In this paper, we investigate a (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili (GVCKP) equation in a fluid or plasma. The Nth-order Wronskian solutions for that equation are derived and proved under certain variable-coefficient constraints, where N is a positive integer. One-, two- and three-soliton solutions in the Wronskian for that equation are given. By means of the Pfaffianization procedure, a coupled (3+1)-dimensional GVCKP system is constructed from that equation. Bilinear form for that coupled system is exported. Under certain variable-coefficient constraints, those Wronski-type and Gramm-type Pfaffian solutions for that coupled system are obtained and proved with the help of the Pfaffian identities.

Wronskian solutions and Pfaffianization for a(3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili equation in a fluid or plasma

The linear and nonlinear characteristics of a dual-mode scramjet combustor are investigated in ground-simulated acceleration and deceleration trajectory experiments. The experiments were conducted in the direct-connected transientFlight Trajectory Simulator 1 (FTS-1) at the Institute of Mechanics, Chinese Academy of Sciences. High-frequencypressure measurements, the Schlieren and CH* chemiluminescence high speed imaging were applied for the diagnostics. Based on the quantitative analysis, the physical processes of acceleration and deceleration in general representsimilar nonlinear characteristics. The linear characteristics are limited to the low frequency oscillation period in thepresence of physical governing mechanisms. A nonlinear predictive model of the dual-mode scramjet combustor based on historical measurements is proposed due to its generality for the acceleration and deceleration trajectory.

Characterization and predictive modeling of a trajectory-oriented dual-mode scramjet combustor

Dynamical properties of vector localized and periodic waves hold significant importance in the study of physical systems. In this work, we investigate the matrix Hirota equation with sign-alternating nonlinearity via the binary Darboux transformation. For the two interacting components, we construct the binary Darboux transformation formulas, vector localized, and periodic wave solutions. Via those solutions, different kinds of nonlinear waves can be achieved, including rogue waves, solitons, positons, and periodic waves. When the imaginary part of the spectral parameter is not zero, eye-shaped rogue waves appear in one component, and the twisted rogue wave pairs in the other component. As the spectral parameter is real, we derive distinct forms of vector localized and periodic waves on the non-zero background, such as the vector solitons, positons, periodic waves, breathers on the periodic wave background, and rational solitons. These results may be valuable in this investigation of nonlinear waves in physical systems.

https://pubs.aip.org/aip/pof/article-pdf/doi/10.1063/5.0157082/18031301/075108_1_5.0157082.pdf

Vector localized and periodic waves for the matrix Hirota equation with sign-alternating nonlinearity via the binary Darboux transformation

This study investigates the characteristics of the shedding vortex around the Coanda surface and its impacts on the circulation control (CC) performance. Delay detach-eddy simulation based on the two-equation k-ω shear stress transport (SST) turbulence model performed to solve the flow field. The simulation results show that near the Coanda trailing edge, large vortices periodically shed from the lip above the jet slot and the shedding vortex is surrounded by a series of strip vortices during its downstream movement. The shedding vortex transfers the disturbance to the jet boundary layer and affects the near-wall velocity. Dynamic mode decomposition shows that the shedding vortex and its high-order harmonic flow structures attenuate very slowly and dominate the flow field. The mode with a sub-harmonic frequency of the shedding vortex displays the strip vortices dragged out by the shedding vortex. A larger shedding vortex can intensify the mixing of the jet shear and boundary layers, making the jet velocity decay faster. The size of the shedding vortex can be reduced by decreasing the lip height, thus slowing down the attenuation of the jet velocity and improving the CC performance.

Characteristics of the shedding vortex around the Coanda surface and its impacts on circulation control airfoil performance

Direct numerical simulations are performed for flow past circular cylinders by the lattice Boltzmann method coupled with immersed moving boundary method. By analyzing the flows past a single cylinder at a wide range of cross-flow or in-line oscillation amplitude (0.25≤A/D≤1.5) and frequency (0.5≤fe/f0≤1.5), the results find that the vortex shedding modes inside and outside “lock-in” interval are of significant difference. The vortex shedding mode in the “unlock-in” state is 2S, but C(2S) and P + S shedding modes can be found in the lock-in state. Dynamic mode decomposition is used to analyze characteristic flow features, which shows that mode 1 is the main factor reflecting the flow field structure and mode 2 represents the vortex shedding mode in this work. The vortex shedding modes of flows past a tandem and side-by-side cross-flow double oscillating cylinders are systemically investigated. For tandem double oscillation cylinders, the results of modal decomposition suggest that the shear layer of upstream oscillating cylinder is separated behind the downstream cylinder at a space rate of L/D≤2, but separated behind the upstream cylinder at L/D≥3. Mode 2 at L/D=4 differs from other vortex shedding modes due to the strong inhibition effect by the downstream cylinder on the vortex formation of upstream cylinder. For side-by-side double oscillation cylinders, the wake of two cylinders is a single vortex street at H/D=1, a bistable flow at H/D=2 or 3, a coupled vortex street at H/D=4, and close to a single cylinder at H/D>4. The results of modal decomposition are disordered at H/D=2 due to the interaction between two cylinders and effect of gap flow.

https://pubs.aip.org/aip/pof/article-pdf/doi/10.1063/5.0153302/17848012/053618_1_5.0153302.pdf

Vortex shedding analysis of flows past forced-oscillation cylinder with dynamic mode decomposition

This study presents an extensive numerical investigation to understand the effect of fluid viscoelasticity on the flow dynamics past a stationary cylinder in the laminar vortex shedding regime. In particular, for the first time, this study presents a detailed analysis of how the fluid viscoelasticity influences the coherent flow structures in this benchmark problem using the dynamic mode decomposition (DMD) technique, which is considered to be one of the widely used reduced order modeling (ROM) technique in the domain of fluidmechanics. We show that this technique can successfully identify the low-rank fluid structures in terms of the spatiotemporal modes from the time-resolved vorticity field snapshots and capture the essential flow features by very few modes. Furthermore, we observe a significant difference in the amplitude and frequency associated with these modes for Newtonian and viscoelastic fluids otherwise under the same conditions. This, in turn, explains the differences seen in the flow dynamics between the two types of fluids in an unambiguous way, such as why the fluid viscoelasticity suppresses the vortex shedding phenomenon and decreases the energy associated with the velocity fluctuations in viscoelastic fluids than that in Newtonian fluids. However, before performing the DMD analysis, we also present a detailed discussion on the various fluid-mechanical aspects of this flow system, such as streamline patterns, vorticity fields, drag and lift forces acting on the cylinder, etc. This will ultimately set a reference platform for delineating the importance of the DMD analysis to get further insights into the flow physics.

Dynamic mode decomposition analysis and fluid-mechanical aspects of viscoelastic fluid flows past a cylinder in laminar vortex shedding regime

This study presents a detailed investigation of how the rheological behaviour of fluid could influence the electrokinetic instability (EKI) phenomenon in a microfluidic T-junction. The non-Newtonian power-law model with different values of the power-law index (n) is used to obtain fluids of different rheological behaviours. We find thatas the fluid rheological behaviour changes from shear-thickening (n > 1) to shear-thinning (n < 1) via the Newtonian (n = 1) one, the EKI phenomenon is significantly influenced under the same conditions. In particular, the intensity of this EKI phenomenon is found to be significantly higher in shear-thinning fluids than in Newtonian and shear-thickening fluids. As a result, the corresponding mixing phenomenon, often achieved using this EKI phenomenon, is also notablyenhanced in shear-thinning fluids compared to that achieved in Newtonian and shear-thickening fluids. We also employ the data-driven dynamic mode decomposition (DMD) technique to analyze the flow field in more detail. In particular, the information on the coherent flow structures obtained with different values of the power-law index facilitates the understanding of both the EKI-induced chaotic convection and mixing phenomena in a better way; for instance, why the mixing efficiency is higher in shear-thinning fluids than that in Newtonian and shear-thickening fluids. Moreover, we observe that the spatial expanse and intensity of these coherent structures differ significantly as the power-law index changes, thereby providing valuable insights into certain aspects of the underlying flow dynamics that otherwise are not clearly apparent from other analyses.

/pdf/strong-effect-of-fluid-rheology-on-electrokinetic-sfmqkjmd.pdf

Strong effect of fluid rheology on electrokinetic instability and subsequent mixing phenomena in a microfluidic T-junction

This study presents a numerical investigation of how ﬂuid viscoelasticity inﬂuences the ﬂow dynamics past a transversely forced oscillating cylinder in the laminar vortex shedding regime at a ﬁxed Reynolds number of Re = 100. In particular, we examine how ﬂuid viscoelasticity inﬂuences the boundary between the lock-in and no lock-in zones and the associated wake topology compared to that seen in a simple Newtonian ﬂuid. All in all, we ﬁnd that the ﬂuid viscoelasticity facilitates the synchronization of the vortex street with the cylinder motion at lower oscillation frequencies than that required for a Newtonian ﬂuid. Consequently, the boundary of the lock-in region for a viscoelastic ﬂuid diﬀers from the Newtonian one and broadens in the non-dimensional cylinder oscillation amplitude and frequency plane. Furthermore, we propose that excess strain generated due to the stretching of polymer molecules in a viscoelastic ﬂuid results in a marked diﬀerence in the wake structure from that seen in a Newtonian ﬂuid. For a Newtonian ﬂuid, only ’2S’ (two single vortices) and ’P+S’ (a pair and a single vortex) vortex shedding modes are detected in the primary synchronization region. However, a ’2P’(two pairs of vortices) vortex mode is detected for a viscoelastic ﬂuid in this region. We also employ the data-driven dynamic mode decomposition (DMD) reduced order modeling technique to extract and analyze underlying coherent ﬂow structures and their associated frequencies to understand the diﬀerences in the ﬂow dynamics of Newtonian and viscoelastic ﬂuids past an oscillating cylinder.

Faheem Hamid

Papers

Dynamic mode decomposition analysis and fluid-mechanical aspects of viscoelastic fluid flows past a cylinder in laminar vortex shedding regime

Strong effect of fluid rheology on electrokinetic instability and subsequent mixing phenomena in a microfluidic T-junction

Significant influence of fluid viscoelasticity on flow dynamics past an oscillating cylinder