Recent zbMATH articles in MSC 76D55https://zbmath.org/atom/cc/76D552021-06-15T18:09:00+00:00WerkzeugFeedback control of flow-induced vibration of a sphere.https://zbmath.org/1460.762422021-06-15T18:09:00+00:00"McQueen, Thomas"https://zbmath.org/authors/?q=ai:mcqueen.thomas"Zhao, J."https://zbmath.org/authors/?q=ai:zhao.jincheng|zhao.jinsong|zhao.juanxia|zhao.jianmin|zhao.junhe|zhao.junning|zhao.jianlin|zhao.jintao|zhao.jingxian|zhao.junxiu|zhao.jianbin|zhao.jinhu|zhao.jiakui|zhao.jinling|zhao.jisheng|zhao.juanping|zhao.jieliang|zhao.jingya|zhao.jikun|zhao.jiafeng|zhao.jinghai|zhao.jichang|zhao.ji|zhao.jing.1|zhao.jinhua|zhao.jun.1|zhao.jihai|zhao.jinshuai|zhao.jianzhe|zhao.jinshi|zhao.jiantao|zhao.jiuhua|zhao.junsong|zhao.jingshan|zhao.jiefeng|zhao.jianye|zhao.jiyin|zhao.jiuli|zhao.jiantang|zhao.jianzhong|zhao.jianyuan|zhao.junyilang|zhao.jianying|zhao.jingtao|zhao.jinman|zhao.jiemei|zhao.justin|zhao.jianhua|zhao.junxi|zhao.jingjun|zhao.jingyi|zhao.jane|zhao.jiyong|zhao.junkun|zhao.jinping|zhao.jixiang|zhao.junhua|zhao.jingtong|zhao.jinbin|zhao.jinglan|zhao.jiaheng|zhao.jingfu|zhao.jianbang|zhao.jiongzhi|zhao.jie|zhao.jinqing|zhao.jing.3|zhao.jiaolian|zhao.jinxing|zhao.jiang|zhao.jinxu|zhao.jinxi|zhao.junping|zhao.jiakun|zhao.jianxin|zhao.jia.1|zhao.jun|zhao.junxiao|zhao.jingsheng|zhao.jiamin|zhao.jiexiu|zhao.jianghai|zhao.jinzhou|zhao.junsan|zhao.junshui|zhao.jianshe|zhao.jinxian|zhao.jianxi|zhao.jingyu|zhao.junfa|zhao.judong|zhao.jiayin|zhao.jingang|zhao.junguang|zhao.junchan|zhao.jingdong|zhao.jizhong|zhao.jize|zhao.jiansheng|zhao.jiaxin|zhao.jialiang|zhao.jingyuan|zhao.jizhen|zhao.junhang|zhao.jidong|zhao.junfeng|zhao.jiman|zhao.junlong|zhao.jiandong|zhao.jianlian|zhao.jianwei|zhao.jiali|zhao.junyong|zhao.ju|zhao.jihong|zhao.jiansen|zhao.jiemin|zhao.jiahong|zhao.jin|zhao.jieling|zhao.junqing|zhao.jisong|zhao.junfang|zhao.jinye|zhao.jiejue|zhao.junkai|zhao.jifeng|zhao.jiaozhi|zhao.jiashu|zhao.jinchao|zhao.jixian|zhao.jingbao|zhao.juanjuan|zhao.jianli|zhao.junhai|zhao.jihui|zhao.jiajia|zhao.jianxing|zhao.jianqing|zhao.jinglin|zhao.jingyue|zhao.jinwei|zhao.jianhui|zhao.jinlou|zhao.junwei|zhao.jianrong|zhao.jiong|zhao.jiangang|zhao.jiaqi|zhao.junli|zhao.jingrui|zhao.junhui|zhao.junpeng|zhao.jinkai|zhao.junyan|zhao.jiaqiang|zhao.jinyan|zhao.junbo|zhao.jianchang|zhao.junzhou|zhao.jinsuo|zhao.jianjun|zhao.jiacheng|zhao.jianyong|zhao.jiancong|zhao.jiao|zhao.jianyu|zhao.jutao|zhao.jiying|zhao.jichao|zhao.jinxin|zhao.jitai|zhao.jianxun|zhao.jiaquan|zhao.jinghui|zhao.jianglin|zhao.juan|zhao.jine|zhao.jiashi|zhao.jiangnan|zhao.junwu|zhao.jinqiu|zhao.jining|zhao.jiaxiang|zhao.jiapei|zhao.jiwei|zhao.jibin|zhao.jing.2|zhao.junling|zhao.junjie|zhao.jiayi|zhao.jianfeng|zhao.jinwen|zhao.jinjun|zhao.jian|zhao.juning|zhao.jianyin|zhao.jijun|zhao.junyin|zhao.jinglei|zhao.junying|zhao.jinbao|zhao.jiangfu|zhao.jianhong|zhao.jing|zhao.jingxin|zhao.jianping|zhao.jiping|zhao.jiabao|zhao.jianguo|zhao.junsheng|zhao.juntao|zhao.junyang|zhao.jiawei|zhao.jinfeng|zhao.junyu|zhao.jinli|zhao.jinghuan|zhao.jinlong|zhao.jinjing|zhao.jianming|zhao.jidi|zhao.jieyu|zhao.jia|zhao.jianzhou|zhao.jiajing|zhao.jianfu|zhao.jinhui|zhao.jingxiang|zhao.jiabin|zhao.jianjie|zhao.junjian|zhao.jiayu|zhao.jun.2|zhao.jiangbo|zhao.jianqiang.1|zhao.jiagui|zhao.jieqiong|zhao.jishen|zhao.jiafei|zhao.jingjing|zhao.jiangming|zhao.jiyun|zhao.junhong"Sheridan, J."https://zbmath.org/authors/?q=ai:sheridan.j-d|sheridan.john-t"Thompson, M. C."https://zbmath.org/authors/?q=ai:thompson.mary-clair|thompson.mark-christopherSummary: The flow-induced vibration of a sphere elastically mounted in the cross-flow direction with imposed feedback rotation was investigated experimentally. The application of rotation provides a means to exercise control over the vibration response of axisymmetric three-dimensional objects. Both the rotational amplitude, which was imposed in proportion to sphere transverse displacement, and the phase of the control signal were varied over a broad parameter space comprising: a non-dimensionalised proportional gain \((0.5\leqslant K_p^* \leqslant 2)\); rotation phase \((0^\circ \leqslant \varphi_{rot}\leqslant 360^\circ)\), which is the phase between the applied sphere rotation and the transverse displacement; and reduced velocity \((3\leqslant U^* \leqslant 20)\). The corresponding Reynolds number range was \((3900\lesssim Re\lesssim 25\,800)\). The structural vibration, fluid forces and wake structure were examined to characterise the effect of the imposed rotation. It was found that the rotation not only altered the magnitude of the vibration response, either amplifying or attenuating the response depending on operating conditions, but it also altered the reduced velocity at which vibrations commenced, the vibration frequency and periodicity and significantly altered the phase between the transverse fluid force and displacement. It was possible to almost completely suppress the vibration in the mode I, mode II and mode III transition regimes for imposed rotation over the ranges \(90^\circ \lesssim \varphi_{rot}\lesssim 180^\circ\), \(15^\circ \lesssim \varphi_{rot}\lesssim 135^\circ\) and \(0^\circ \lesssim \varphi_{rot}\lesssim 120^\circ\), respectively. In particular, this could be achieved at effective rotation rates well below those required by using open-loop control [\textit{A. Sareen} et al., ibid. 837, 258--292 (2018; Zbl 1419.76167)]. Past the peak of mode II, a `galloping-like' response, similar to that reported by \textit{D. Vicente-Ludlam} et al. [ibid. 847, 93--118 (2018; Zbl 1404.76153)] for the circular cylinder, was observed with an increase in vibration amplitude of up to 368 \% at the highest reduced velocity tested \((U^* =20)\). Particle image velocimetry measurements revealed a change in the timing and spatial position of the streamwise vortex structures with imposed rotation. Contrary to what has been observed for the circular cylinder, however, no de-synchronisation between vortex shedding and sphere motion was observed.Optimal suppression of a separation bubble in a laminar boundary layer.https://zbmath.org/1460.761982021-06-15T18:09:00+00:00"Karp, Michael"https://zbmath.org/authors/?q=ai:karp.michael"Hack, M. J. Philipp"https://zbmath.org/authors/?q=ai:hack.m-j-philippSummary: By means of nonlinear optimization, we seek the velocity disturbances at a given upstream position that suppress a laminar separation bubble as effectively as possible. Both steady and unsteady disturbances are examined and compared. For steady disturbances, an informed guess based on linear analysis of transient perturbation growth leads to significant delay of separation and serves as a starting point for the nonlinear optimization algorithm. It is found that the linear analysis largely captures the suppression of the separation bubble attained by the nonlinear optimal perturbations. The mechanism of separation delay is the generation of a mean flow distortion by nonlinear interactions during the perturbation growth. The mean flow distortion enhances the momentum close to the wall, counteracting the deceleration of the flow in that region. An examination of the effect of the disturbance spanwise wavenumber reveals that perturbations maximizing the mean flow distortion also approximately maximize the peak wall pressure, which is beneficial for lowering form drag. The optimal spanwise wavenumber leading to maximal peak wall pressure is significantly larger than the one maximizing the shift in separation onset. For unsteady disturbances, the mechanism of separation delay relies on enhancing wall-normal momentum transfer by triggering instabilities of the separated shear layer. It is found that Tollmien-Schlichting waves obtained from linear stability theory provide accurate estimates of the nonlinearly optimal disturbances. Comparison of optimal steady and unsteady perturbations reveals that the latter are able to obtain a higher time-averaged peak wall pressure.Flow state estimation in the presence of discretization errors.https://zbmath.org/1460.762872021-06-15T18:09:00+00:00"da Silva, Andre F. C."https://zbmath.org/authors/?q=ai:da-silva.andre-f-c"Colonius, Tim"https://zbmath.org/authors/?q=ai:colonius.timSummary: Ensemble data assimilation methods integrate measurement data and computational flow models to estimate the state of fluid systems in a robust, scalable way. However, discretization errors in the dynamical and observation models lead to biased forecasts and poor estimator performance. We propose a low-rank representation for this bias, whose dynamics is modelled by data-informed, time-correlated processes. State and bias parameters are simultaneously corrected online with the ensemble Kalman filter. The proposed methodology is then applied to the problem of estimating the state of a two-dimensional flow at modest Reynolds number using an ensemble of coarse-mesh simulations and pressure measurements at the surface of an immersed body in a synthetic experiment framework. Using an ensemble size of 60, the bias-aware estimator is demonstrated to achieve at least 70\% error reduction when compared to its bias-blind counterpart. Strategies to determine the bias statistics and their impact on the estimator performance are discussed.Phase-synchronization properties of laminar cylinder wake for periodic external forcings.https://zbmath.org/1460.762902021-06-15T18:09:00+00:00"Khodkar, M. A."https://zbmath.org/authors/?q=ai:khodkar.m-a"Taira, Kunihiko"https://zbmath.org/authors/?q=ai:taira.kunihikoSummary: We investigate the synchronization properties of the two-dimensional periodic flow over a circular cylinder using the principles of phase-reduction theory. The influence of harmonic external forcings on the wake dynamics, together with the possible synchronization of the vortex shedding behind the cylinder to these forcings, is determined by evaluating the phase response of the system to weak impulse perturbations. These horizontal and vertical perturbations are added at different phase values over a period, in order to develop a linear one-dimensional model with respect to the limit cycle that describes the high-dimensional and nonlinear dynamics of the fluid flow via only a single scalar phase variable. This model is then utilized to acquire the theoretical conditions for the synchronization between the cylinder wake and the harmonic forcings added in the global near-wake region. Valuable insights are gained by comparing the findings of the present research against those rendered by the dynamic mode decomposition and adjoint analysis of the wake dynamics in earlier works. The present analysis reveals regions in the flow which enable phase synchronization or desynchronization to periodic excitations for applications such as active flow control and fluid-structure interactions.The von Kármán street behind a circular cylinder: flow control through synthetic jet placed at the rear stagnation point.https://zbmath.org/1460.762882021-06-15T18:09:00+00:00"Greco, Carlo Salvatore"https://zbmath.org/authors/?q=ai:greco.carlo-salvatore"Paolillo, Gerardo"https://zbmath.org/authors/?q=ai:paolillo.gerardo"Astarita, Tommaso"https://zbmath.org/authors/?q=ai:astarita.tommaso"Cardone, Gennaro"https://zbmath.org/authors/?q=ai:cardone.gennaroSummary: The present paper aims at establishing the synthetic jet technology capabilities in controlling the von Kármán street behind a circular cylinder. The circular cylinder, placed in an open-circuit wind tunnel, presents a slot in its rear position, through which the synthetic jet is issued. The Reynolds number, based on the circular cylinder diameter and the free-stream velocity, is equal to 4600 and the von Kármán street is characterized, in the baseline configuration (i.e. without synthetic jet), by a shedding frequency of 16.2 Hz. Several synthetic jet operating conditions are tested. Therefore, the effects of the momentum coefficient \((C_\mu =5.4\%\), 10.8\% and 21.6\%) and the dimensionless frequency \((f^+ = 0.49, 0.98\) and 1.96) on the von Kármán street behaviour can be analysed. Instantaneous two-dimensional in-plane velocity fields are measured in a plane containing the synthetic jet slot axis using multigrid/multipass cross-correlation digital particle image velocimetry. These measurements have been used to investigate the mean flow quantities and turbulent statistics of the phenomenon. In addition, the wake extent and behaviour (i.e. symmetric or asymmetric) are analysed as well as the drag coefficient, for each configuration. The extent of the wake region decreases as the momentum coefficient and/or the dimensionless frequency increase, while the symmetric/asymmetric wake behaviour is found to be governed by a different control parameter: the synthetic jet Reynolds number based on its impulse. As regards the drag coefficient, a maximum reduction, of approximately 35\%, is found for the configuration at \(C_\mu=10.8\%\) and \(f^+=0.98\).Improved model of isothermal and incompressible fluid flow in pipelines versus the Darcy-Weisbach equation and the issue of friction factor.https://zbmath.org/1460.762912021-06-15T18:09:00+00:00"Kowalczuk, Zdzisław"https://zbmath.org/authors/?q=ai:kowalczuk.zdzislaw"Tatara, Marek S."https://zbmath.org/authors/?q=ai:tatara.marek-sSummary: In this article, we consider the modelling of stationary incompressible and isothermal one-dimensional fluid flow through a long pipeline. The approximation of the average pressure in the developed model by the arithmetic mean of inlet and outlet pressures leads to the known empirical Darcy-Weisbach equation. Most importantly, we also present another improved approach that is more accurate because the average pressure is estimated by integrating the pressure along the pipeline. Through appropriate transformation, we show the difference between the Darcy-Weisbach equation and the improved model that should be treated as a Darcy-Weisbach model error, in multiplicative and additive form. This error increases when the overall pressure drop increases. This symptomatic phenomenon is discussed in detail. In addition, we also consider four methods of estimating the coefficient of friction, assess the impact of pressure difference on the estimated average flow velocity and, based on experimental data, we show the usefulness of new proposals in various applications.Analysis of amplification mechanisms and cross-frequency interactions in nonlinear flows via the harmonic resolvent.https://zbmath.org/1460.761762021-06-15T18:09:00+00:00"Padovan, Alberto"https://zbmath.org/authors/?q=ai:padovan.alberto"Otto, Samuel E."https://zbmath.org/authors/?q=ai:otto.samuel-e"Rowley, Clarence W."https://zbmath.org/authors/?q=ai:rowley.clarence-wSummary: We propose a framework that elucidates the input-output characteristics of flows with complex dynamics arising from nonlinear interactions between different time scales. More specifically, we consider a periodically time-varying base flow, and perform a frequency-domain analysis of periodic perturbations about this base flow. The response of these perturbations is governed by the harmonic resolvent, which is a linear operator similar to the harmonic transfer function introduced by \textit{N. M. Wereley} [Analysis and control of linear periodically time varying systems. Massachusetts: Massachusetts Institute of Technology (PhD Thesis) (1991)]. This approach makes it possible to explicitly capture the triadic interactions that are responsible for the energy transfer between different time scales in the flow. For instance, perturbations at frequency \(\omega\) are coupled with perturbations at frequency \(\alpha\) through the base flow at frequency \(\omega -\alpha\). We draw a connection with resolvent analysis, which is a special case of the harmonic resolvent when evaluated about a steady base flow. We show that the left and right singular vectors of the harmonic resolvent are the optimal response and forcing modes, which can be understood as full spatio-temporal signals that reveal space-time amplification characteristics of the flow. Finally, we illustrate the method on examples, including a three-dimensional system of ordinary differential equations and the flow over an airfoil at near-stall angle of attack.Feedback control of vortex shedding using a resolvent-based modelling approach.https://zbmath.org/1460.762892021-06-15T18:09:00+00:00"Jin, Bo"https://zbmath.org/authors/?q=ai:jin.bo"Illingworth, Simon J."https://zbmath.org/authors/?q=ai:illingworth.simon-j"Sandberg, Richard D."https://zbmath.org/authors/?q=ai:sandberg.richard-dSummary: An investigation of optimal feedback controllers' performance and robustness is carried out for vortex shedding behind a two-dimensional cylinder at low Reynolds numbers. To facilitate controller design, we present an efficient modelling approach in which we utilise the resolvent operator to recast the linearised Navier-Stokes equations into an input-output form from which frequency responses can be computed. The difficulty of applying modern control design techniques to high-dimensional flow systems is overcome by using low-order models identified from frequency responses. These low-order models are used to design optimal controllers using \(\mathcal{H}_\infty\) loop shaping. Two distinct single-input single-output control arrangements are considered. In the first arrangement, a velocity sensor located in the wake drives a pair of body forces near the cylinder. Complete suppression of shedding is observed up to \(Re=110\). Due to the convective nature of vortex shedding and the corresponding time delays, we observe a fundamental trade-off: the sensor should be close enough to the cylinder to avoid excessive time lag, but it should be kept sufficiently far from the cylinder to measure unstable modes developing downstream. These two conflicting requirements become more difficult to satisfy for larger Reynolds numbers. In the second arrangement, we consider a practical set-up with an actuator that oscillates the cylinder according to the lift measurement. The system is stabilised up to \(Re=100\), and we demonstrate why the performance of the resulting feedback controllers deteriorates more rapidly with increasing Reynolds number. The challenges of designing robust controllers for each control set-up are also analysed and discussed.Multiplicative control problems for nonlinear reaction-diffusion-convection model.https://zbmath.org/1460.352772021-06-15T18:09:00+00:00"Brizitskii, R. V."https://zbmath.org/authors/?q=ai:brizitskii.roman-victorovich|brizitskii.r-v|brizitskii.roman-viktorovich"Saritskaia, Zh. Yu."https://zbmath.org/authors/?q=ai:saritskaia.zh-yuSummary: Global solvability of a boundary value problem for a generalized Boussinesq model is proved in the case, when reaction coefficient depends nonlinearly on concentration of substance. Maximum principle is stated for substance's concentration. Solvability of control problem is proved, when the role of controls is played by diffusion and mass exchange coefficients from the equations and from the boundary conditions of the model. For a considered multiplicative control problem, optimality systems are obtained. On the base of the analysis of these systems for particular reaction coefficients and cost functionals, local stability estimates are deduced for optimal solutions.Work-minimizing kinematics for small displacement of an infinitely long cylinder.https://zbmath.org/1460.762002021-06-15T18:09:00+00:00"Mandre, Shreyas"https://zbmath.org/authors/?q=ai:mandre.shreyas-dSummary: We consider the time-dependent speed of an infinitely long cylinder that minimizes the net work done on the surrounding fluid to travel a given distance perpendicular to its axis in a fixed amount of time. The flow that develops is two-dimensional. An analytical solution is possible using calculus of variations for the case that the distance travelled and the viscous boundary layer thickness that develops are much smaller than the circle radius. If \(t\) represents the time since the commencement of motion and \(T\) the final time, then the optimum speed profile is \(Ct^{1/4}(T-t)^{1/4}\), where \(C\) is determined by the distance travelled. The result also holds for rigid-body translations and rotation of cylinders formed by extrusion of smooth but otherwise arbitrary curves.Upstream actuation for bluff-body wake control driven by a genetically inspired optimization.https://zbmath.org/1460.762432021-06-15T18:09:00+00:00"Minelli, G."https://zbmath.org/authors/?q=ai:minelli.guglielmo"Dong, T."https://zbmath.org/authors/?q=ai:dong.teng|dong.tingting|dong.tianhang|dong.tao|dong.thinh|dong.ting|dong.tianzhen|dong.tuochuan|dong.tianxue|dong.tianxin|dong.tong|dong.tianwen|dong.tiansi|dong.tiandu|dong.tianbao|dong.tian|dong.tianyu|dong.taiheng"Noack, B. R."https://zbmath.org/authors/?q=ai:noack.bernd-r"Krajnović, S."https://zbmath.org/authors/?q=ai:krajnovic.sinisaSummary: The control of bluff-body wakes for reduced drag and enhanced stability has traditionally relied on the so-called direct-wake control approach. By the use of actuators or passive devices, one can manipulate the aerodynamic loads that act on the rear of the model. An alternative approach for the manipulation of the flow is to move the position of the actuator upstream, hence interacting with an easier-to-manipulate boundary layer. The present paper comprises a bluff-body flow study via large-eddy simulations to investigate the effectiveness of an upstream actuator (positioned at the leading edge) with regard to the manipulation of the wake dynamics and its aerodynamic loads. A rectangular cylinder with rounded leading edges, equipped with actuators positioned at the front curvatures, is simulated at \(Re=40\,000\). A genetic algorithm (GA) optimization is performed to find an effective actuation that minimizes drag. It is shown that the GA selects superharmonic frequencies of the natural vortex shedding. Hence, the induced disturbances, penetrating downstream in the wake, significantly reduce drag and lateral instability. A comparison with a side-recirculation-suppression approach is also presented, the latter case being worse in terms of reduced drag (only 8 \% drag reduction achieved), despite the total suppression of the side recirculation bubble. In contrast, the GA optimized case contributes to a 20 \% drag reduction with respect to the unactuated case. In addition, the large drag reduction is associated with a reduced shedding motion and an improved lateral stability.Feedback control of unstable flow and vortex-induced vibration using the eigensystem realization algorithm.https://zbmath.org/1460.762312021-06-15T18:09:00+00:00"Yao, W."https://zbmath.org/authors/?q=ai:yao.wangjin|yao.wenhao|yao.wancong|yao.wenpo|yao.wang.1|yao.weigang|yao.wanying|yao.wangshu|yao.weiguo|yao.wenying|yao.weixin|yao.wensong|yao.wenlin|yao.weiping|yao.weiwei|yao.weijie|yao.weihong|yao.weiguang|yao.wen-li|yao.wei.1|yao.weixing|yao.weilie|yao.weifeng|yao.wen|yao.weiran|yao.weili|yao.wei|yao.wenqing|yao.wanghe|yao.wenqi|yao.weijian|yao.wenqiang|yao.wenxiu|yao.wang|yao.wenjuan|yao.wensheng|yao.weian|yao.wensu|yao.weijia|yao.wenju"Jaiman, R. K."https://zbmath.org/authors/?q=ai:jaiman.rajeev-kumarSummary: We present an active feedback blowing and suction (AFBS) procedure via model reduction for unsteady wake flow and the vortex-induced vibration (VIV) of circular cylinders. The reduced-order model (ROM) for the AFBS procedure is developed by the eigensystem realization algorithm (ERA), which provides a low-order representation of the unsteady flow dynamics in the neighbourhood of the equilibrium steady state. The actuation is considered via vertical suction and a blowing jet at the porous surface of a circular cylinder with a body-mounted force sensor. While the optimal gain is obtained using a linear quadratic regulator (LQR), Kalman filtering is employed to estimate the approximate state vector. The feedback control system shifts the unstable eigenvalues of the wake flow and the VIV system to the left half-complex-plane, and subsequently results in suppression of the vortex street and the VIV in elastically mounted structures. The resulting controller designed by a linear low-order approximation is able to suppress the nonlinear saturated state of wake vortex shedding from the circular cylinder. A systematic linear ROM-based stability analysis is performed to understand the eigenvalue distribution for the flow past stationary and elastically mounted circular cylinders. The results from the ROM analysis are consistent with those obtained from full nonlinear fluid-structure interaction simulations, thereby confirming the validity of the proposed ROM-based AFBS procedure. A sensitivity study on the number of suction/blowing actuators, the angular arrangement of actuators and the combined versus independent control architectures has been performed for the flow past a stationary circular cylinder. Overall, the proposed control concept based on the ERA-based ROM and the LQR algorithm is found to be effective in suppressing the vortex street and the VIV for a range of reduced velocities and mass ratios.Model reduction and mechanism for the vortex-induced vibrations of bluff bodies.https://zbmath.org/1460.762302021-06-15T18:09:00+00:00"Yao, W."https://zbmath.org/authors/?q=ai:yao.wangjin|yao.wenhao|yao.wancong|yao.wenpo|yao.wensong|yao.weiguo|yao.wenjuan|yao.weifeng|yao.wen|yao.wensheng|yao.weijian|yao.wenqing|yao.wanying|yao.wei.1|yao.wenlin|yao.weijie|yao.weiran|yao.wang.1|yao.wanghe|yao.weiwei|yao.wensu|yao.wenqi|yao.weian|yao.weilie|yao.weixing|yao.weigang|yao.wangshu|yao.wenying|yao.weiguang|yao.weili|yao.weixin|yao.wei|yao.wen-li|yao.weiping|yao.wang|yao.wenxiu|yao.wenqiang|yao.weihong|yao.weijia|yao.wenju"Jaiman, R. K."https://zbmath.org/authors/?q=ai:jaiman.rajeev-kumarSummary: We present an effective reduced-order model (ROM) technique to couple an incompressible flow with a transversely vibrating bluff body in a state-space format. The ROM of the unsteady wake flow is based on the Navier-Stokes equations and is constructed by means of an eigensystem realization algorithm (ERA). We investigate the underlying mechanism of vortex-induced vibration (VIV) of a circular cylinder at low Reynolds number via linear stability analysis. To understand the frequency lock-in mechanism and self-sustained VIV phenomenon, a systematic analysis is performed by examining the eigenvalue trajectories of the ERA-based ROM for a range of reduced oscillation frequency \((F_s)\), while maintaining fixed values of the Reynolds number \((Re)\) and mass ratio \((m^*)\). The effects of the Reynolds number \(Re\), the mass ratio \(m^*\) and the rounding of a square cylinder are examined to generalize the proposed ERA-based ROM for the VIV lock-in analysis. The considered cylinder configurations are a basic square with sharp corners, a circle and three intermediate rounded squares, which are created by varying a single rounding parameter. The results show that the two frequency lock-in regimes, the so-called resonance and flutter, only exist when certain conditions are satisfied, and the regimes have a strong dependence on the shape of the bluff body, the Reynolds number and the mass ratio. In addition, the frequency lock-in during VIV of a square cylinder is found to be dominated by the resonance regime, without any coupled-mode flutter at low Reynolds number. To further discern the influence of geometry on the VIV lock-in mechanism, we consider the smooth curve geometry of an ellipse and two sharp corner geometries of forward triangle and diamond-shaped bluff bodies. While the ellipse and diamond geometries exhibit the flutter and mixed resonance-flutter regimes, the forward triangle undergoes only the flutter-induced lock-in for \(30\leqslant Re\leqslant 100\) at \(m^*=10. In\) the case of the forward triangle configuration, the ERA-based ROM accurately predicts the low-frequency galloping instability. We observe a kink in the amplitude response associated with \(1:3\) synchronization, whereby the forward triangular body oscillates at a single dominant frequency but the lift force has a frequency component at three times the body oscillation frequency. Finally, we present a stability phase diagram to summarize the VIV lock-in regimes of the five smooth-curve- and sharp-corner-based bluff bodies. These findings attempt to generalize our understanding of the VIV lock-in mechanism for bluff bodies at low Reynolds number. The proposed ERA-based ROM is found to be accurate, efficient and easy to use for the linear stability analysis of VIV, and it can have a profound impact on the development of control strategies for nonlinear vortex shedding and VIV.Optimal feedback control for one motion model of a nonlinearly viscous fluid.https://zbmath.org/1460.762932021-06-15T18:09:00+00:00"Zvyagin, Viktor Grigor'evich"https://zbmath.org/authors/?q=ai:zvyagin.viktor-grigorevich"Zvyagin, Andreĭ Viktorovich"https://zbmath.org/authors/?q=ai:zvyagin.andrey-v"Hong, Nguyen Minh"https://zbmath.org/authors/?q=ai:hong.nguyen-minhSummary: An optimal control problem with a feedback is considered for an initial boundary problem describing a motion of non-linearly viscous liquid. An existence of an optimal solution minimising a given quality functional is proved. A topological approximation approach to study of mathematical problems of hydrodynamics is used in the proof of existence of an optimal solution.Optimal feedback control problem for inhomogeneous Voigt fluid motion model.https://zbmath.org/1460.762922021-06-15T18:09:00+00:00"Zvyagin, Victor"https://zbmath.org/authors/?q=ai:zvyagin.victor-g"Turbin, Mikhail"https://zbmath.org/authors/?q=ai:turbin.mikhail-vSummary: In the present paper, we study weak solvability of the optimal feedback control problem for the inhomogeneous Voigt fluid motion model. The proof is based on the approximation-topological approach. This approach involves the approximation of the original problem by regularized operator inclusion with the consequent application of topological degree theory. Then, we show the convergence of the sequence of solutions for the approximation problem to the solution for the original problem. For this, we use independent on approximation parameter a priori estimates. Finally, we prove that the cost functional achieves its minimum on the weak solution set.