hand, have led to a significantly different notion that steady external forcing generally results in an unsteady stratigraphic configuration (non-equilibrium response). To advance this debate, it is necessary to clarify what exactly is meant by a steady stratigraphic configuration. Here, we propose a quantitative criterion for defining the latter concept in terms of the straightness of the shoreline trajectory, and specifically a straight shoreline trajectory or the shoreline being held still as a sign to express steady stratigraphic configurations. In such a definition, a steady stratigraphic configuration means that the ratio of the rate of aggradation and the rate of progradation is constant, or one of these two rates is zero. Based on this criterion, a total of 7 types of steady stratigraphic configurations can be clarified, most of which require unsteady external forcing and are thus realized by non-equilibrium response, although special cases exist. The reason that non-equilibrium responses dominate the stacking of strata is that it is common for a growing basin-margin depositional system to change its surface area. The size-changing system will easily change the stacking pattern (unsteady stratigraphic configuration) if the external forcing is steady, or, if the steady stratigraphic configuration is maintained, the rate of external forcing must change in a particular pattern (unsteady external forcing). Equilibrium responses can occur, but in very special cases. Conventional sequence stratigraphy should take into account the importance of non-equilibrium response.

Flow physics during durge of an axial-centrifugal compressor

Aerodynamic instability design is one of the crucial elements when designing a compressor. Unstable phenomenon such as surge harms the compressor in both performance and structure integrity. The complex unsteady flow process during instability strongly relates to the compressor design. This paper investigates the transient instability process using URANS on a three-stage-axial and one-stage-centrifugal combined compressor under its off-design conditions. Results show that the compressor suffers two surge patterns. The mild surge happens first, with a higher frequency than the traditional mild surge. Then, with the decrease of valve opening, the deep surge is initiated, and the axial stages work at the peak pressure ratio because the mass flow rate is limited by the choked radial diffuser. Moreover, analysis of aerodynamic loads reveals that IGV and the first rotor have the largest unsteady force among all blade rows. According to the flow field, the rotor root and stator tip suffer the most serious impulse caused by reversed flow during surge conditions.

Wavelength-induced shedding frequency modulation of seal whisker inspired cylinders

The spanwise undulated cylinder geometry inspired by seal whiskers has been shown to alter shedding frequency and reduce fluid forces significantly compared to smooth cylindrical geometry. Prior research has parameterized the whisker-inspired geometry and demonstrated the relevance of geometric variations on force reduction properties. Among the geometric parameters, undulation wavelength was identified as a significant contributor to forcing changes. To analyze the effect of undulation wavelength, a thorough investigation isolating changes in wavelength is performed to expand upon previous research that parameterized whisker-inspired geometry and the relevance of geometric variations on the force reduction properties. A set of five whisker-inspired models of varying wavelength are computationally simulated at a Reynolds number of 250 and compared with an equivalent aspect ratio smooth elliptical cylinder. Above a critical non-dimensional value, the undulation wavelength reduces the amplitude and frequency of vortex shedding accompanied by a reduction in oscillating lift force. Frequency shedding is tied to the creation of wavelength-dependent vortex structures which vary across the whisker span. These vortices produce distinct shedding modes in which the frequency and phase of downstream structures interact to decrease the oscillating lift forces on the whisker model with particular effectiveness around the wavelength values typically found in nature. The culmination of these location-based modes produces a complex and spanwise-dependent lift frequency spectra at those wavelengths exhibiting maximum force reduction. Understanding the mechanisms of unsteady force reduction and the relationship between undulation wavelength and frequency spectra is critical for the application of this geometry to vibration tuning and passive flow control for vortex-induced vibration (VIV) reduction.

Geometric control analysis of the unsteady aerodynamics of a pitching–plunging airfoil in dynamic stall

Geometric control theory is the application of differential geometry to the study of nonlinear dynamical systems. This control theory permits an analytical study of nonlinear interactions between control inputs, such as symmetry breaking or force and motion generation in unactuated directions. This paper studies the unsteady aerodynamics of a harmonically pitching–plunging airfoil in a geometric control framework. The problem is formulated using the Beddoes–Leishman model, a semi-empirical state space model that characterizes the unsteady lift and drag forces of a two-dimensional airfoil. In combination with the averaging theorem, the application of a geometric control formulation to the problem enables an analytical study of the nonlinear dynamics behind the unsteady aerodynamic forces. The results show lift enhancement when oscillating near stall and thrust generation in the post-stall flight regime, with the magnitude of these force generation mechanisms depending on the parameters of motion. These findings demonstrate the potential of geometric control theory as a heuristic tool for the identification and discovery of unconventional phenomena in unsteady flows.

Active Flutter Suppression of a Wing Section in the Subsonic, Sonic and Supersonic Regimes by the H∞ Control Method

This paper compares various procedures for determining the optimal control law for a wing section in compressible flow. The flow regime includes subsonic, sonic and supersonic flows. For the evolution of the system in the Laplace plane, the present method makes use of the exact unsteady aerodynamic forces in this plane once the control law is established. This is a great advantage over other results previously published, where the unsteady aerodynamics in the Laplace plane are merely approximations of the curve-fitted values in the frequency domain (imaginary axis). A comparison of different control techniques like pole placement, LQR and H-infinity control demonstrates that the H-infinity controller is the optimal choice, exhibiting an H-infinity norm approximately two orders of magnitude lower than the LQR case. Furthermore, the H-infinity controller demonstrates lower pole values than those of the pole placement and LQR compensator, showing the advantage of the H-infinity controller in terms of economic efficiency.

Mechanism of single-mode panel flutter in low supersonic flow

Supersonic panel flutter can be of two possible types: single-mode flutter and coupled-mode flutter. Compared to coupled-mode flutter, the physical mechanism of single-mode flutter is less studied at present. In order to reveal the inducing mechanism of single-mode flutter, the present paper constructed a reduced-order fluid model by using the system identification and the Auto Regressive with eXogenous input (ARX) model. Coupling the reduced-order model (ROM) for unsteady aerodynamics in low supersonic flow with the structural equation, a highly efficient ROM-based aeroelastic model in state space is formulated, then the flutter boundaries are obtained and the stability of aeroelastic modes are investigated by the complex eigenvalue analysis. According to the physical meaning of relevant parameters in unsteady aerodynamic reduced order model ARX, it is found that the unsteady characteristic of the flow, specifically the history effects of the unsteady aerodynamic forces, plays a dominant role in causing the single-mode panel flutter at low supersonic speeds. It is also shown that the higher modes are indeed weakly unstable in the absence of any structural damping or a viscous boundary layer.

Influence of gap thickness on aerodynamic forces and flow structures of circular cylinders under passive-suction-jet control

A parametric study of the passive-suction-jet control scheme was experimentally performed for the cylinder model. The dependence of the control effectiveness on the gap thickness was determined for a cylinder model controlled by passive-suction-jet pipes at Reynolds number (Re) values ranging from 20,000 to 60,000. The fluid forces and flow structure were measured on a cylinder model without any control and used to evaluate the control effectiveness. Proper orthogonal decomposition (POD) analysis, phase average, and triple decomposition were applied to the flow fields to explore the control mechanism. The results show that the pipe control was most effective when the gap thickness was 0.075D. Too large or too small a gap thickness was not beneficial for controlling the resistance level, and the fluctuating lift was reduced to a tiny level as the thickness increased to 0.075D. The steady jets ejected from the leeward slots rolled up into several small-scale standing vortices. These vortices modified the streamline topology of the model, developing a new saddle point in the wake. Moreover, the roll-up of the separated shear layers was restrained by the pipe, which inhibited the vortex formation and shedding processes and the unsteady forces exerted on the model.

An innovative EFD using FBG pressure sensors for ship seakeeping

AbstractThis paper examines the acquisition of the measurement data of the spatial distribution of unsteady pressure on a ship advancing in waves. The purpose of the study is to investigate the reliability of the pressure data obtained by the unprecedented experiment and to provide experimental data of unsteady pressure which can be used for validation of arbitrary computation methods. The optical fiber sensing technology, so-called FBG (fiber Bragg gratings) sensing, is employed as the pressure sensors. In the experiment, 379 FBG pressure sensors (version 7; the latest version) in total are attached to the port side surface of ship model and also ordinary strain-type pressure sensors are embedded in the starboard side for validating reliability of FBG pressure sensors by comparing both results. In addition to the pressure distribution, measurement is made for unsteady hydrodynamic forces such as added mass, damping coefficients, and wave exciting forces, and also for ship motions and added resistance. Most of the measurement is repeated at least five times for each condition, and results of measured pressures are evaluated with mean value and standard deviation. Regarding the added resistance, the distribution for estimating added resistance is also extracted from obtained pressure distribution and its pressure contour is illustrated to show visually which hull region affects the added resistance significantly. Validation of the measured pressure with FBG pressure sensors is carried out also by integrating measured pressures over the ship model surface and comparing it with forces directly measured with load cells. The measured pressure distribution is compared with typical calculation results with the Rankine panel method in frequency domain to demonstrate usefulness of the spatial pressure data for validating the calculation method. Through these studies, it is confirmed that the measured unsteady pressures with FBG pressure sensors are accurate enough and valuable as the validation data for any calculation method.

Investigation of radial force in a high-speed miniature pump

A high-speed miniature pump design is put forth for utilization in the aerospace sector, where the pump’s reliability holds critical importance under microgravity operational conditions. This study focuses on a dynamic bearing-equipped miniature centrifugal pump, chosen for its suitability in investigating radial forces. The prototype of the miniature pump is manufactured and tested by experiments at the rotational speed of 10,000r/min. A good agreement is observed between the numerical predictions and the experimental results. The radial force acting on different blade part has been analyzed for several flow rate conditions using the steady state CFD calculation. It has been found that the radial force exerted on the blade trailing edge exit is the main cause of the total radial force for the impeller. Moreover, using the unsteady CFD simulation, the evolution process of the radial force changing for both the direction and the magnitude with respect to the annular position due to the shaft rotation is discussed in details. The pressure pulsation is also monitored in impeller and volute casing. The results show that the amplitude of the unsteady radial force has a strong relationship with the time it takes for the blade trailing edge exit passing the volute tongue region, while the direction of the radial force hardly changes. The findings of this study contribute to facilitating the broader implementation of the high-speed miniature pump across diverse sectors of society.

Unsteady rotor force suppression of a pump-jet by stator actuated oscillating trailing edge flaps: A numerical study

The unsteady rotor force is the main source of the pump-jet-shafting system vibration. The coupling between rotor rotation and stator wake results in the characteristic line spectra of rotor unsteady force. The actuated oscillating trailing edge flaps (AOTEF) is introduced to the stator. The secondary flow generated by AOTEF is used to suppress the unsteady rotor force. A numerical model is established based on the unsteady Reynolds averaged Navier-Stokes equation (URANS) method of the shear stress transport (SST k-ω) turbulence model, taking the SUBOFF and pump-jet propulsor with AOTEF as the research object. Aiming at suppressing unsteady force at rotor blade passing frequency (BPF), the expression of AOTEF harmonic oscillation law is given and optimized. Under the optimal control of the AOTEF, the hydrodynamic performance remains unaffected. At BPF, the axial unsteady force of the rotor and a single blade decrease by 15.6 dB and 14.8 dB, separately. Further analysis shows that the AOTEF can manipulate the stator wake and the velocity on the rotor inlet plane. The research results show that the AOTEF can significantly suppress the unsteady rotor force while maintaining the hydrodynamic performance, which will shed some light on controlling the unsteady force of the pump-jet.

Performance characterization and modeling of an oscillating surge wave energy converter

Testing wave energy converters in the ocean could be expensive and complex, which necessitates the use of numerical modeling. However, accurately modeling the response of wave energy converters with high-fidelity simulations can be computationally intensive in the design stage where different configurations must be considered. Reduced-order models based on simplified equations of motion can be very useful in the design, optimization, or control of wave energy converters. Given the complex dynamics of wave energy converters, accurate representation, and evaluation of relative contributions by different forces are required. This effort is concerned with a performance characterization of the hydrodynamic response of an oscillating surge wave energy converter that is based on a reduced-order model. A state-space model is used to represent the radiation damping term. Morison’s representation of unsteady forces is used to account for the nonlinear damping. Wave tank tests are performed to validate simulations. A free response simulation is used to determine the coefficients of the state-space model. Torque-forced simulations are used to identify the coefficients of the nonlinear damping term for different amplitudes and wave frequencies. The impact of varying these coefficients on the response is investigated. An assessment of the capability of the model in predicting the hydrodynamic response under irregular forcing is performed. The results show that the maximum error is 3% when compared with high-fidelity simulations. It is determined that the nonlinear damping is proportional to the torque amplitude and its effects are more pronounced as the amplitude of the flap oscillations increases.

Real-Time Ground Aeroservoelastic Test for Slender Vehicles Based on Condensed Aerodynamic Force Loading

Slender vehicles often encounter significant aeroservoelastic challenges due to their low elastic mode frequencies and wide servo control system bandwidths. Traditional analysis methods have limitations, including low modeling accuracy for real vehicles in numerical methods, scale errors in wind tunnel tests, and significant risks in flight tests. The ground aeroelastic stability test is an innovative experimental method designed to address these challenges. This novel method employs shakers to apply condensed unsteady aerodynamic forces in real-time to actual vehicles, serving for both the ground flutter test (GFT) and the ground aeroservoelastic test (GAT). While extensive research exists on the GFT, there is limited exploration of the GAT. For the GAT of a slender vehicle in this paper, the condensed aerodynamic forces are calculated using the quasi-steady aerodynamic derivative method. An improved, partially decoupled inverse model controller is designed for force control, guided by an assessment of coupling strength among different shakers. Ground experiments under various flight control laws and flight dynamic pressures produce accurate results. Numerical simulations and experimental results demonstrate high precision, with excitation force amplitude deviations within ±10% and phase deviations within ±5° within the frequency range relevant to aeroservoelastic stability.

Investigations on bifurcation behavior of wind turbine airfoil response at a high angle of attack

Design load and vibration for parked conditions are gaining in importance for large-scale modern wind turbines with increasing flexibility, especially edgewise vibration when the blade is at a high angle of attack. In this work, flow-induced vibration of the wind turbine airfoil at 90 degrees of attack angle is studied with the fluid-structure interaction (FSI) simulation. The unsteady aerodynamic force due to flow separation and vortex shedding at the high angle of attack causes the chordwise vibration of the airfoil. When the vortex shedding frequency fv gets close to the chordwise natural frequency fn of the airfoil, vortex-induced vibration (VIV) of high amplitude occurs accompanied with the frequency lock-in phenomenon. In the post lock-in regime, it is found that period-3 and torus bifurcation occur successively and the vibration response becomes aperiodic. Dynamic mode decomposition(DMD) technique is used to investigate the mechanism of bifurcation from the perspective of energy balance, through analyzing the vorticity field in the wake and pressure distribution on the airfoil surface. For the certain incoming velocity in the post lock-in regime, since the frequency of the DMD mode f=2fv/3 is close to the natural frequencyfn, both the vibration of frequency 2fv/3 and fv get excited, leading to the onset of bifurcation. The Lissajou curves are obtained through reconstructing the transient pressure of each DMD mode, which indicates that energy transfer mainly exists in modes f=fv. In addition, the reconstructed Lissajou curves based on the leading DMD modes agree well with the original time-domain Lissajou curves.

Transonic Aerodynamic–Structural Coupling Characteristics Predicted by Nonlinear Data-Driven Modeling Approach

Accurate prediction of nonlinear aerodynamics is essential for the transonic aeroelastic analysis of flight vehicles. Though reduced-order aerodynamic models are cheap and reasonable tools, it is still a tough problem to accurately evaluate the unsteady pressure distributions on the surface of an elastic structure. This paper presents a nonlinear data-driven modeling approach based on the high-fidelity simulations in the following three steps. The first step is to compute the dominant modes of unsteady pressure distributions through the proper orthogonal decomposition. The pressure snapshots used for the feature extraction are sampled under a multilevel sine-sweep excitation. The second step is to obtain the low-dimensional temporal dynamics of the coefficients of these modes via polynomial nonlinear state-space identification. The linear estimation implemented by employing the dynamic mode decomposition with control algorithm serves as the initialization of the nonlinear optimization. The third step is to reconstruct the unsteady pressure distributions under arbitrary structural excitation from the temporal coefficients. The paper validates the approach via two numerical examples of the transonic aerodynamic–structural coupling problem. One is an NACA0012 airfoil, and the other is an AGARD 445.6 wing. The examples show that the proposed approach exhibits both accurate and robust performance in the prediction of unsteady pressure distributions, aerodynamic forces, and aeroelastic responses. In particular, the approach well predicts the physical features at the fluid–structure coupling interface, previously neglected in the system identification of aerodynamic systems. Therefore, the approach serves as a promising tool for data-driven aeroelastic analysis.

Study on the wall-pressure fluctuation characteristics of a pump-jet propulsor duct in turbulent boundary layer

This study presents the distribution of excitation sources and pressure fluctuation characteristics on the duct wall of pump-jet propulsor. A modified submarine geometry based on the SUBOFF model is developed to provide a stern flow filed with turbulent characteristics for pump-jet. The Turbulent Boundary Layer (TBL) of outer wall is obtained by using Large Eddy Simulation (LES) numerical method to understand the velocity distributions. The characteristics of unsteady excitation force spectra are investigated respectively under different excitations excited by the internal and external flow field of duct. Besides, a spatial-temporal distribution of TBL pressure energy on duct wall excited by external flow field is emphatically revealed through the spectral analysis method. The results show that the force spectra excited by external flow field display an obvious broadband characteristic and discrete components appear at Blade Passing Frequency (BPF). While the force spectra excited by internal flow field present a remarkable discrete peak at BPF and its multiple. The BPF has a significant influence on the energy convergence range of excitation forces on outer wall of duct and a rapid decay trend starts to occur near BPF. The scale of vortices with most dominant energy contribution is determined by BPF and corresponding wavenumber, rather than the energetic wavenumber.

Aeroelasticity Analysis of Folding Wing with Structural Nonlinearity Using Modified DLM

The structural nonlinear aeroelastic analysis of folding wings is conducted by integrating the modified Doublet Lattice Method in this paper. Firstly, a modified Doublet Lattice Method is investigated to relax the aspect ratio limitation of aerodynamic elements, and its correctness is verified through numerical examples. Secondly, the rational function approximation method is discussed, and the modified Doublet Lattice Method is approximated using the minimum state method to obtain the unsteady aerodynamic forces in the time domain. Finally, the aeroelastic characteristics of a folding wing with free-play and friction nonlinearity are studied by integrating time-domain unsteady aerodynamics with the nonlinear structural dynamics model. The results show that the modified Doublet Lattice Method, which relaxes the aspect ratio limitation of aerodynamic grid elements, is feasible and effective; Friction can suppress the influence of free-play nonlinearity on aeroelastic response.

Asymptotic model of long-wave vibrations of an ultrathin strip-beam taking into account surface effects

The paper is concerned with the derivation of asymptotically consistent equations governing long-wave vibrations of an ultrathin elastic strip-beam taking into account surface effects within the framework of the Gurtin-Murdoch theory of the surface elasticity. Two dimensional equations of motion of an elastic isotropic medium are used as the initial ones. In the general case, the strip-beam is under the action of variable unsteady surface forces. The presence of residual shear stresses is assumed on the face surfaces. The ratio of the strip thickness to the characteristic length of bending deformation is considered as a small parameter. Within the framework of the Gurtin-Murdoch theory, two cases are considered, providing for the presence of large a) residual stresses on the faces, b) effects of surface inertia. Using the method of asymptotic integration over the transverse direction, relations for displacements and stresses in an ultra-thin strip-beam are obtained, and equivalent one dimensional the Timoshenko type equations taking into account surface effects are derived. As an example, free vibrations of a simply supported beam accounting for the surface effects are considered.