Stokes Analysis Research Articles

Terahertz-absorbing,dual-polarization converting supersurface structures based on the phase-change material VO2

Dynamically tunable multifunctional hypersurface structures have attracted the interest of researchers due to their good control of electromagnetic waves. Based on this, we have designed a dynamically tunable multifunctional hypersurface structure using the phase change material vanadium dioxide. By changing the state of vanadium dioxide, three functions of efficient broadband wave absorption, linear polarization conversion (LPC) and linear circular polarization conversion (LCPC) can be achieved. At room temperature, the hypersurface is used as a polarization converter to achieve broadband linear polarization conversion in the 0.903 THz range and line-circular polarization conversion with a total bandwidth of 0.608 THz in the 0.522 THz, 0.964 THz and 1.448 THz bands. When the temperature is raised to 68 °C, the hypersurface structure can be used as a broadband absorber, absorbing more than 90% of the incident wave in a wide frequency range of 1.348 THz and showing a large tolerance to variations in the angle of incidence and polarization. The electromagnetic field distribution is used to illustrate the absorption mechanism, and Stokes analysis is introduced to evaluate the polarization transition state. The designed structure can realize three electromagnetic modulation functions by changing the excitation conditions and can cover a wide range of frequency bands. Finally, we used coding to simulate the effect of loss on the wave absorption results in real applications and verified the stability of the structure. Our design provides new ideas for the development of terahertz communication and multifunctional integrated devices.

Aerodynamic Analysis of Low-Pressure Axial Fans Installed in Parallel

Abstract Ducted rotor-only low-pressure axial fans play an integral role in automotive thermal management. The tightly packed under-hood region and down-stream heat-exchanger shape limit the fan diameter. In order to circumvent this limitation, multiple cooling fans of small diameters are tightly packaged and placed in parallel. Currently, there is limited scientific work, that study the aerodynamics of low-pressure axial fans when installed in parallel. This work aims to quantify the aerodynamic performance and the flow-field as a result of installing low-pressure axial fans in parallel through computational fluid dynamics (CFD). Publicly available experimental data from Friedrich-Alexander University is used for the validation of the numerical setup. Three-dimensional, full-annulus, unsteady Reynolds-averaged Navier-Stokes (URANS) analysis has been performed for both a single-fan and two-fans installed in parallel and their respective aerodynamic performance has been compared for the operation condition identified as the best efficiency point in experiments. Only small differences are observed in the overall aerodynamic performance of the two-fans in parallel compared to a single-fan. A circumferential nonuniformity in the form of a local high-pressure zone at the inlet of the fan is observed when the two-fans are placed in parallel. The resulting circumferential nonuniformity is quantified, both in space and time. A strong correlation is found between the pressure fields of the two-fans installed in parallel.

Improvements in the Prediction of Steady and Unsteady Transition and Mixing in Low-Pressure Turbines by Means of Machine-Learnt Closures

Abstract In this article, novel machine-learnt transition and turbulence models are applied to the prediction of boundary-layer transition and wake mixing in a low-pressure turbine (LPT) cascade, including unsteady inflow cases with incoming wakes. A laminar kinetic energy (LKE) transport approach is employed as baseline transition framework. The application of the machine-learnt explicit algebraic Reynolds stress models (EARSMs) takes advantage of a zonal strategy based on a newly developed sensing function that allows automated wake demarcation. This work compares the performance of several approaches that are based on the application of improved transition models without machine learnt EARSMs, baseline transition model with EARSMs trained for improved wake mixing, and new transition and turbulence closures that are simultaneously developed in a fully coupled way and aimed at improving both transition and wake mixing predictions in LPTs. The investigation is carried out on a cascade of industrial footprint, representative of modern LPT bladings. First, the various modeling frameworks are evaluated, without bar wakes (steady conditions), over a wide range of Reynolds number values. Unsteady Reynolds-averaged Navier–Stokes (URANS) analyses have also been carried out to investigate the predictive capabilities of machine-learnt closures in the presence of incoming bar wakes. Reynolds-averaged Navier–Stokes (RANS)/URANS results are scrutinized against large eddy simulation (LES) calculations and experimental data. It will be demonstrated that machine-learnt EARSMs are capable of producing realistic wake mixing when simply applied on top of the baseline transition models. However, the most accurate predictions will be shown to be provided by fully integrated machine-learnt transition/turbulence closures.

Estimation of wavenumber–frequency spectra of wall pressure due to turbulent flow over a flat plate using large-eddy simulation

The wavenumber–frequency spectra (WFS) of turbulent wall pressure fluctuations are used to design underwater acoustic systems, and a method is presented to determine them for flat plate flow using large-eddy simulations (LES). First, the Reynolds averaged Navier–Stokes (RANS) analysis is carried out for flow over the plate using k–ω shear-stress transport model. Flow parameters are extracted from the output of this analysis and used to impose boundary conditions for large-eddy simulations using a smaller domain with finer mesh. Mesh convergence studies are done to establish the adequacy of the proposed meshing scheme for estimating the turbulent boundary layer wall pressures. The stream-wise velocity profiles, turbulence intensities, and power spectra obtained using LES are compared with other computational and experimental results. The time history of fluctuating pressure on the wall at various stream-wise locations is used to estimate the WFS. Estimations are made of the convective ridge as well as sub-convective and low wavenumber portions of the spectrum. The computations are performed at momentum thickness-based Reynolds numbers (Rθ) of 5761, 7988, and 7709. The effect of downstream distance on the WFS is studied by computing it at three downstream locations and shown that the downstream distance has little effect on the WFS once the flow has become fully turbulent. The use of a desktop workstation for the estimation of WFS has not been reported earlier. The results show that the WFS of turbulent pressure due to flow over more complex geometries can be estimated using a similar method.

Validation of Broadband Noise Prediction Methodology Based on Linearized Navier–Stokes Analyses

Abstract This article presents an integral validation of a synthetic turbulence broadband noise prediction methodology for fan/outlet-guide-vane (OGV) interaction. The test vehicle is the ACAT1 fan, a modern scaled-down fan, experimentally analyzed in 2018 within the TurboNoiseBB project. Three operating points, namely, Approach, Cutback, and Sideline, and two different rig configurations in terms of the axial gap between the fan and OGV are examined within this work. The methodology consists of using a Reynolds-averaged Navier–Stokes (RANS) solver to model the fan wake and the use of two-dimensional frequency domain linearized Navier–Stokes simulations to resolve the acoustics, including quasi-3D corrections to obtain representative results. The RANS results with no ad hoc tuning are compared in detail against hotwire data to determine the degree of uncertainty incurred by this kind of approach. The predicted broadband noise spectra and noise azimuthal decompositions are compared against the experimental data. The spectral levels are well predicted despite an average underprediction of around 3dB. The noise azimuthal decompositions feature a remarkable agreement with the experiment, denoting accurate modeling of the main physics governing the problem. The impact of increasing the fan/OGV axial gap is quantified numerically for the first time. It is concluded that increasing the gap is detrimental for the broadband noise footprint, unlike intuitively could be expected. Overall, the presented broadband noise methodology yields robust broadband noise predictions at an industrially feasible cost and enables a deeper understanding of the problem.

Synthetic spin dynamics with Bessel-Gaussian optical skyrmions.

Skyrmions are topologically stable fields that cannot be smoothly deformed into any other field configuration that differs topologically, that is, one that possesses a different integer topological invariant called the Skyrme number. They have been studied as 3-dimensional and 2-dimensional skyrmions in both magnetic and, more recently, optical systems. Here, we introduce an optical analogy to magnetic skyrmions and demonstrate their dynamics within a magnetic field. Our optical skyrmions and synthetic magnetic field are both engineered using superpositions of Bessel-Gaussian beams, with time dynamics observed over the propagation distance. We show that the skyrmionic form changes during propagation, exhibiting controllable periodic precession over a well defined range, analogous to time varying spin precession in homogeneous magnetic fields. This local precession manifests as the global beating between skyrmion types, while still maintaining the invariance of the Skyrme number, which we monitor through a full Stokes analysis of the optical field. Finally, we outline, through numerical simulation, how this approach could be extended to create time varying magnetic fields, offering free-space optical control as a powerful analogue to solid state systems.

Effects of an Unsteady Morphing Wing with Seamless Side-Edge Transition on Aerodynamic Performance

This paper presents an unsteady flow analysis of a 3D wing with a morphing trailing edge flap (TEF) and a seamless side-edge transition between the morphed and static parts of a wing by introducing an unsteady parametrization method. First, a 3D steady Reynolds-averaged Navier–Stokes (RANS) analysis of a statically morphed TEF with seamless transition is performed and the results are compared with both a baseline clean wing and a wing with a traditional hinged flap configuration at a Reynolds number of 0.7 × 106 for a range of angles of attack (AoA), from 4° to 15°. This study extends some previous published work by examining the inherent unsteady 3D effects due to the presence of the seamless transition. It is found that in the pre-stall regime, the statically morphed wing produces a maximum of a 22% higher lift and a near constant drag reduction of 25% compared with the hinged flap wing, resulting in up to 40% enhancement in the aerodynamic efficiency (i.e., lift/drag ratio). Second, unsteady flow analysis of the dynamically morphing TEF with seamless flap side-edge transition is performed to provide further insights into the dynamic lift and drag forces during the flap motions at three pre-defined morphing frequencies of 4 Hz, 6 Hz, and 8 Hz, respectively. Results have shown that an initially large overshoot in the drag coefficient is observed due to unsteady flow effects induced by the dynamically morphing wing; the overshoot is proportional to the morphing frequency which indicates the need to account for dynamic morphing effects in the design phase of a morphing wing.

On a reduced-order model-based optimization of rotor electro-thermal anti-icing systems

PurposeResponsible for lift generation, the helicopter rotor is an essential component to protect against ice accretion. As rotorcraft present a smaller wing cross-section and a lower available onboard power compared to aircraft, electro-thermal heating pads are favored as they conform to the blades’ slender profile and limited volume. Their optimization is carried out here taking into account, for the first time, the highly three-dimensional (3D) nature of the flow and ice accretion, in contrast to the current state-of-the-art that is limited to two-dimensional (2D) airfoils.Design/methodology/approachConjugate heat transfer simulation results are provided by the truly 3D finite element Navier–Stokes analysis package-ICE code, embedded in a proprietary rotorcraft simulation toolkit, with reduced-order modeling providing a time-efficient evaluation of the objective and constraint functions at every iteration. The proposed methodology optimizes heating pads extent and power usage and is versatile enough to address in a computationally efficient manner a wide variety of optimization formulations.FindingsLow-error reduced-order modeling strategies are introduced to make the tackling of complex 3D geometries feasible in todays’ computers, with the developed framework applied to four problem formulations, demonstrating marked reductions to power consumption along with improved aerodynamics.Originality/valueThe present paper proposes a 3D framework for the optimization of electro-thermal rotorcraft ice protection systems, in hover and forward flight. The current state-of-the-art is limited to 2D airfoils.

Design Optimization of a Dual-Bleeding Recirculation Channel to Enhance Operating Stability of a Transonic Axial Compressor

The present work performed a comprehensive investigation to find the effects of a dual-bleeding port recirculation channel on the aerodynamic performance of a single-stage transonic axial compressor, NASA Stage 37, and optimized the channel’s configuration to enhance the operating stability of the compressor. The compressor’s performance was examined using three parameters: The stall margin, adiabatic efficiency, and pressure ratio. Steady-state three-dimensional Reynolds-averaged Navier–Stokes analyses were performed to find the flow field and aerodynamic performance. The results showed that the addition of a bleeding channel increased the recirculation channel’s stabilizing effect compared to the single-bleeding channel. Three design variables were selected for optimization through a parametric study, which was carried out to examine the influences of six geometric parameters on the channel’s effectiveness. Surrogate-based design optimization was performed using the particle swarm optimization algorithm coupled with a surrogate model based on the radial basis neural network. The optimal design was found to increase the stall margin by 51.36% compared to the case without the recirculation channel with only 0.55% and 0.28% reductions in the peak adiabatic efficiency and maximum pressure ratio, respectively.

Performance Enhancement of the Micromixer by the Multiobjective Genetic Algorithm and Surrogate Model Based on a Navier–Stokes Analysis Using Trade-Off Objective Functions

Optimal structure of the micromixer with a two-layer serpentine crossing device was accomplished by a multiobjective genetic algorithm and surrogate modeling based on a Navier–Stokes analysis using the trade-off objective functions behavior. The optimization analysis was conducted with three design parameters, i.e., channel width to the pitch span ( w / P ) ratio, major channel width to the pitch span (H/P) ratio, and channel depth to the pitch span (d/P) ratio. Two objective functions (i.e., mixing index and pressure drop) with trade-off characteristics have been used to solve the multiobjective optimization problem. The design domain was predetermined by a parametric investigation; afterward, the Latin hypercube sampling method was employed to select the appropriate design points surrounded by the design domain. The numerical data of the thirty-two design points were used to create the surrogate model; among the different surrogate models, in this study, the Kriging metamodel has been used. The concave pareto-optimal curve signifies the trade-off characteristics linking the objective functions.

Effect of Air Injection on the Internal Flow Characteristics in the Draft Tube of a Francis Turbine Model

Under low flow-rate conditions, a Francis turbine exhibits precession of a vortex rope with pressure fluctuations in the draft tube. These undesirable flow phenomena can lead to deterioration of the turbine performance as manifested by torque and power output fluctuations. In order to suppress the rope with precession and a swirl component in the tube, the use of anti-swirl fins was investigated in a previous study. However, vortex rope generation still occurred near the cone of the tube. In this study, unsteady-state Reynolds-averaged Navier–Stokes analyses were conducted with a scale-adaptive simulation shear stress transport turbulence model. This model was used to observe the effects of the injection in the draft tube on the unsteady internal flow and pressure phenomena considering both active and passive suppression methods. The air injection affected the generation and suppression of the vortex rope and swirl component depending on the flow rate of the air. In addition, an injection level of 0.5%Q led to a reduction in the maximum unsteady pressure characteristics.

Hybrid Large Eddy Simulation/Reynolds-Averaged Navier–Stokes Analysis of a Premixed Ethylene-Fueled Dual-Mode Scramjet Combustor

Hydrocarbon fuels offer optimal high energy per volume for scramjet applications for sustained hypersonic flight but require additional residence time due to slower ignition delays (compared with hydrogen fuel). The injection of ethylene at the start of the isolator of a dual-mode scramjet combustor, operating in ramjet mode, allows sufficient mixing to achieve efficient premixed turbulent combustion. A cavity flameholder anchors the flame, supplying sufficient radicals to sustain a stable flame in the high-speed environment. This work investigates flame structure and stabilization limits of a new configuration with a scaled-down cavity embedded in the flow path of the combustor with a strut and insert. The cavity is reduced in size by one-third to enable eventual direct numerical simulations of the flame stabilization process. This work, however, focuses on modeling the full isolator/combustor geometry using a hybrid large eddy simulation/Reynolds-averaged Navier–Stokes simulation strategy. Particle image velocimetry, planar laser-induced fluorescence, coherent anti-Stokes Raman spectroscopy, and pressure measurements are compared with numerical predictions to analyze and characterize the conditions within the combustor, including flame structure, flow velocities, species composition, and wall pressure. An adjustable air throttle in the extender is able to control the placement of the shock train in the isolator and maintain a stable flame at various equivalence ratios. The simulations show reasonably good agreement with the experimental scalar and velocity data and predict a flame angle consistent with premixed turbulent flame-speed correlations.

Flow Distortion Into the Core Engine for an Installed Variable Pitch Fan in Reverse Thrust Mode

Abstract The flow distortion at core engine entry for a variable pitch fan (VPF) in reverse thrust mode is described from a realistic flow field obtained using an integrated airframe-engine model. The model includes the VPF, core entry splitter, complete bypass nozzle flow path wrapped in a nacelle, and installed to an airframe in landing configuration through a pylon. A moving ground plane to mimic the rolling runway is included. 3D Reynolds-averaged Navier–Stokes (RANS) solutions are generated at two combinations of VPF stagger angle and rotational speed settings for the entire aircraft landing run from 140 to 20 knots. The internal reverse thrust flow field is characterized by bypass nozzle lip separation, pylon wake, and recirculation of flow turned back from the VPF. A portion of the reverse stream flow turns 180 deg with separation at the splitter leading edge to feed the core engine. The core engine feed flow exhibits circumferential and radial nonuniformities that depend on the reverse flow development at different landing speeds. The temporal dependence of the distorted flow features is also explored by an unsteady Reynolds-averaged Navier–Stokes (URANS) analysis. Total pressure and swirl angle distortion descriptors, as defined by the Society of Automotive Engineers (SAE) S-16 committee, and, total pressure loss into the core engine are described for the core feed flow at different operating conditions and landing speeds. It is observed that the radial intensity of total pressure distortion is critical to core engine operation, while the circumferential intensity is within acceptable limits. Therefore, the baseline sharp splitter edge is replaced by two larger rounded splitter edges of radii, ∼0.1x and ∼0.2x times the core duct height. This was found to reduce the radial intensity of total pressure distortion to acceptable levels. The description of the installed core feed flow distortion, as described in this study, is necessary to ascertain stable core engine operation, which powers the VPF in reverse thrust mode.

Theoretical and numerical analyses for PDM-IM signals using Stokes vector receivers

Different from current coherent-detection-based long-haul transmission systems, inter- and intradatacenter transmissions require a simpler transmitter and receiver. A promising way to significantly meet the demands of datacenter transmission is polarization division multiplexing intensity modulation with direct detection (PDM-IM-DD) using a Stokes vector receiver (SVR). However, for different SVR architectures, the corresponding demultiplexing matrix is required to recover the Stokes vectors from the detected signals, which are combined with an arbitrary state of polarization (SOP), will change the effect of noise dynamically and significantly influence the system performance. In this study, PDM-IM signals using four SVRs, i.e., a 90° optical hybrid with 2 balanced photodetectors (BPDs) and 2 photodetectors (PDs), a 90° optical hybrid with 4 PDs, a Stokes analyzer and a 3 × 3 coupler with 4 PDs, are studied theoretically and numerically. Theoretical system models using the four SVRs are developed, and the noise power variations are analyzed quantitatively based on these models. Moreover, the performance of the systems is also investigated for 224 Gbit/s polarization division multiplexing pulse amplitude modulation 4 level with direct detection (PDM-PAM4-DD) transmission in a simulation. The simulation results show that the bit error rate (BER) performance of the systems is consistent with the theoretical noise power variation curves. The theoretical analysis scheme is helpful for the practical design of SVR-based systems.

Relationship Between Flow Instability and Performance of a Centrifugal Pump With a Volute

Abstract Flow instability and its correlations with performance characteristics were investigated for a centrifugal pump with a volute. Unsteady three-dimensional Reynolds-averaged Navier–Stokes analysis was performed to analyze the flow and performance characteristics using the shear stress transport (SST) turbulence model. The grid dependence and temporal resolution were tested to evaluate the numerical uncertainties, and the numerical solutions were validated using experimental data. The total-to-static head coefficient, the impeller's total-to-static head coefficient, and the volute static pressure recovery coefficient were selected as performance parameters. To identify the flow instability, pressure fluctuations were monitored upstream of the impeller, at the volute inlet, and on the shroud wall of the impeller. Three different types of flow instability were detected in partial-load conditions: inside the volute, upstream of the impeller, and at the interface between the impeller and volute. The time-dependent flow structures were investigated to obtain insight into the onset of the flow instability. The correlation of the onset of the flow instability with the performance curves was discussed.

Analysis of Interaction Between Oscillating Jet Issuing from a Fluidic Oscillator and a Crossflow

In the present study, numerical simulation was conducted to study both the internal and external flows of a fluidic oscillator in a quiescent environment and with a crossflow. Unsteady Reynolds-averaged Navier–Stokes analysis was used to evaluate the flow field. The blowing ratio was varied to understand the interaction between the free stream and the oscillating jet. Results for the time-averaged and the time-resolved flow fields were presented. The outlet velocity from the oscillator was not affected by the freestream flow for the tested three blowing ratios. Q criterion was used to evaluate the interaction of turbulent vortical structures from the fluidic oscillator with the crossflow. It was observed that two counter-rotating vortices and ring-like vortices were the important flow features of the external flow. As blowing ratio increases, the counter-rotating vortices become more asymmetric, move further from the wall, and are more spread.

Design Optimization of the Impeller and Volute of a Centrifugal Pump to Improve the Hydraulic Performance and Flow Stability

Abstract Multi-objective design optimization was applied to the impeller and volute of a centrifugal pump using surrogate-based optimization techniques and three-dimensional Reynolds-averaged Navier–Stokes (RANS) analysis. The objective functions used to improve the hydraulic performance and operating stability of the pump were the hydraulic efficiency at the design condition and the flow rate at which the maximum volute pressure recovery coefficient occurs. Three design variables were selected based on the results of a sensitivity analysis: the blade outlet angle, the constants in determining the impeller outlet width, and the cross-sectional area of the volute. Using response surface approximation (RSA), surrogate models were constructed for the objective functions based on numerical results at experimental points obtained by Latin hypercube sampling (LHS). The representative Pareto-optimal solutions obtained by the multi-objective genetic algorithm (MOGA) show enhanced objective function values compared to the baseline design. The results of unsteady calculation show that the flow instability of the centrifugal pump was successfully suppressed by the optimization.

Base drag reduction concept for commercial road vehicles

An Active Flow Control drag reduction device concept is presented and a numerical study of the proposed device is carried out. The operating principle of the device is based on the Coanda effect. The device is tested by means of the Reynolds Averaged Navier Stokes (RANS) analysis and the Delayed Detached Eddy Simulation (DDES) analysis. A hybrid multiblock hexagonal mesh with tetrahedral farfield is created. The resolution of the mesh is fitted so as to fulfill the DDES requirements of resolving 80% of the turbulent kinetic energy. The proposed device achieved 11% reduction of drag coefficient. An 8% discrepancy of results between the methods used is presented. Comparisons of flow-field for baseline and concept case is presented. Differences between RANS and DDES results are given. The presented concept is in line with requirements of the EU directive No. 2015/719 [1].

Effect of Fins on the Internal Flow Characteristics in the Draft Tube of a Francis Turbine Model

Undesirable flow phenomena in Francis turbines are caused by pressure fluctuations induced under conditions of low flow rate; the resulting vortex ropes with precession in the draft tube (DT) can degrade performance and increase the instability of turbine operations. To suppress these DT flow instabilities, flow deflectors, grooves, or other structures are often added to the DT into which air or water is injected. This preliminary study investigates the effects of anti-cavity fins on the suppression of vortex ropes in DTs without air injection. Unsteady-state Reynolds-averaged Navier–Stokes analyses were conducted using a scale-adaptive simulation shear stress transport turbulence model to observe the unsteady internal flow and pressure characteristics by applying anti-cavity fins in the DT of a Francis turbine model. A vortex rope with precession was observed in the DT under conditions of low flow rate, and the anti-cavity fins were confirmed to affect the mitigation of the vortex rope. Moreover, at the low flow rate conditions under which the vortex rope developed, the application of anti-cavity fins was confirmed to reduce the maximum unsteady pressure.

Discrete Adjoint Optimization of a Hypersonic Inlet

Shape optimization of modern three-dimensional hypersonic inlets requires many geometric design parameters. Because the flow physics is complex, a Reynolds-averaged Navier–Stokes (RANS) analysis is also desirable when performing optimization. A computationally efficient means of handling many-parameter optimization with expensive cost functions is to use gradient-based searches informed by an adjoint flow solution. In this work, a discrete adjoint method for high-speed flows is documented. It is implemented in the open-source compressible-flow solver Eilmer. One difficulty with extending a hypersonic flow solver to include an adjoint solver is the differentiation of complex, nonlinear (and sometimes nondifferentiable) algorithms. Here, it is shown that difficulty can be overcome using flow Jacobians constructed with finite differences based on complex variables. The coupled flow and adjoint solvers are packaged together with a gradient-based optimizer. The flow and adjoint solvers are verified and validated for high-speed RANS analysis. The discrete adjoint method for optimization is demonstrated using the NASA P2 hypersonic inlet as a test case. The results show that the optimization method can remove an undesirable shock present in the original geometry, while achieving the desired compression ratio and improving overall performance metrics.