Three-dimensional time-resolved Lagrangian flow field reconstruction based on constrained least squares and stable radial basis function

The effect of airfoil design parameters, such as airfoil thickness and camber, are well understood in steady-state aerodynamics. But this knowledge cannot be readily applied to the flapping flight in insects and birds: flow visualizations and computational analyses of flapping flight have identified that in many cases, a leading-edge vortex (LEV) contributes substantially to the generation of aerodynamic force. In flapping flight, very high angles of attack and partly separated flow are common features. Therefore, it is expected that airfoil design parameters affect flapping wing aerodynamics differently. Existing studies have focused on force measurements, which do not provide sufficient insight into the dominant flow features. To analyse the influence of wing morphology in slow-speed bird flight, the time-resolved three-dimensional flow field around different flapping wing models in translational motion at a Reynolds number of$22\,000<\mathit{Re}<26\,000$was studied. The effect of several Strouhal numbers ($0.2<\mathit{St}<0.4$), camber and thickness on the flow morphology and on the circulation was analysed. A strong LEV was found on all wing types at high$\mathit{St}$. The vortex is stronger on thin wings and enhances the total circulation. Airfoil camber decreases the strength of the LEV, but increases the total bound circulation at the same time, due to an increase of the ‘conventional’ bound circulation at the inner half of the wing. The results provide new insights into the influence of airfoil shape on the LEV and force generation at low$\mathit{Re}$. They contribute to a better understanding of the geometry of vertebrate wings, which seem to be optimized to benefit from LEVs in slow-speed flight.

The characteristics of the circulation flow were investigated for the water flow with the air entrainment slightly from the free water surface in a three-dimensional rectangular outlet pit. At first, the air entrainment pattern was classified into two types by the visual observations.Measurement of the flow velocity distribution in the pit revealed that the dominant types of flow include circulating flow and vertical eddies. And relation of the three-dimensional steady flow field and the primary factor of the air entrainment were clarified. The primary factor of air entrainment made clear that it was the velocity of the radiated surface flow from the end wall, the flow velocity along the side wall and the instantaneous velocity of downward flow at water surface in outlet pit. Turbulent flow velocities in the three-dimensional flow field near the water surface were also investigated. It was concluded from these results that air entrainment is caused by interference between the steady circulating flow and instantaneous velocity variations near the water surface.

The spectral characterization of flow-field parameters provides a new perspective for understanding the spatiotemporal evolution of unsteady supersonic exhaust plumes and for extracting typical structures. In this study, a large-eddy simulation is performed to calculate the three-dimensional unsteady supersonic plume flow field of rocket engines, and a spectral proper orthogonal decomposition (SPOD) method with a spatiotemporal separation is established. This approach is used to extract the coherent structural features of the unsteady exhaust plume flow field and analyze the mode space structure at different frequencies. The three-dimensional reconstruction and denoising of the exhaust plume flow-field parameters can be achieved via the frequency- and time-domain reconstructions of the SPOD algorithm and oblique projection method, respectively. The ground rocket exhaust plume of ballistic evaluation motor-II is analyzed. The results indicate that the SPOD method can effectively extract the single-frequency mode structure of the reactive supersonic flow field, and that low-order behavior appears in the m = 0 and m = 1 azimuth modes. The potential core exhibits a high-frequency wave-packet structure that is affected by shock waves and shear layers. Time-domain reconstruction based on the oblique projection method facilitates the capture of the dynamic characteristics of the flow field. For the first-order SPOD mode, the frequency- and time-domain reconstruction errors are 3.3% and 1.5%, respectively. The frequency-domain reconstruction method exhibits a 4% improvement in denoising ability compared to low-pass filters. This study provides a novel method for the spectral characterization and spatiotemporal feature extraction of supersonic exhaust plume flow fields.

In the field of fluid mechanics, inferring high-dimensional data from low-dimensional observations enables the reconstruction of the high-dimensional flow field, allowing for a more comprehensive understanding of the flow, which is of great importance for analyzing flow mechanisms and optimizing aerodynamic designs. However, the lack of theoretical methodologies makes reconstructing three-dimensional (3D) flow fields a challenging task. To overcome this difficulty, a diffusion transformer-based method is proposed in this paper for reconstructing two-dimensional (2D) flow fields into 3D flow fields. The method introduces plane position embedding to enable reconstruction from arbitrary 2D planes, significantly enhancing flexibility. Furthermore, a local attention mechanism based on windows and planes is introduced to replace the vanilla global attention mechanism, improving computational efficiency by approximately 25%–40%. The developed method is applied to the reconstruction of several 3D turbulent flow fields both with and without objects. The results show that the diffusion transformer-based method in this paper exhibits high accuracy in flow field reconstruction for all numerical experiments compared to other methods such as U-Net and generative adversarial network-based approaches and achieves an average structural similarity index measure improvement of 20%, with normalized root mean square error improvements exceeding 50% in some test cases, and due to its lower resource consumption, the method demonstrates tremendous potential for reconstructing complex 3D fluid flows.

This paper reports the measurement and prediction of the three-dimensional flow field in an axial flow inducer operating at a flow coefficient of 0.065 with air as the test medium. The experimental investigations included measurement of the blade static pressure and blade limiting streamline angle, and measurement of the three components of mean velocity, turbulence intensities and turbulence stresses at locations inside the inducer blade passage utilizing a rotating three-sensor hot-wire probe. Analytical investigations were conducted to predict the three-dimensional inviscid flow and to approximately predict the three-dimensional viscid flow by incorporating the dominant viscous terms into the exact equations of motion in rotating coordinate system. Radial velocities are found to be of the same order as axial velocities and total relative velocity distributions indicate a substantial velocity deficiency near the tip at mid-passage. High turbulence intensities and turbulence stresses are concentrated within this core region. Evidence of boundary layer interactions, blade blockage effects, radially inward flows, annulus wall effects and back-flows are all found to exist within the long, narrow passages of the inducer, emphasizing the complex nature of inducer flow which makes accurate prediction of the flow behavior extremely difficult.

The complex three-dimensional flow field in an axial-flow impeller incorporating high-Reynolds-number k-ε turbulence model is studied in this paper. The fully three-dimensional Reynolds averaged Navier-Stokes equations are solved. A computational procedure has been developed for predicting three-dimensional incompressible separated turbulent flows in the impeller. The SIMPLE-like algorithm is used. Convective terms are approximated with higher-order upstream-weighted approximations and a TVD-type MUSCL scheme. Physical covariant velocity components are selected as dependent solving variables. The non-orthogonal boundary-fitted coordinate system and collocated grid arrangement are also employed. Rhie and Chow’s momentum interpolation method is adopted to eliminate the non-physical pressure and velocity oscillations. Periodic boundary condition and moving wall boundary condition are considered to simulate truthfully the turbulent flow field in impeller. Two types of axial-flow impellers are computed. The first one is designed by ordinary method and the other is a improved design that has been considered with eliminating flow separation and viscous vortex in the first design. The computed results show that the fully tree-dimensional turbulent flows computation can efficiently predict three-dimensional separated flows and viscous vortex in axial-flow impeller and vaneless clearance. Using the program, a designer can improve passage geometric design to enhance the performance of the fan.

The gaseous cavity resulting from a hydrodynamic ram (HRAM) event in a fluid-filled tank is composed of entrained ambient gases and vaporized local fluid. However, the relative composition during initial cavity formation requires additional research. By measuring and studying the entrained flow through the projectile penetration orifice, calculations to aide in determining the relative composition of entrained gases and vaporized fluid are achieved. Additionally, qualitative assessments on how orifice mass flow correlates with internal cavity dynamics are possible. To complete the measurement, a technique to capture the time-resolved flow field at projectile impact velocities ranging from 100 to 180 m/s is needed. The developed technique utilizes non-invasive diagnostics to include high-speed digital imagery and a continuous wave laser in conjunction with particle image streak analysis to visualize and measure the entrained flow field.

Numerical modelling of hook and claw-type vacuum pump performance based on cut cell Cartesian method

Numerical study on the performance of a novel three-dimensional stepped wavy flow field in PEMFC

Temporal prediction of three-dimensional spatial fields of ocean temperature, salinity and flow is important for a number of civilian and military applications. For accurate prediction of regional ocean environments, combing an accurate dynamic ocean model with optimized in-situ observations of ocean states provided by a network of marine vehicles (such as unmanned surface vehicles, autonomous underwater vehicles, and underwater gliders) is an important approach. To realize fast and accurate three-dimensional spatial prediction of regional ocean environments via ocean models and fast optimization of ocean observation strategies of marine vehicles guided by ocean models, this paper proposes a data driven dynamic model for temporal prediction of three-dimensional regional ocean environments. The proposed model is based on the deep learning method, and is developed based on the Convolutional-LSTM (long short-term memory) network. The feature of the proposed model is that the correlation of temperature, salinity and flow is considered and implemented in the neural network, with which the joint prediction of three-dimensional ocean temperature, salinity and flow fields is achieved. Data set form a numerical ocean model is used to conduct the training of the model and the results demonstrate that the proposed model could provide more accurate prediction than implementing prediction of single ocean temperature, salinity or flow field. The proposed model could be integrated with marine vehicles to form an accurate, high-resolution three-dimensional regional ocean prediction and fast-response adaptive sensing system.

The present paper is the second part of a two-part paper focused on the design and the analysis of an optimized rotor blade for a geared open rotor engine. This part is focused on the experimental investigation of the three-dimensional unsteady flow field at the exit plane of a rotor row installed in a large scale single-stage low speed research turbine. The investigation is aimed at in depth characterizing the wake-boundary layer and the vortex-vortex interaction processes induced by the rotor-stator relative motion. Measurements have been carried out at a typical aeroengine cruise condition Reynolds number. The rotor blade aerodynamic loadings at different blade spans have been measured. A five-hole probe has been used to assess the row efficiency and detailed hot-wire phase-locked ensemble-averaged data have been analyzed to characterize the three-dimensional time-dependent flow field at the rotor exit plane. Results clearly highlight a significant distortion of the rotor blade wake and tip vortex during the migration of the high turbulence regions (wake and secondary flows) associated with the upstream stator. The unsteady interaction between the stator secondary flows and the rotor passage vortex provokes a time dependent movement of the low momentum area at the hub surface, sensibly modifying the penetration of the rotor secondary flows in an incoming stator wake passage period. The comparison of deterministic and random velocity fluctuations also allows the distinction between the structures generated by the stator and those due to the rotor.

For a strictly inviscid barotropic flow with conservative body forces, the Helmholtz vorticity theorem shows that material or Lagrangian surfaces which are vortex surfaces at time t = 0 remain so for t > 0. In this study, a systematic methodology is developed for constructing smooth scalar fields φ(x, y, z, t = 0) for Taylor–Green and Kida–Pelz velocity fields, which, at t = 0, satisfy ω·∇φ = 0. We refer to such fields as vortex-surface fields. Then, for some constant C, iso-surfaces φ = C define vortex surfaces. It is shown that, given the vorticity, our definition of a vortex-surface field admits non-uniqueness, and this is presently resolved numerically using an optimization approach. Additionally, relations between vortex-surface fields and the classical Clebsch representation are discussed for flows with zero helicity. Equations describing the evolution of vortex-surface fields are then obtained for both inviscid and viscous incompressible flows. Both uniqueness and the distinction separating the evolution of vortex-surface fields and Lagrangian fields are discussed. By tracking φ as a Lagrangian field in slightly viscous flows, we show that the well-defined evolution of Lagrangian surfaces that are initially vortex surfaces can be a good approximation to vortex surfaces at later times prior to vortex reconnection. In the evolution of such Lagrangian fields, we observe that initially blob-like vortex surfaces are progressively stretched to sheet-like shapes so that neighbouring portions approach each other, with subsequent rolling up of structures near the interface, which reveals more information on dynamics than the iso-surfaces of vorticity magnitude. The non-local geometry in the evolution is quantified by two differential geometry properties. Rolled-up local shapes are found in the Lagrangian structures that were initially vortex surfaces close to the time of vortex reconnection. It is hypothesized that this is related to the formation of the very high vorticity regions.

Nonlinear modes of the three-dimensional flow field around a cylinder were extracted by distributed learning on Fugaku. Mode decomposition is an approach used to decompose flow fields into physically important flow structures known as modes. In this study, convolutional neural network-based mode decomposition was applied to the three-dimensional flow field. However, because this process is costly in terms of calculation and memory usage for even a small flow field problem, the enormous computational and memory resources of the supercomputer Fugaku were employed. A hybrid parallelism method combining the distribution of network structure (model parallelism) and the input data (data parallelism) using up to 10,500 nodes on Fugaku was employed for learning. Further, we constructed a reduced-order model to predict the time evolution of latent vector, using the long short-term memory networks. Finally, we compared the reproduced flow field of the model with that of the original full-order model. In addition, we evaluated the execution performance of the learning process. Using a single core memory group, the whole learning process indicates a value of 129.50 GFLOPS being achieved, 7.57% of the single-precision floating-point arithmetic peak performance. Notably, the convolution calculation for backward-propagation achieved 1103.09 GFLOPS, which is 65.39% of the peak. Furthermore, with the weak scaling test, the whole learning process indicates 72.9% with 25,250 nodes (1,212,000 cores) relative to 750 nodes, the sustained performance is 7.8 PFLOPS. In particular, the convolution calculation for backward-propagation indicates a result of 113 PFLOPS (66.2% of the peak performance).

Compact axial compression systems are of interest to the domestic appliance industry. The associated low Reynolds number leads to high losses compared to large-scale compressors due to a transitional flow field with large regions of separation. This paper investigates how Reynolds number variations affect the three-dimensional and unsteady flow field in a compact compressor both pre-stall and in stall. An experimental study has been conducted using a scaled-up singlestage axial compressor across a Reynolds number range of 104 to 105. Steady and unsteady casing static pressure measurements, along with rotor upstream and downstream unsteady velocity measurements, have been used to observe the rotor flow field. As the Reynolds number is reduced below a critical value, 60,000 in the case of the compressor studied, the pressure rise coefficient of the compressor decreases. The exact value of the critical Reynolds number is expected to vary with the compressor geometry. This fall off in performance corresponds to an increase in the compressor rotor secondary flows. Prior to stall, a broadband hump at around 50% of the blade passing frequency is present in the near-field casing static pressure spectra. At Reynolds numbers below the critical value, multiple equally spaced peaks also appear around the peak of the broadband hump. The spacing of these peaks has been found to be exactly equal to the measured stall cell speed once rotating stall is established. When operating in stall, the stall cell is found to increase in size and slow down as Reynolds number decreases. The measured spectra and observed flow structures show that disturbances exist prior to stall at frequencies consistent with the frequencies within stall. The size and shape of the stall cells that form are related to the extent of the three-dimensional flow field present prior to stall. Below a critical value, all of these flow features are highly sensitive to Reynolds number.

Three-dimensional flow field reconstruction in the wake of a confined square cylinder using planar PIV data