Unsteady Reynolds-averaged Navier Research Articles

On the relevance of the runner crown for flow instabilities in a Francis turbine

The precessing vortex core (PVC), also known as vortex rope, in a draft tube of a Francis-99 hydro turbine is investigated. The goal is to increase our comprehension of the root of the PVC in order to attenuate or suppress the PVC, thus extending the stable operational range below the best efficiency point at part load conditions. Unsteady Reynolds-averaged Navier– Stokes simulations are conducted and used as a basis for all the analyses performed in this work. The discrete Fourier transform (DFT) and the spectral proper orthogonal decomposition (SPOD) as data-driven methods and the linear stability analysis (LSA) as a physics-based, operator-driven method are used to examine the PVC in detail. With the DFT and SPOD, two dominant modes are found inside the draft tube. Likewise, the LSA reveals two distinct linear instabilities of single-helical and double-helical shape, which agree with the findings of the SPOD in terms of spatial shape and temporal frequency. A particular focus is laid upon the region upstream of the draft tube. An adjoint-based sensitivity analysis reveals that both instability modes are highly sensitive to mean flow modifications inside the transitional segment between runner and draft tube, such as induced by passive control devices. The knowledge of these sensitivities will guide to an optimized runner and draft tube design for controlling the PVC and the double-helical mode.

Trapped Acoustic Modes in an Axial Multi-Stage Compressor Leading to Non-Synchronous Blade Vibrations

Non-synchronous blade vibrations have been observed in an experimental multi-stage high-speed compressor setup at part-speed conditions. A detailed numerical study has been carried out to understand the observed phenomenon by performing unsteady full-annulus Reynolds-Averaged Navier–Stokes (RANS) simulations of the whole setup using the solver elsA. Several operating conditions have been simulated to observe this kind of phenomena along a speedline of interest. Based on the simulation results, the physical source of the non-synchronous blade vibration is identified: An aerodynamic disturbance appears in a highly loaded downstream rotor and excites a spinning acoustic mode. A “lock-in” phenomenon occurs between the blade boundary layer oscillations and the spinning acoustic mode. The establishment of axially propagating acoustic waves can lead to a complex coupling mechanism and this phenomenon is highly relevant in understanding the multi-physical interactions appearing in modern compressors. It is shown that aerodynamic disturbances occurring downstream can lead to critical excitation of rotor blades in upstream stages due to an axially propagating acoustic wave. The paper includes the analysis of a relevant transient test and a detailed analysis of the numerical results. The study shows the capability and necessity of a full-annulus multistage simulation to understand the phenomenon.

Airfoil leading edge blowing to control bow shock waves

This manuscript presents a detailed characterization of active control of bow shock waves via leading edge injection, including subsonic coolant ejection and the appearance of Coanda effects. The flow phenomena occurring at steady and pulsating flow injection regimes were analyzed using steady and unsteady two-dimensional Reynolds-Averaged Navier Stokes, leading to a precise evaluation of the thermal load and drag reductions. Steady supersonic injection yields the largest abatement in thermal load and aerodynamic drag, while subsonic or fluctuating ones can also provide significant improvements at reduced cooling mass flow rates. Furthermore, a Coanda effect, causing a non-symmetric flow topology, was observed and analyzed for reduced injection port size. This Coanda effect is due to the sudden expansion happening from the injection port to the main flow and it causes the flow topology at the leading edge to become non-symmetric despite the complete symmetry of the problem. This is the first time in the literature such a phenomenon is documented for a supersonic airfoil leading edge injection. Furthermore, it enables the design of novel flow control strategies for the leading edge shock topology and flow structures in supersonic flows.

Design of an Annular-Radial Diffuser for Operation With a Supercritical CO2 Radial Inflow Turbine

Radial inflow turbines are a relevant architecture for energy extraction from supercritical CO2 power cycles for scales less than 10 MW. To ensure stage and overall cycle efficiency, it is desirable to recover exhaust energy from the turbine stage through the inclusion of a suitable diffuser in the turbine exhaust stream. In supercritical CO2 Brayton cycles, the high turbine inlet pressure can lead to sealing challenges at small scale if the rotor is supported from the rotor rear side in the conventional manner. An alternative is a layout where the rotor exit faces the bearing system. While such a layout is attractive for the sealing system, it limits the axial space claim of the diffuser. Designs of a combined annular-radial diffuser are considered as a means to meet the aforementioned packaging challenges of this rotor layout. Diffuser performance is assessed numerically with the use of Reynolds-averaged Navier--Stokes (RANS) and unsteady Reynolds-averaged Navier--Stokes (URANS) calculations. To appropriately account for cross coupling with the stage, a single blade passage of the entire stage is modeled. Assessment of diffuser inlet conditions, and off-design performance analysis, reveals that the investigated diffuser designs are performance robust to high swirl, high inlet blockage, and highly nonuniform mass flux distribution. Diffuser component performance is dominated by the annular-radial bend. The incorporation of a constant sectional area bend is the key geometric feature in rendering the highly nonuniform turbine exit flow (dominated by tip clearance flows at the shroud) more uniform.

Detailed flow characteristic analysis of a three-stage centrifugal pump at design and off-design conditions

This paper presents a detailed analysis of the internal flow characteristics of a three-stage centrifugal pump at design and off-design conditions. Numerical analysis is conducted by solving three-dimensional steady and unsteady Reynolds-averaged Navier – Stokes equations with the shear stress transport (SST) turbulence model. The results of steady and unsteady numerical analyses are analyzed and compared with experimental data throughout the flow region. Moreover, a reattachment modification in the SST turbulence model is applied to better capture the characteristics of flow separations arising from boundary layers reattaching at design and off-design conditions. The results show that the unsteady numerical results are in good agreement with the experimental data. Additionally, hydraulic performance with and without the reattachment modification is similar throughout entire flow region whereas the respective flow characteristics for each impeller component are considerably different, especially at low-flow-rate conditions.

Numerical Simulations of Unsteady Separation Bubbles over Turbine Blades

Numerical simulations are often performed assuming the steadiness of the laminar separation bubbles. Even if computational time is saved, it results in a weak convergence of the computations and a lack of precision in the results. URANS (Unsteady Reynolds Average Navier−Stokes equations) computations using the ONERA in-house code elsA are proposed here for a range of chord Reynolds numbers from 80000 to 160000. The numerical results for the mean flow part are compared with the experimental data obtained in the framework of the European programme TATMo (Turbulence and Transition Modelling for Special Turbomachinery Application). The unsteadiness of separation bubbles is clearly demonstrated detecting the vortical structures of the flow. A spectral analysis allows to highlight the flow behaviour depending on the Reynolds number. Characteristic frequencies of the flow are also identified.

3D Unsteady Simulation of a Modern High Pressure Turbine Stage Using Phase Lag Periodicity: Analysis of Flow and Heat Transfer

Unsteady 3D Reynolds-averaged Navier–Stokes (RANS) simulations have been performed on a highly loaded transonic turbine stage, and results are compared with steady calculations and experiments. A low Reynolds number k-ε turbulence model is employed to provide closure for the RANS system. A phase lag boundary condition is used in the tangential direction. This allows the unsteady simulation to be performed by using only one blade from each of the two rows. The objective of this paper is to study the effect of unsteadiness on rotor heat transfer and to glean any insight into unsteady flow physics. The role of the stator wake passing on the pressure distribution at the leading edge is also studied. The simulated heat transfer and pressure results agree favorably with the experiment. The time-averaged heat transfer predicted by the unsteady simulation is higher than the heat transfer predicted by the steady simulation everywhere, except at the leading edge. The shock structure formed, due to stator-rotor interaction, is analyzed. Heat transfer and pressure at the hub and casing are also studied. Thermal segregation is observed that leads to the heat transfer patterns predicted by steady and unsteady simulations to be different.

Simulation and modelling of turbulent trailing-edge flow

Computations of turbulent trailing-edge flow have been carried out at a Reynolds number of 1000 (based on the free-stream quantities and the trailing-edge thickness) using an unsteady 3D Reynolds-Averaged Navier–Stokes (URANS) code, in which two-equation (k–e) turbulence models with various low-Re near wall treatments were implemented. Results from a direct numerical simulation (DNS) of the same flow are available for comparison and assessment of the turbulence models used in the URANS code. Two-dimensional URANS calculations are carried out with turbulence mean properties from the DNS used at the inlet; the inflow boundary-layer thickness is 6.42 times the trailing-edge thickness, close to typical turbine blade flow applications. Many of the key flow features observed in DNS are also predicted by the modelling; the flow oscillates in a similar way to that found in bluff-body flow with a von Karman vortex street produced downstream. The recirculation bubble predicted by unsteady RANS has a similar shape to DNS, but with a length only half that of the DNS. It is found that the unsteadiness plays an important role in the near wake, comparable to the modelled turbulence, but that far downstream the modelled turbulence dominates. A spectral analysis applied to the force coefficient in the wall normal direction shows that a Strouhal number based on the trailing-edge thickness is 0.23, approximately twice that observed in DNS. To assess the modelling approximations, an a priori analysis has been applied using DNS data for the key individual terms in the turbulence model equations. A possible refinement to account for pressure transport is discussed.