arXiv subjects

Artur Gesla

Publications and source records attributed to Artur Gesla.

6 recordsLinked to original sources

arXiv2026

Vortex breakdown in a hydro turbine draft tube swirling jet

The swirling flow in a Francis type hydropower turbine is known to be susceptible to the formation of a large helical structure, commonly referred to as a vortex rope. This vortex rope can be interpreted as an unstable mode associated with vortex breakdown. This perspective is adopted here in a simplified laminar flow setting. The helical vortex rope mode is shown to bifurcate supercritically from an axisymmetric baseflow in a Hopf bifurcation within a turbine draft tube. When wall friction effects are neglected, a large recirculation region at the axis can form and a range of subcritical solutions is identified for a flow regime corresponding to partial load of the turbine. The existence of these subcritical solutions promotes the emergence of a hysteresis loop. We further describe a regular dynamics of a formation of recirculation bubble at the axis and its destruction due to the emergence of a helical vortex rope at its periphery. Increasing the axial flow discharge towards the regime corresponding to nominal turbine load leads to an unfolding of the steady solutions branch in a transcritical bifurcation. This bifurcation takes place at finite Reynolds number and complements existing evidence of transcritical bifurcation of the swirling jet flows, previously reported only in the inviscid limit.

physics.flu-dyn↗

arXiv2026

Linear Stability and Structural Sensitivity of a Swirling Jet in a Francis Turbine Draft Tube

Motivated by the need to better understand flow unsteadiness in hydraulic turbines, we perform a local linear stability and adjoint-based sensitivity analysis of the turbulent swirling jet at the outlet of a Francis turbine. We use measured mean flow and turbulence profiles at several operating conditions (below, at, and above the best efficiency point (BEP) flow rate) and perform a stability analysis. Incorporating eddy viscosity $ν_t$ into the analysis strongly damps inviscid growth rates and restricts instability to low azimuthal modes $m\in [-1,2]$, in better agreement with experiments. Three turbulent viscosity closures (constant, mixing-length and measured $k-\varepsilon$ based) yield similar spectra, with close agreement between mixing length and measured models, all identify partial load (0.92 BEP) as the most unstable regime. Sensitivity results show that axial velocity modifications primarily control growth rates, whereas azimuthal velocity changes mainly shift frequencies. We also derive the sensitivity kernel of the spectrum to turbulent viscosity modifications and find that spatial variations of eddy viscosity are essential for predicting the unstable mode range. The predictions accurately estimate stability changes for small variations in operating point. We further analyze the flow using classical inviscid swirling jet instability criteria (the generalized Rayleigh discriminant) and WKB analysis to predict the stability to broader operating points and reconcile these results to the stability and sensitivity analyses. The approach used in this study is fast and simple to model, but it neglects draft tube geometry (non-parallel effects), motivating future global stability and sensitivity analyses.

physics.flu-dyn↗

arXiv2025

Computation and stability analysis of periodic orbits using finite differences, Fourier or Chebyshev spectral expansions in time

We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are discretised in time either using finite differences, Fourier-Galerkin or Chebyshev expansions. The resulting nonlinear set of equations describing the periodic orbit is solved using a Newton-Raphson algorithm. The linearised equations determining the stability lead to a generalised eigenvalue problem. Unlike the Fourier-Galerkin method, the use of Chebyshev polynomials or finite differences has the advantage that the relevant Floquet exponents are directly given without the well known issue of having to sort out the eigenvalues. The speed of convergence of these three methods is illustrated with examples from the Lorenz system, the Langford system and a two-dimensional thermal convection flow inside a differentially heated cavity. This last example demonstrates the potential of the newly proposed Chebyshev expansion for large-scale problems arising from the discretisation of the incompressible Navier-Stokes equations.

physics.flu-dyn↗

arXiv2025

From annular cavity to rotor-stator flow: nonlinear dynamics of axisymmetric rolls

Spatio-temporally complex flows are found at the onset of unsteadiness in (axisymmetric) rotor-stator turbulence in the shape of concentric rolls. The emergence of these rolls is rationalised using a homotopy approach, where the original flow configuration is continuously deformed into a simpler, better understood configuration. We deform here rotor-stator flow into an annular flow, thereby controlling curvature effects, and we investigate numerically the transition scenarios as functions of the Reynolds number. Increasing curvature starting from the planar limit reveals a clear path towards a subcritical scenario as a function of the Reynolds number. As the rotor-stator configuration is approached, supercritical branches shift to increasing Reynolds number while a subcritical branch of chaotic states takes over. Modal selection in the supercritical scenario involves the competition between two modal families. It rests on a specific radial localisation property of all eigenmodes, linked to the space-dependent convective radial velocity which intensifies as curvature is increased. A new nonlinear mechanism for the pairing of rolls is proposed based on multiple resonances. The critical point where the original rotor-stator flow loses its stability to axisymmetric perturbations is identified for the first time for the geometry under study.

physics.flu-dyn↗

arXiv2024

Subcritical axisymmetric solutions in rotor-stator flow

Rotor-stator cavity flows are known to exhibit unsteady flow structures in the form of circular and spiral rolls. While the origin of the spirals is well understood, that of the circular rolls is not. In the present study the axisymmetric flow in an aspect ratio $R/H=10$ cavity is revisited {numerically using recent concepts and tools from bifurcation theory}. It is confirmed that a linear instability takes place at a finite critical Reynolds number $Re=Re_c$, and that there exists a subcritical branch of large amplitude chaotic solutions. This motivates the search for subcritical finite-amplitude solutions. The branch of periodic states born in a Hopf bifurcation at $Re=Re_c$, identified using a Self-Consistent Method (SCM) and arclength continuation, is found to be supercritical. The associated solutions only exist, however, in a very narrow range of $Re$ and do not explain the subcritical chaotic rolls. Another subcritical branch of periodic solutions is found using the Harmonic Balance Method with an initial guess obtained by SCM. In addition, edge states separating the steady laminar and chaotic regimes are identified using a bisection algorithm. These edge states are bi-periodic in time for most values of $Re$, {where} their dynamics is {analysed in detail}. Both solution branches fold around at approximately the same value of $Re$, which is lower than $Re_c$ yet still larger than the values reported in experiments. This suggests that, at least in the absence of external forcing, sustained chaotic rolls have their origin in the bifurcations from these unstable solutions.

physics.flu-dyn↗

arXiv2024

On the origin of circular rolls in rotor-stator flow

Rotor-stator flows are known to exhibit instabilities in the form of circular and spiral rolls. While the spirals are known to emanate from a supercritical Hopf bifurcation, the origin of the circular rolls is still unclear. In the present work we suggest a quantitative scenario for the circular rolls as a response of the system to external forcing. We consider two types of axisymmetric forcing: bulk forcing (based on the resolvent analysis) and boundary forcing using direct numerical simulation. Using the singular value decomposition of the resolvent operator the optimal response is shown to take the form of circular rolls. The linear gain curve shows strong amplification at non-zero frequencies following a pseudo-resonance mechanism. The optimal energy gain is found to scale exponentially with the Reynolds number $Re$ (for $Re$ based on the rotation rate and interdisc spacing $H$). The results for both types of forcing are compared with former experimental works and previous numerical studies. Our findings suggest that the circular rolls observed experimentally are the effect of the high forcing gain together with the roll-like form of the leading response of the linearised operator. For high enough Reynolds number it is possible to delineate between linear and nonlinear response. For sufficiently strong forcing amplitudes, the nonlinear response is consistent with the self-sustained states found recently for the unforced problem. The onset of such non-trivial dynamics is shown to correspond in state space to a deterministic leaky attractor, as in other subcritical wall-bounded shear flows.

physics.flu-dyn↗