High-speed supersonic radial compressors are a critical enabling technology for meeting the requirements of future aviation-propulsion and thermal-management systems. These turbomachines must be designed to be both efficient and robust on the widest possible operating range. Flow instabilities in the form of rotating stall and surge are therefore phenomena that must be accurately predicted early in the design process. Unsteady full-Annulus computational fluid dynamics (CFD) can be used to get accurate information about the onset of instabilities, but at the expense of costly simulations. As a result, the design of new compressors continues to rely on existing correlations for the prediction of the critical mass flowrate. This approach, however, leads to suboptimal compressor designs. This article provides a review of the numerical methodologies that can be used for the accurate prediction of the critical mass flowrate in high-speed centrifugal compressors. Methods of different fidelity level and computational cost are described. Two particularly promising models, namely, those proposed by Spakovszky and Sun, are subsequently examined in more detail. Exemplary applications of these two models are finally discussed.

Simulations of reacting multiphase flows tend to display an inhomogeneously distributed computational intensity over the spatial and temporal domains. The time-to-solution of chemical reaction rates can span multiple orders of magnitude due to the emergence of combustible kernels and thin turbulent reaction zones. Similarly, the time to solve the equation of state (EoS) for non-ideal fluid mixtures deviates substantially between the grid cells. These effects result in a performance profile that is unbalanced and rapidly changing for transient simulations, and therefore beyond the capabilities of traditional (quasi-)static mesh partitioning methods. We analyse this loss of parallel efficiency for large-eddy simulations of the ECN Spray-A benchmark with the multi-physics solver INCA and propose to mitigate the problem by introducing two independent repartitioning stages in addition to the classic domain decomposition for fluid transport: one for the EoS and one for chemical reactions. We explore various scalable repartitioning strategies in this context and observe that rebalancing computational load yields a significant speedup that is robust for various mesh resolutions and process numbers. The dynamic multistage load-balancing thus effectively removes obstacles towards good parallel scaling of INCA and similar solvers for reacting and/or multiphase flows.

Stationary velocity-perturbation streaks have recently been identified in laminar swept-wing boundary-layer flow interacting with a surface forward-facing step. Streaky structures at the step promote early laminar-turbulent transition under certain conditions. This work utilizes direct numerical simulations to explore the mechanisms of growth of stationary streaks at the step and provides insight into their origin, nature, and spatial organization. The analysis is mainly focused on, but not restricted to, incoming perturbations in the form of stationary crossflow instability. Stationary streaky structures are found to be universal to swept forward-facing-step flow subjected to three-dimensional perturbations in the incoming boundary layer. The streaks at the step are primarily ascribed to the lift-up effect. They appear as a linear perturbation response of the highly sheared step flow to the cross-stream pattern of incoming perturbations. A mechanism of base-flow deceleration additionally contributes to feeding growth to the streaks. Linear stability analysis carried out through the harmonic Navier-Stokes method confirms that the streaks are a linear perturbation phenomenon. Effects of spanwise perturbation wavelength and effective sweep angle on the mechanisms of the streaks are also assessed.

Leading-edge protuberances on airfoils have been shown to soften the onset of aerodynamic stall and to increase lift in the post-stall regime. The present study examines the effect of tubercles during dynamic stall. Pitching airfoils with tubercles of different amplitudes are studied by wind-tunnel experiments, where the three-dimensional time-resolved velocity field is determined using large-scale particle-tracking velocimetry. Computational fluid dynamics simulations are carried out that complement the experimental observations providing pressure distribution and aerodynamic forces. The dynamic stall is dominated by a vortex formed at the leading edge; we characterize the vorticity, circulation, and advection path of this dynamic-stall vortex (DSV). The presence of the tubercles profoundly modifies the boundary layer from the leading edge. The roll-up of the vorticity sheet is significantly delayed compared to a conventional airfoil, resulting in a weaker DSV. The vortex formation is shifted downstream, with the overall effect of a weaker and shorter lift overshoot, in turn enabling a quicker transition to deep stall. Regions of flow separation (stall cells) are visibly compartmentalized with a stable spacing of two tubercles wavelengths.

We propose several enhancements to improve the accuracy and performance of the digital filter turbulent inflow generation technique and assess their efficacy in the context of wall-resolved large-eddy simulations of a compressible turbulent boundary layer. Improvements of accuracy include a more realistic correlation function for the transversal directions, target length scales that vary with wall-distance, and a counter-intuitive approach that involves the suppression of streamwise velocity fluctuations at the inflow. For improving the computational performance, we propose to generate the inflow data in parallel in single precision and at a prescribed time interval based on the turbulence time scale, and not at every time-step of the simulation. Based on the results of 7 wall-resolved large-eddy simulations, we find that the new correlation functions and the considered performance improvements are beneficial and therefore desired. Suppressing streamwise velocity fluctuations at the inflow leads to the fastest relaxation of the pressure fluctuations; however, this approach increases the adaptation length defined in terms of compliance with the von Kármán integral equation. The adaptation length can be shortened by artificially increasing the wall-normal Reynolds stresses, thereby preserving the desired turbulence kinetic energy level. A detailed inspection of the Reynolds stress transport budgets reveals that the observed spurious spatial transients are largely driven by pressure-related terms. For instance, increased values of u^′p^′¯ are found throughout the computational domain when a physical Reynolds stress distribution is prescribed at the inflow. Therefore, efforts to enhance digital filter techniques should aim at modeling pressure fluctuations as well as their correlation with the velocity components.

High-speed supersonic radial compressors are a critical enabling technology for meeting the requirements of future aviation-propulsion and thermal-management systems. These turbomachines must be designed to be both efficient and robust on the widest possible operating range. Flow instabilities in the form of rotating stall and surge are therefore phenomena that must be accurately predicted early in the design process. Unsteady full-annulus computational fluid dynamics can be used to get accurate information about the onset of instabilities, but at the expense of costly simulations. As a result, the design of new compressors continues to rely on existing correlations for the prediction of the critical mass flow rate. This approach, however, leads to sub-optimal compressor designs. This article provides a review of the numerical methodologies that can be used for the accurate prediction of the critical mass flow rate in high-speed centrifugal compressors. Methods of different fidelity level and computational cost are described. Two particularly promising models, namely those proposed by Spakovszky and Sun, are subsequently examined in more detail. Exemplary applications of these two models are finally discussed.

The dynamic coupling between a Mach 2.0 shock-wave/turbulent boundary-layer interaction (STBLI) and a flexible panel is investigated. Wall-resolved large-eddy simulations are performed for a baseline interaction over a flat-rigid wall, a coupled interaction with a flexible panel, and a third interaction over a rigid surface that is shaped according to the mean panel deflection of the coupled case. Results show that the flexible panel exhibits self-sustained oscillatory behavior over a broad frequency range, confirming the strong and complex fluid-structure interaction (FSI). The first three bending modes of the panel oscillation are found to contribute most to the unsteady panel response, at frequencies in close agreement with natural frequencies of the mean deformed panel rather than those for the unloaded flat panel. This highlights the importance of the mean panel deformation and the corresponding stiffening in the FSI dynamics. The time-averaged flow shows an enlarged reverse-flow region in the presence of mean surface deformations. The separation-shock unsteadiness is enhanced due to the panel motion, leading to higher wall-pressure fluctuations in the coupled interaction. Spectral analysis of the separation-shock location and bubble-volume signals shows that the STBLI flow strongly couples with the first bending mode of the panel oscillation. This is further confirmed by dynamic mode decomposition of the flow and displacement data, which reveals variations in the reverse-flow region that follow the panel bending motion and appear to drive the separation-shock unsteadiness. Low-frequency modes that are not associated with the fluid-structure coupling, in turn, are qualitatively similar to those obtained for the rigid-wall interactions, indicating that the characteristic low-frequency unsteadiness of STBLI coexists with the dynamics emerging from the fluid-structure coupling. Based on the present results, unsteady FSIs involving STBLIs and flexible panels are likely to accentuate rather than mitigate the undesirable features of STBLIs.

We revisit the origin of low-frequency unsteadiness in turbulent recirculation bubbles (TRBs), and, in particular, the hypothesis of a dynamic feedback mechanism between unconstrained separation and reattachment locations. To this end, we conduct wall-resolved large-eddy simulations of a novel experimental configuration where a shock-induced TRB forms over a backward-facing step that is intended to intercept the hypothesized dynamic feedback. Our results demonstrate, for the first time, effective suppression of the low-frequency characteristics of the TRB without reducing its size, strongly supporting our hypothesis.

The efficacy of immersed boundary (IB) methods with adaptive mesh refinement (AMR) techniques is assessed in the context of atmospheric entry applications, including effects of chemical nonequilibrium (CNE) and gas–surface interactions (GSI). We scrutinize a conservative cut-cell IB method and two non-conservative IB methods, comparing their results with analytical solutions, data from the literature, and results obtained with a reference solver that operates on body-fitted grids. All solvers employ the same external thermochemistry library, ensuring that all observed differences can be attributed solely to differences in the underlying numerical methodologies. We present results for eight benchmark cases. Four verification cases verify the implementation of chemistry, transport properties, catalytic boundary conditions, and shock capturing. Four validation cases encompass blunt geometries with adiabatic and isothermal, as well as inert, catalytic and ablative boundary conditions. Overall, the results obtained with the IB solvers are in very good agreement with the reference data. Discrepancies arise in cases with large temperature or concentration gradients at the wall, and these are linked to conservation errors inherent to ghost-cell and interpolation-based IB methods. Only a strictly conservative cut-cell IB method is on par with body-fitted grid methods.

Direct numerical simulations (DNS) are performed over a 15° compression ramp undergoing ablation at Mach 8 to examine fluid-ablation interactions (FAI) on transitional high-speed boundary layers. The experiments at these conditions with a rigid wall are first numerically replicated for a laminar flow. Heating streaks are introduced by introducing perturbations in the baseflow informed by prior stability calculations. The ramp is then replaced by a low-temperature ablator in our DNS and the interaction of the streaks with the recessing ablator surface are examined. Different approaches from two independently developed solvers are used to study this problem. Overall, both solvers provide qualitatively and quantitatively very similar results; however, differences in streak amplification and mass blowing magnitudes are observed. We discuss the difficulties in accurately predicting ablation and present the first findings regarding its influence on the perturbation evolution and transition to turbulence for this configuration.

A novel passive flow-control method for shock-wave/turbulent boundary-layer interactions (STBLI) is investigated. The method relies on a structured roughness pattern constituted by streamwise-aligned ridges. Its effectiveness is assessed with wall-resolved large-eddy simulations of the interaction of a Mach 2 turbulent boundary layer flow with an oblique impinging shock with shock angle 40^∘. The structured roughness pattern, which is fully resolved by a cut-cell based immersed boundary method, covers the entire computational domain. Results show that this rough surface induces large-scale secondary streamwise vortices, which energize the boundary layer by transporting high-speed fluid closer to the wall. A parametric study is performed to investigate the effect of the spacing between the ridges. This investigation is further substantiated through spectral analysis and sparsity-promoting dynamic mode decomposition. We find that ridges with small spacing effectively mitigate the low-frequency unsteadiness of STBLI and slightly reduce total-pressure loss.

A novel mechanism is identified, through which a spanwise-invariant surface feature (a two-dimensional forward-facing step) significantly stabilizes the stationary crossflow instability of a three-dimensional boundary layer. The mechanism is termed here as reverse lift-up effect, inasmuch as it acts reversely to the classic lift-up effect; that is, kinetic energy of an already-existing shear-flow instability is transferred to the underlying laminar flow through the action of cross-stream perturbations. To characterize corresponding energy-transfer mechanisms, a theoretical framework is presented, which is applicable to generic three-dimensional flows and surface features of arbitrary shape with one invariant spatial direction. The identification of a passive geometry-induced effect responsible for dampening stationary crossflow vortices is a promising finding for laminar flow control applications.

Wall-resolved large-eddy simulations (LES) are performed to investigate Reynolds number effects in supersonic turbulent boundary layers (TBLs) at Mach 2.0. The resulting database covers more than a decade of friction Reynolds number Re_τ, from 242 to 5554, which considerably extends the parameter range of current high-fidelity numerical studies. Reynolds number trends are identified on a variety of statistics for skin-friction, velocity and thermodynamic variables. The efficacy of recent scaling laws as well as compressibility effects are also assessed. In particular, we observe the breakdown of Morkovin's hypothesis for third-order velocity statistics, in agreement with previous observations for variable-property flows at low Mach number. Special attention is also placed on the size and topology of the turbulent structures populating the TBL, with an emphasis on the outer-layer motions at high Reynolds number. The corresponding streamwise spectra of streamwise velocity fluctuations show a clear separation between inner and outer scales, where energetic peaks are found at streamwise wavelengths of λ_x⁺≈700 and λ_x/δ₀≈6. The spanwise spacing of the outer-layer structures, in turn, is found to be insensitive to the Reynolds number and equal to ∼0.7δ₀. It is also found that the integral length-scales in spanwise direction for the temperature, streamwise and spanwise velocity fields appear to progressively collapse with increasing Reynolds number. The modulating influence that the outer-layer structures exert on the near-wall turbulence is also clearly visible in many of the metrics discussed. In addition, the present LES data is further exploited to assess the Re_τ-sensitivity of uniform momentum regions in the flow. We find that the resulting probability density function of the number of zones as well as its evolution with Re_τ agrees well with incompressible data. This suggests that uniform zones, which have been associated with outer-layer dynamics, are not strongly influenced by compressibility at the considered Mach number.

We investigate Reynolds number effects in strong shock-wave/turbulent boundary-layer interactions (STBLI) by leveraging a new database of wall-resolved and long-integrated large-eddy simulations. The database encompasses STBLI with massive boundary-layer separation at Mach 2.0, impinging-shock angle 40^◦ and friction Reynolds numbers Re_τ 355, 1226 and 5118. Our analysis shows that the shape of the reverse-flow bubble is notably different at low and high Reynolds number, while the mean-flow separation length, separation-shock angle and incipient plateau pressure are rather insensitive to Reynolds number variations. Velocity statistics reveal a shift in the peak location of the streamwise Reynolds stress from the separation-shock foot to the core of the detached shear layer at high Reynolds number, which we attribute to increased pressure transport in the separation-shock excursion domain. Additionally, in the high Reynolds case, the separation shock originates deep within the turbulent boundary, resulting in intensified wall-pressure fluctuations and spanwise variations associated with the passage of coherent velocity structures. Temporal spectra of various signals show energetic low-frequency content in all cases, along with a distinct peak in the bubble-volume spectra at a separation-length-based Strouhal number St_Lsep ≈ 0.1. The separation shock is also found to lag behind bubble-volume variations, consistent with the acoustic propagation time from reattachment to separation and a downstream mechanism driving the shock motion. Finally, dynamic mode decomposition of three-dimensional fields suggests a Reynolds-independent statistical link among separation-shock excursions, velocity streaks and large-scale vortices at low frequencies.

Achieving and maintaining laminar flow on large swept lifting surfaces of subsonic aircraft poses a considerable challenge.

Linear stability analyses are performed to study the dynamics of linear convective instability mechanisms in a laminar shock-wave/boundary-layer interaction at Mach 1.7. In order to account for all two-dimensional gradients elliptically, we introduce perturbations into an initial-value problem that are found as solutions to an eigenvalue problem formulated in a moving frame of reference. We demonstrate that this methodology provides results that are independent of the numerical setup, frame speed, and type of eigensolutions used as initial conditions. The obtained time-integrated wave packets are then Fourier-transformed to recover individual-frequency amplification curves. This allows us to determine the dominant spanwise wavenumber and frequency yielding the largest amplification of perturbations in the shock-induced recirculation bubble. By decomposing the temporal wave-packet growth rate into the physical energy-production processes, we provide an in-depth characterization of the convective instability mechanisms in the shock-wave/boundary-layer interaction. For the particular case studied, the largest growth rate is achieved in the near-vicinity of the bubble apex due to the wall-normal (productive) and streamwise (destructive) Reynolds-stress energy-production terms. We also observe that the Reynolds heat-flux effects are similar but contribute to a smaller extent.

Although several previous studies have reported a potential drag-reducing effect of dimpled surfaces in turbulent boundary layers, there is a lack of replicability across experiments performed by different research groups. To contribute to the dialogue, we scrutinize one of the most studied dimple geometries reported in the literature, which has a dimple diameter of 20 mm and a depth of 0.5 mm. There is no general consensus in literature on the drag-reduction performance of this particular dimple geometry, with some studies suggesting a drag reduction, while others report a drag increase. The present combined experimental and numerical study comprises two sets of wind tunnel experiments and a well-resolved large-eddy simulation. The wind tunnel experiments and the large-eddy simulation both depict a total drag increase of around 1%–2% compared to the flat reference case. This finding agrees with a recent study by Spalart et al. (2019). Furthermore, the present wind tunnel experiments have shed light on a plausible reason behind the discrepancy between the study by Spalart et al. (2019) and earlier results from van Nesselrooij et al. (2016). Lastly, the large-eddy simulation results reveal that the pressure drag is the main contributor to the increase in the total drag of the dimpled surface. We believe that these results will contribute to a new consensus on the drag performance of this dimple geometry.