De-Jun Sun

Hopf bifurcation in wakes behind a rotating and translating circular cylinder

A low‐dimensional Galerkin method, initiated by Noack and Eckelmann [Physica D 56, 151 (1992)], for the prediction of the flow field around a stationary two‐dimensional circular cylinder in a uniform stream at low Reynolds number is generalized to the case of a rotating and translating cylinder. The Hopf bifurcation describing the transition from steady to time‐periodic solution is investigated. A curve indicating the transitional boundary is given in the two‐dimensional parameter plane of Reynolds number Re and rotating parameter α. Our results show that rotation may delay the onset of vortex street and decrease the vortex‐shedding frequency.

Wake Patterns of Flow Past a Pair of Circular Cylinders in Side-by-Side Arrangements at Low Reynolds Numbers

A flow past two side-by-side identical circular cylinders was numerically investigated with the unstructured spectral element method. From the computational results at various non-dimensional distances between cylinder centers T/D and the Reynolds number Re, a total of nine kinds of wake patterns were observed: four steady wake patterns, including single bluff-body steady pattern, separated double-body steady pattern and transition steady pattern for sub-critical Reynolds numbers and biased steady pattern for super-critical Reynolds numbers, and five unsteady wake patterns, including single bluff-body periodic pattern, biased quasi-steady pattern, quasi-periodic (flip-flopping) pattern, in-phase-synchronized pattern and anti-phase-synchronized pattern. Time evolution of lift and drag coefficients corresponding to each unsteady wake pattern was given.

Absolute and convective instability character of slender viscous vortices

Motivated by the need for effective vortex control, the character of absolute and convective instabilities (AI/CI) of incompressible and high-Mach number slender vortices with axial-velocity deficit is studied. Attention is focused on the disturbance modes which lead to the maximum absolute growth rate, and their dependence on flow conditions such as axial-flow profile, Reynolds number, and Mach number. A significant difference between the AI/CI and temporal-instability characters of the vortices occurs as the axial velocity deficit reduces. These theoretical results are applied to the flow region where vortex breakdown happens. It is found that the breakdown region is absolutely unstable, where waves are dominated by the spiral disturbance with lowest azimuthal wave number, in reasonable agreement with measurement.

A numerical study of dynamics of a temporally evolving swirling jet

Direct numerical simulation (DNS) of a swirling jet near the outlet of a nozzle with axisymmetric and non-axisymmetric disturbances is performed to investigate the dynamic characteristics of the flow. The early (linear) stage of the jet evolution agrees well with the predictions of linear stability theory. In the nonlinear stage, the axisymmetric DNS shows that the interaction between the primary vortex ring and the streamwise columnar vortex creates a secondary vortex structure with opposite azimuthal vorticity near the columnar vortex. Then a vortex pair consisting of the primary and secondary vortices forms and travels radially away from the symmetry axis, causing a rapid increase of the thickness of mixing layer. The non-axisymmetric DNS shows that the streamwise vortex layer developed in the early stage of evolution due to azimuthal instability breakdowns into small eddies under the joint stretch of the axial and azimuthal shear. The results reveal several mechanisms of mixing enhancement by swirl, i...

Perturbation analysis on gas flow in a straight microchannel

In the present paper, a steady subsonic gas flow either in a circular micropipe or in a planar microchannel driven by pressure within the slip flow regime is studied theoretically by using a perturbation expansion method to solve compressible Navier-Stokes equations. The isothermal flow assumption used in previous theoretical studies is given up. High-order boundary conditions of velocity slip and temperature jump are adopted at the wall. The set of dimensionless governing equations with two small similarity parameters, namely, the ratio of height to length e, and the Knudsen number Kn, is approximated successively by using the perturbation expansions. The various cases such as e≪Kn2, e∼Kn2, and e∼Kn1.5 are studied in detail. Explicit analytical solutions for pressure, density, velocity, temperature, and mass flow rate are obtained up to order of O(Kn2). It is shown that the solution formulas for long channels (e≪Kn2) in lower order are in exact agreement with previous theoretical results. In particular, ...

Large eddy simulation of flow development and noise generation of free and swirling jets

Large eddy simulation is performed for investigating the local and far-field behaviors of free and swirling jets at moderate Reynolds number. By solving compressible boundary layer equations, the inflow profiles with different swirl number are calculated, and then their stability characteristics are analyzed based on linear stability theory. The amplification rates of swirling jets are higher than the free one, particularly for higher or negative azimuthal wavenumber modes. Multiple unstable modes are superimposed to construct inflow forcing. The quantities of flow and acoustic are presented and compared against the results of existed experiments and other computations, besides, the comparisons are also made among themselves. For swirling jets, the spreadings of jet half-width and vorticity thickness at the initial and transition stage are enhanced, but they are surpassed by the free jet at turbulent mixing stage. In all cases, the development of mixing layer initially is greatly influenced by frequencies...

Stability and temporal evolution of a swirling jet with centrifugally unstable azimuthal velocity

A temporal linear instability analysis by the normal mode method and a direct numerical simulation (DNS) are performed to investigate the stability and temporal evolution of a swirling jet with centrifugally unstable Taylor vortex-like azimuthal velocity. A marked instability character is that the Kelvin–Helmholtz modes are dominant at lower axial wave numbers and the modes of centrifugal instability are dominant at higher axial wave numbers. The results of DNS show that the early linear stage of evolution of swirling jet agrees well with that predicted by linear stability theory. In the nonlinear stage, the centrifugally unstable velocity profile has important influences on the evolution dynamics. For the basic flow with small vortex core (ρ=1), the negative axial vorticity suppresses the eruption of vorticity from the core and the formation of secondary vortex ring pairs with opposite vorticity. For the basic flow with larger vortex core (ρ=4.5), the negative axial vorticity is away from the core region...

Sound generation by different vortex interactions in mixing layers

To understand the correlation between far-field sound and near-field vortex dynamics, in this paper, we numerically investigate the sound generation from different types of vortex interaction (e.g. vortex pairing, vortex tearing, triple/quadruple-vortex merging). Direct numerical simulation (DNS) of the compressible Navier-Stokes equations is carefully conducted for an accurate description of far-field sound radiation. By choosing different phase delays between the fundamental frequency and its sub-harmonics, the vortex interaction changes from perfect pairing to tearing. The sound generated by vortex tearing is much quieter than the one from vortex pairing at the same excitation level. However, the directivity of sound radiations keeps almost the same. When different combinations of forcing frequencies are chosen, there are more complex triple and quadruple vortex mergings, The sound intensity of such cases is stronger than the one of either vortex pairing or vortex tearing. With more frequencies being involved, multi-directivity appears in triple/quadruple-vortex merging cases.

Mode decomposition of a noise suppressed mixing layer

Noise is generated in atwo-dimensional mixing layer due to the growing of instability waves and vortex pairings. The adjoint-based control methodology has shown to be arobust tool to suppress noise radiation. The mode decomposition algorithms such as the compressible versionof proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are employed toanalyze thespatial/spatial-temporal coherent structures for a consecutive data sets of the controlled mixing layer and itsuncontrolled counterpart. The analyses of POD indicate that the y-direction body forcecontrol mainly modify themost energetic spatialstructures, and increase the uniformity of the flow. The analyses of DMD show us prevalent frequencies andcorresponding mode structures, and the stability characteristics of each mode can be obtained fromDMD-spectrum. The spectral signatures illustrate that a lot of neutral/slightly damping modesemerging in uncontrolled flow within the frequency range (ω < 0.4) are suppressed due to control, relevant spatial-temporal structures are also varied, which iscoincident with the change of far-field noise spectra. From the view of mode decomposition, the action of control redistribute the energy forfrequency components of ω < 0.4 by weakening nonlinearities and regularizing corresponding dynamicstructures in streamwise direction, and thus suppress the noise radiation. Moreover, the POD- and DMD-analysis in this studydemonstrate that DMD can serve as an important supplement for POD in analyzing a time-resolved physicalprocess.

Numerical investigation of Rayleigh–Bénard convection in a cylinder of unit aspect ratio

Thermal convection in a vertical cylindrical cavity with a heated bottom, cooled top and insulated sidewall is investigated numerically. The radius to height ratio (Γ = height/radius) is fixed to unity and the Prandtl number is varied from 0.04 to 1. Rayleigh numbers up to 16 000 are considered in this study. Ten different kinds of flow regime have been identified, including both steady and unsteady patterns. The transition from steady to oscillatory flow occurs at a much lower Rayleigh number for small Prandtl number flow than for large Prandtl number flow. A bifurcation analysis shows the coexistence of two flow patterns in a certain parameter regime. The effect of flow structure on heat transfer is studied for a Prandtl number of unity.