Unsteady Flow Field Research Articles

An improved mode time coefficient for dynamic mode decomposition

Dynamic mode decomposition (DMD) is widely used for extracting dominant structures of unsteady flow fields. However, the traditional mode time coefficient of DMD is assumed to change exponentially over the time. Consequently, it cannot deal with the unstable flow fields whose modes present nonexponential evolution regularities. Also, the inaccurate mode time coefficient might cause an unreasonable rank of decomposed modes, leading to the dominant modes to be ignored. To overcome these shortcomings, an improved mode time coefficient based on the Moore–Penrose pseudoinverse is proposed for the DMD, and a new integrated parameter based on the improved mode time coefficient is defined to rank the decomposed modes. The DMD with the improved mode time coefficient (abbreviated as DMD-TC) is expected to accurately describe the temporal evolutions of modes in complex forms for unstable systems and results in a more reasonable rank for the modes. To validate the DMD-TC, two complex analytical functions (a continuous case and an intermittent case) and two typical unstable flows (the flow around a cylinder and the dynamic stall of a pitching airfoil) are investigated. The results indicate that the DMD-TC can accurately describe temporal evolutions of modes with complex nonlinear regularities, including exponential, logarithmic, linear, gradually intermittent, transiently intermittent, and other complex regularities. Also, due to the improved mode time coefficient, the DMD-TC can provide a more reasonable rank for unstable modes. These improvements help to identify instantaneous dominant dynamic modes (even with minor initial amplitudes) of real unstable flow fields and accurately describe their temporal evolutions.

Numerical investigation of the dynamic stall reduction on the UAS-S45 aerofoil using the optimised aerofoil method

AbstractThis paper investigates the effect of the optimised morphing leading edge (MLE) and the morphing trailing edge (MTE) on dynamic stall vortices (DSV) for a pitching aerofoil through numerical simulations. In the first stage of the methodology, the optimisation of the UAS-S45 aerofoil was performed using a morphing optimisation framework. The mathematical model used Bezier-Parsec parametrisation, and the particle swarm optimisation algorithm was coupled with a pattern search with the aim of designing an aerodynamically efficient UAS-45 aerofoil. The $\gamma - R{e_\theta }$ transition turbulence model was firstly applied to predict the laminar to turbulent flow transition. The morphing aerofoil increased the overall aerodynamic performances while delaying boundary layer separation. Secondly, the unsteady analysis of the UAS-S45 aerofoil and its morphing configurations was carried out and the unsteady flow field and aerodynamic forces were analysed at the Reynolds number of 2.4 × 106 and five different reduced frequencies of k = 0.05, 0.08, 1.2, 1.6 and 2.0. The lift ( ${C_L})$ , drag ( ${C_D})$ and moment ( ${C_M})\;$ coefficients variations with the angle-of-attack of the reference and morphing aerofoils were compared. It was found that a higher reduced frequencies of 1.2 to 2 stabilised the leading-edge vortex that provided its lift variation in the dynamic stall phase. The maximum lift $\left( {{C_{L,max}}} \right)$ and drag $\left( {{C_{D,max}}} \right)\;$ coefficients and the stall angles of attack are evaluated for all studied reduced frequencies. The numerical results have shown that the new radius of curvature of the MLE aerofoil can minimise the streamwise adverse pressure gradient and prevent significant flow separation and suppress the formation of the DSV. Furthermore, it was shown that the morphing aerofoil delayed the stall angle-of-attack by 14.26% with respect to the reference aerofoil, and that the ${C_{L,max}}\;$ of the aerofoil increased from 2.49 to 3.04. However, while the MTE aerofoil was found to increase the overall lift coefficient and the ${C_{L,max}}$ , it did not control the dynamic stall. Vorticity behaviour during DSV generation and detachment has shown that the MTE can change the vortices’ evolution and increase vorticity flux from the leading-edge shear layer, thus increasing DSV circulation. The conclusion that can be drawn from this study is that the fixed drooped morphing leading edge aerofoils have the potential to control the dynamic stall. These findings contribute to a better understanding of the flow analysis of morphing aerofoils in an unsteady flow.

Flow field characteristics analysis of vortex-induced vibration of bridge tower based on dynamic mode decomposition method

As a high-rise structure, the tower of a suspension bridge has low stiffness due to the lack of cable system constraints when it is self-supporting. Wind-induced vibration is one of the key factors in design and construction. In this paper, the wind tunnel test of the bridge tower aeroelastic model is carried out in two different flow fields, and the wind vibration response under a self-supporting state is systematically studied. Meanwhile, numerical simulation of the unsteady flow field around the tower section is carried out, and the dynamic modal decomposition (DMD) method is used to study the modal frequency of the flow field, the surface pressure of the section, flow field reconstruction error, and the stability of the flow field around tower section is discussed. The results show that in the self-supporting state, the displacement of the tower top presents a quadratic curve relationship with the wind speed, and no galloping phenomenon occurs under the test wind speed. However, in the uniform flow, when the wind attack angle is 90°, the bridge tower has an obvious vortex-induced vibration (VIV) phenomenon. After decomposing the flow field by the DMD method, it is found that there is strong aerodynamic interference between the double rectangular column sections, the first seven orders of modal energy play a major role in the flow field, and when the main modal energy accounts for more than 90%, the reconstruction can realize the accurate restoration of the information such as the surface pressure. For the complex flow field structure, it shows that the method can more accurately identify the coherent structure and background part in the unsteady flow field. This paper provides an idea for future research on the characteristics of the flow field around complex sections and helps to further improve the understanding of the VIV mechanism.

Efficient numerical prediction of blade forced response under inlet distortion

The compressor blade in an aircraft gas turbine engine may suffer from forced vibration problems under the unsteady aerodynamic force due to inlet distortion. This paper develops an efficient numerical method combination to predict the forced response. The computational fluid dynamics (CFD) method is combined with the Fourier transform method to simulate the unsteady flow field under inlet distortion. Then, the forced response of the blade is obtained by the frequency-domain method based on the modal force. The results show that the developed method combination improves the unsteady flow calculation efficiency by 20 times and the response calculation efficiency by 48 times at the cost of less than 5% accuracy compared with the traditional method combination, including the unsteady flow field calculation method based on the three-row full-annulus model and the transient analysis method for calculating the forced response. Finally, the developed method combination is used to analyze the forced response of the blade under different inlet total pressure distributions. The results indicate that the forced response can be effectively decreased by decreasing the total pressure difference and increasing the sector angle difference between the high-pressure and low-pressure areas.

Space-time adaptive model order reduction utilizing local low-dimensionality of flow field

The cost of unsteady flow simulations, such as large eddy simulations, has been increasing because of the large number of mesh cells and the use of high-order numerical schemes. In contrast, recent data-driven reduced-order models (ROMs) predict a flow field quickly; however, their application is often limited to relatively simple flow problems. In this study, we investigate space-time adaptive model order reduction for unsteady flow simulation, where full-order Navier-Stokes equations and a proper orthogonal decomposition (POD)-based reduced-order model are adaptively switched in a block-by-block manner on a multi-block Cartesian mesh. The full-order model (FOM) is switched to the ROM when POD modes effectively represent the unsteady flow field in each block. Owing to the local low-dimensionality of a flow field, the degree of freedom of fluid flow in each block can be smaller than that of the entire flow field; hence, the flow field is effectively represented by a small number of POD modes. First, the hybrid FOM/ROM approach is tested with a low-Reynolds-number flow around a circular cylinder, where the reduction in computational time and the accuracy of the simulated flow field are evaluated. We then consider a flow around a circular cylinder with a Reynolds number of 1000, where the flow field is reduced except for the highly unsteady wake. The potential computational advantage of this method is demonstrated by load balancing on a distributed memory computer. In addition, we utilize bred vector dimensions to quantify the degree of freedom of the flow field in each block, which is closely related to whether ROMs effectively reduce the flow field.

A Fourier-based methodology without numerical diffusion for conducting dye simulations and particle residence time calculations

Dye experimentation is a widely used method in experimental fluid mechanics for flow analysis or for the study of the transport of particles within a fluid. This technique is particularly useful in biomedical diagnostic applications ranging from hemodynamic analysis of cardiovascular systems to ocular circulation. However, simulating dyes governed by convection-diffusion partial differential equations (PDEs) can also be a useful post-processing analysis approach for computational fluid dynamics (CFD) applications. Such simulations can be used to identify the relative significance of different spatial subregions in particular time intervals of interest in an unsteady flow field. Additionally, dye evolution is closely related to non-discrete particle residence time (PRT) calculations that are governed by similar PDEs. This contribution introduces a pseudo-spectral method based on Fourier continuation (FC) for conducting dye simulations and non-discrete particle residence time calculations without numerical diffusion errors. Convergence and error analyses are performed with both manufactured and analytical solutions. The methodology is applied to three distinct physical/physiological cases: 1) flow over a two-dimensional (2D) cavity; 2) pulsatile flow in a simplified partially-grafted aortic dissection model; and 3) non-Newtonian blood flow in a Fontan graft. Although velocity data is provided in this work by numerical simulation, the proposed approach can also be applied to velocity data collected through experimental techniques such as from particle image velocimetry.

Nonlinear mode decomposition via physics-assimilated convolutional autoencoder for unsteady flows over an airfoil

I have developed a physics-assimilated convolutional autoencoder (CAE) neural network, namely, PhyAENet, to carry out nonlinear mode decomposition of the unsteady flow field around a National Advisory Committee for Aeronautics 4412 airfoil near stall conditions. The flow field snapshots are mapped into latent modes by the encoder part of the well-trained CAE, which are used for dynamic mode decomposition (DMD) analysis. The computed DMD modes are split into modes covering different frequency ranges. These high and low-frequency DMD modes are used to form reconstructed encoded sequences, which are then mapped back to generate the nonlinear decomposed spatiotemporal modes by the decoder of the CAE. As such, physics is assimilated into the neural network by incorporating the frequencies of the DMD modes into the latent modes in the latent space. The proposed PhyAENet is capable of extracting the dominant features of the flow fields, accounting for the nonlinearity of the underlying dynamics. Furthermore, the extracted nonlinear modes are evolving with time and physically interpretable. It is revealed that the nonlinear modes can be well represented when using more DMD modes for reconstruction of the encoded sequences. The energy spectrum of the nonlinear modes are obtained by ranking the Frobenius norm of the mode vector.

Forecasting three-dimensional unsteady multi-phase flow fields in the coal-supercritical water fluidized bed reactor via graph neural networks

The study of three-dimensional unsteady multi-phase flows inside the coal-supercritical water fluidized bed (SCWFB) reactor coupled with fluid dynamics, heat transfer and chemical reactions usually relies on time-consuming numerical simulation. Recently, to provide quick spatio-temporal estimation of the SCWFB reactor, the data-driven deep learning techniques have been adopted to build a digital yet fast reactor forecasting model. However, due to the irregular 3D geometry, it usually uses unstructured meshes to discrete the domain of reactor and builds the corresponding simulation model, which poses difficulties for the convolutional neural networks based deep learning models. Hence, this article develops a 3D unstructured spatio-temporal forecasting model, named GraphReactorNet, via graph neural networks for learning the dynamics under multi-phase flow fields inside the SCWFB reactor. It utilizes an efficient strategy to tackle large-scale 3D transient flow graphs and proposes an effective unstructured spatio-temporal learning module to extract the underlying flow dynamics. This model is trained on data collected from the transient simulator at different conditions. Numerical experiments reveal that in comparison to the counterparts, the GraphReactorNet not only achieves accurate multi-step-ahead predictions of the multi-phase flow fields at unseen conditions, but also performs thousands of times faster than the numerical simulator.

Numerical analysis of the internal biased flow mechanism of the siphon outlet pipe under the action of axial flow pump

One of the often employed flow structures in vertical pumping stations is the siphon outlet pipe. It has a complicated geometric structure and internal flow field, which directly affects how effectively, safely, and steadily pumping stations operate. The entire flow conduit of the vertical axial flow pump device was adopted as the study object in order to elucidate the mechanism of the internal biased flow of the siphon outlet pipe caused by the axial flow pump under different flow conditions, and the three-dimensional unsteady flow field of the vertical axial flow pump device was numerically solved using the numerical simulation technique. Physical model tests were used to confirm the results of the numerical simulation. The findings demonstrate that there is a horizontal bias in the flow of the inlet surface and outlet surface of the elbow pipe of the siphon outlet pipe, and that when the flow rate rises, the degree of the horizontal bias in the flow gradually diminishes, and the ratio of biased flow gradually decreases. The flow in hump segment presents up-and-down flow, and when the flow rate increases, the ratios of biased flow first rises before falling. The major causes of the production of biased flow in the outlet pipe are residual velocity circulation at the guide vane's outlet, wall constraint at the elbow pipe, and flow inertia; Under various flow conditions, the morphologies of the vortex structures in the outlet pipe vary; the characteristics of the energy conversion of each part of the pump device are disclosed, with the inlet pipe having the lowest proportion of energy conversion. Under the optimal flow condition, the elbow-inlet pipe's proportion of energy conversion is only around 1.04%, and the proportions of the guide vane, 60° elbow pipe, and siphon outlet pipe's energy conversion are significant and fluctuate with time. The proportion of energy conversion in the elbow-inlet pipe and siphon outlet pipe steadily increases as flow rate rises, but the proportion in the guide vane and 60° elbow pipe drops initially before increasing.

Study of Unsteady Surface Flowfields on and Around Turrets with Different Protrusions

Wind-tunnel experiments were conducted to measure the unsteady surface pressure field on and around a hemisphere-on-cylinder turret of varying protrusion in subsonic flow. These measurements were obtained using fast-response pressure-sensitive paint coupled with pressure transducers. The surface pressure field data resulting from Mach 0.5 flow () over a partially submerged hemisphere, a hemisphere, and a hemisphere on a cylinder were analyzed using proper orthogonal decomposition modal analysis, as well as a variant of this approach referred to as joint proper orthogonal decomposition. The results showed that decreased turret protrusion into the freestream flow reduced the prevalence of antisymmetric surface pressure field fluctuations caused by antisymmetrical vortex shedding. The frequency associated with this fluctuation was found to be around . When a partial hemispherical turret geometry was used, it was shown that the antisymmetric mode was greatly suppressed; and the wake was dominated by a symmetric mode with a broadband spectral peak at a higher frequency of . This suggests that there is a “mode switching” as the protrusion is changed from the hemisphere to the partial hemisphere configuration. An optical flow approach was used to find the convective velocity field in the wake, from which topological flow features could be identified. The size of the wake separation region was found to grow smaller with the decreased protrusion while keeping a similar shape.

Multilevel method for predicting flow fields in radial turbines based on sparsity-promoting dynamic mode decomposition

PurposeThe purpose of this study is to propose a fast method for predicting flow fields with periodic behavior with verification in the context of a radial turbine to meet the urgent requirement to effectively capture the unsteady flow characteristics in turbomachinery. Aiming at meeting the urgent requirement to effectively capture the unsteady flow characteristics in turbomachinery, a fast method for predicting flow fields with periodic behavior is proposed here, with verification in the context of a radial turbine (RT).Design/methodology/approachSparsity-promoting dynamic mode decomposition is used to determine the dominant coherent structures of the unsteady flow for mode selection, and for flow-field prediction, the characteristic parameters including amplitude and frequency are predicted using one-dimensional Gaussian fitting with flow rate and two-dimensional triangulation-based cubic interpolation with both flow rate and rotation speed. The flow field can be rebuilt using the predicted characteristic parameters and the chosen model.FindingsUnder single flow-rate variation conditions, the turbine flow field can be recovered using the first seven modes and fitted amplitude modulus and frequency with less than 5% error in the pressure field and less than 9.7% error in the velocity field. For the operating conditions with concurrent flow-rate and rotation-speed fluctuations, the relative error in the anticipated pressure field is likewise within an acceptable range. Compared to traditional numerical simulations, the method requires a lot less time while maintaining the accuracy of the prediction.Research limitations/implicationsIt would be challenging and interesting work to extend the current method to nonlinear problems.Practical implicationsThe method presented herein provides an effective solution for the fast prediction of unsteady flow fields in the design of turbomachinery.Originality/valueA flow prediction method based on sparsity-promoting dynamic mode decomposition was proposed and applied into a RT to predict the flow field under various operating conditions (both rotation speed and flow rate change) with reasonable prediction accuracy. Compared with numerical calculations or experiments, the proposed method can greatly reduce time and resource consumption for flow field visualization at design stage. Most of the physics information of the unsteady flow was maintained by reconstructing the flow modes in the prediction method, which may contribute to a deeper understanding of physical mechanisms.

A hybrid deep learning framework for unsteady periodic flow field reconstruction based on frequency and residual learning

Reconstructing a complete flow field from limited sensor measurement is quite essential for state evaluation, optimization, monitoring, and control of the flow system. Unsteady periodic flow, as a widespread phenomenon in science and engineering, attracts in-depth research over decades. Deep learning has been employed in flow field reconstruction, whereas the accurate estimation for the unsteady flow field with strong nonlinearity is still difficult. To address this problem, we propose a hybrid deep learning framework that incorporates frequency and residual learning to accurately reconstruct an unsteady periodic flow field from limited sensor measurement. First, to extract the frequency features, the historical flow field data is decomposed into different modes with different frequencies named frequency modes via fast Fourier transform (FFT). Next, we construct a hybrid deep neural network framework consisting of an inverse fast Fourier transform (IFFT) block and a residual block. The IFFT block maps sensor measurements to frequency mode temporal coefficients, which are multiplied with frequency modes to recover an IFFT field. Meanwhile, the residual block adaptively generates a residual field to complement the information lost by the IFFT field. Finally, the IFFT field and residual field are combined to produce the final reconstructed flow field. We conduct numerical experiments on the unsteady periodic flow around a cylinder and transonic flow around a NACA0012 airfoil to demonstrate the feasibility and high accuracy of our proposed method. Compared to the widely used proper orthogonal decomposition (POD) and shallow decoder (SD) methods, our approach achieves at least 83.9% and 72.2% reduction in mean absolute error, respectively.

Manipulating near-wall flow instability and transport characteristics by the airfoil probe: Investigation on a transonic compressor cascade

The flow field exhibits complex features, such as shock waves, wakes, and end wall vortices in a transonic cascade. Installation of airfoil probes exacerbates the multi-scale and unsteady behavior of the internal passage flow. Apart from inducing measurement errors, it also generates extra flow loss inevitably and further affects the measuring accuracy. This paper investigates the impact of airfoil probes on a transonic compressor cascade's unsteady behavior and transport characteristics. Using high-fidelity numerical simulations, the influence of pipe layouts on the flow field of instrumented blades is visualized, revealing highly radial asymmetry. Loss analysis uncovers entropy transport induced by the streamwise vortices, primarily manifested by large-scale angular deformation at the outlet. The vortex structures in the wake region are dominated by momentum transport, displaying regional evolution and momentary equilibrium. The vortex expansion plays a leading role in the global vortex transport process, which is strengthened by the presence of the probes. Spatiotemporal analysis of the unsteady flow field can reveal some features overlooked by conventional fluid mechanics analysis. Using proper orthogonal decomposition, wake vortex pairs' high-frequency oscillations and shedding behaviors are captured in adjacent modes for the first time. The proposed approach can provide a theoretical basis for in-depth investigations of instrumented blade flow fields at the transonic regime. Furthermore, corresponding research can promote the refinement of instrument design by enabling experimentalists to understand the effects of intrusive instruments on transonic flow fields.

Information-Based Sensor Placement for Data-Driven Estimation of Unsteady Flows

Estimation of unsteady flowfields around flight vehicles may improve flow interactions and lead to enhanced vehicle performance. Although flowfield representations can be very high-dimensional, their dynamics can sometimes have low-order representations that may be estimated using a few, appropriately placed measurements. This paper presents a sensor-selection framework for the intended application of data-driven, flowfield estimation. This framework combines data-driven modeling, steady-state Kalman filter design, and sparse, sequential sensor selection. This paper also uses the sensor selection framework to design sensor arrays that can perform well for a collection of operating conditions. Flow estimation results on numerical data show that the proposed framework produces arrays that are highly effective at flowfield estimation for the flow behind and an airfoil at a high angle of attack using embedded pressure sensors. Analysis of the flowfields reveals that paths of impinging stagnation points along the airfoil’s surface during a shedding period of the flow are highly informative locations for placement of pressure sensors.

Effect of Aspect Ratio on Swept-Wing Dynamic Stall

The role of aspect ratio on the dynamic stall process of swept finite wings is investigated using high-fidelity implicit large-eddy simulations. Two aspect ratios ( and 8) are explored for a 30 deg swept wing (NACA 0012) pitching sinusoidally from an initial incidence of 4 deg to a maximum angle of attack of 22 deg with a reduced frequency of over one pitching cycle. The flow is simulated at a chord Reynolds number of and a freestream Mach number of . The unsteady three-dimensional flowfield for the higher-aspect-ratio wing showed similarity with the lower-aspect-ratio wing through the initial flow separation at the leading edge. Motion-induced effects promoted earlier initiation of the unsteady vortical structures at higher aspect ratios. The vortex tube at the larger span underwent significant distortion, which contrasted with the vortex observed at the lower span. The vortical structure eventually interacted with the trailing-edge vortex, which was not observed at . Examination of the unsteady loads detailed a larger lift slope, mean values, peak values, and earlier stall as the aspect ratio increased. Analysis of the aerodynamic pitch damping suggests the wing is less susceptible to local torsional instabilities than the wing.

Numerical Investigation of a Pulsed Jet Actuator Having Non-Negligible Switching Time

An internal unsteady compressible flowfield of a pulsed jet actuator (PJA) is simulated by unsteady Reynolds-averaged Navier–Stokes (URANS) and large-eddy simulation (LES) frameworks. The PJA’s feedback loops are short enough to have non-negligible jet switching time compared to the oscillation period. The results show that within a range of inlet pressure (which is the only control parameter) where the jet goes from subsonic to supersonic regime, the oscillation frequencies and the exit velocity waveform predicted by LES are in better agreement with the measured data than those predicted by URANS. Although URANS is able to capture the flowfield inside the feedback loops, it fails to predict the exit jet dynamics, unlike LES. This indicates the importance of a proper resolution of turbulence in the interaction region where jet switching occurs. Using LES data, it is found that the total jet switching time remains constant as the inlet pressure changes. It is also found that only the part of the jet switching period that ends at the first moment when the jet attaches to the opposite wall is involved in the oscillation period. Therefore, a new lumped model is proposed to estimate the oscillation frequency, which also explains the trend observed for the low inlet pressure values.

Numerical study of the effects of ventilation rates on supercavity dynamics and acoustic characteristics

This paper presents a numerical simulation investigation of the hydrodynamic and acoustic characteristics of ventilated supercavities that operate at various ventilation rates. The large eddy simulation (LES) and Ffowcs Williams–Hawkings (FW-H) methods are used to solve the unsteady flow field and noise. The results show that the ventilation rate plays an important role in cavity closure forms and can improve hydrodynamic performance. There is a transition from re-entrant flow closure to a stable double-vortex tube closure form at the supercavity tail as the ventilation rate increases. Meanwhile, under the condition of a high ventilation rate, the re-entrant flow region in the cavity gradually shrinks and hairpin vortices appear, the body length of the cavity increases,and the unsteadiness at the supercavity tail is weakened. However, the turbulence intensity and integral scale both increase with the ventilation rate. Moreover, it is found that the noise is closely related to supercavity closure form. Ventilated supercavities with closure forms of double-vortex tubes have better noise performance. Interestingly, as the ventilation rate increases, the total sound pressure levels are improved. The wavenumber-frequency spectra of supercavity turbulent pulsating pressures under studied ventilation rates are similar, but there are some differences in some local areas.

Multi-wave effects on stability and performance in rotating detonation combustors

Recently, with the development of detonation-based propulsion systems, scholars have begun to study how to perform mode control on the rotating detonation combustor (RDC). It is important to figure out the influence of operation mode transition on the RDC. Actually, the essential of different modes is the different multi-wave structures. In this study, two-dimensional numerical simulations of the RDC are conducted to study the multi-wave effect on the stability and performance of the RDC. A uniform inlet condition is adopted in simulations to eliminate the impact of discrepancy mass flow rates, and a mode-locked ignition method is used to induce RDC flow fields with different detonation wave numbers. It is found that the flow field stability and outlet uniformity are improved with increasing detonation counts, and the energy proportion in the flow field is little affected by the multi-wave structure. However, the increase in detonation number will cause a reduction of the mass-averaged total pressure ratio at the exit. Underlying relationship between the unsteady flow field and the total pressure gain is discussed. The total pressure gain is directly linked with the non-uniformity of the circumferential flow field. Then, by utilizing particle trace, the envelope of the thermodynamic cycle is illustrated and the pseudo-thermal efficiency of each case is given. The result implies that the wave number has hardly effect on the thermal efficiency of the combustion chamber. By summarizing the perimeter, axial length, and wave number in the combustor, parameter ξ is carried out and its effects on the uniformity and total pressure ratio in the RDC are concluded.

Analysis of pressure pulsation and energy characteristics of guide vane for axial flow pump based on Hilbert-Huang transform considering impeller-guide vane interaction.

In order to explore the characteristics of pressure pulsation signals and energy distribution of water flow at the guide vane considering impeller-guide vane interaction. The numerical simulation of the vertical axial flow pump device's steady and unsteady three-dimensional flow fields was carried out. The Hilbert-Huang method was used to conduct empirical mode decomposition decomposition and Hilbert spectrum analysis of pressure pulsation signal at each monitoring point in the inlet and outlet regions of the guide vane. The results show: Under the condition of 0.3Qbep, the internal pressure of the guide vane is obviously affected by the impeller, and there are large block-shaped vortex structures in the guide vane. Under the operating conditions of 1.0Qbep and 1.2Qbep, the size of the pressure area in the guide vane is basically not affected by the impeller, and the vortex structures in the guide vane are concentrated near the outlet of the guide vanes, and there are long strip-shaped vortex structures at the edge of the guide vane. The size and number of vortex structures decrease with the increase in flow rate. The pressure pulsation signal at the inlet of the guide vane is affected by the rotation of the impeller and exhibits good periodicity, with the main frequency centered around 146 Hz, and the energy ratio of the main frequency is up to 97.7%. There are low-frequency signals below 100 Hz and high-frequency signals fluctuating around 146 Hz in all three flow conditions. When the flow rate increases, the fluctuation amplitude of the high-frequency signal increases. The flow rate has a significant impact on the water flow at the outlet of the guide vane. At 0.3Qbep, its frequency is distributed in the range of 0-500 Hz, mainly concentrated in the area below 400 Hz. At 1.0Qbep, the frequency of pressure pulsation is distributed below 250 Hz after the guiding function of the guide vane. At 1.2Qbep, the water flow is mainly controlled by the rotation of the impeller, and after the energy recovery of the guide vane, its main frequency is still concentrated around 150 Hz, which is 337.2% and 268.5% of 0.3Qbep and 1.0Qbep. Under the working condition of 0.3Qbep, the proportion of intrinsic mode function energy corresponding to the dominant frequency at the center of the guide vane inlet is as high as 95.9%, and the proportion of intrinsic mode function energy corresponding to the dominant frequency at the shroud side and hub side of the guide vane is rather low. If the flow rate rises from 0.3Qbep to 1.2Qbep, the proportion of intrinsic mode function energy increases by more than 42%. Under the working conditions of 0.3Qbep and 1.0Qbep, the main frequency of pressure pulsation signal of water flow at the guide vane outlet is less affected by the impeller and the corresponding energy proportion is low. Under the working condition of 1.2Qbep, the main frequency of pressure pulsation signal is 4 times the rotational frequency and the corresponding energy proportion is higher than 60%.

Comparison of reduced order models based on dynamic mode decomposition and deep learning for predicting chaotic flow in a random arrangement of cylinders

Three reduced order models are evaluated in their capacity to predict the future state of an unsteady chaotic flow field. A spatially fully developed flow generated in a random packing of cylinders at a solid fraction of 0.1 and a nominal Reynolds number of 50 is investigated. For deep learning (DL), convolutional autoencoders are used to reduce the high-dimensional data to lower dimensional latent space representations of size 16, which were then used for training the temporal architectures. To predict the future states, two DL based methods, long short-term memory and temporal convolutional neural networks, are used and compared to the linear dynamic mode decomposition (DMD). The predictions are tested in their capability to predict the spatiotemporal variations of velocity and pressure, flow statistics such as root mean squared values, and the capability to predict fluid forces on the cylinders. Relative errors between 15% and 20% are evident in predicting instantaneous velocities, chiefly resulting from phase differences between predictions and ground truth. The spatial distribution of statistical second moments is predicted to be within a maximum of 5%–10% of the ground truth with mean error in the range of 1%–2%. Using the predicted fields, instantaneous fluid drag force predictions on individual particles exhibit a mean relative error within 20%, time-averaged drag force predictions to within 5%, and total drag force over all particles to within 1% of the ground truth values. It is found that overall, the non-linear DL models are more accurate than the linear DMD algorithm for the prediction of future states.