Unsteady Flow Structures Research Articles

Control of the flow in the near wake of an airfoil at full stall using fixed trailing-edge plates

This work aims to control the unsteady flow structure of a NACA0012 under full stall by limiting the vortex roll-up from its trailing edge. In this regard, plates with varying lengths at zero incidences were attached at the trailing edge of the airfoil at an angle of attack of α = 16° and low Reynolds number of Rec = 2.0 × 104. Under these conditions, the flow separates near the leading edge and rolls up (without reattachment) into the wake with a subsequent supercritical mode vortex shedding corresponding to the full stall condition. Planar PIV measurements were performed in a closed-loop water channel to analyze the effect of plate length on the wake characteristics of the airfoil. Turbulent flow structures of baseline airfoil and airfoil with various plate lengths (l /c = 0.1, 0.2, 0.3) were revealed and elaborated with time-averaged turbulent statistics, two-point correlations, spectral analysis, and instantaneous vorticity contours. According to the results, vortex roll-up from the trailing edge and corresponding turbulent structures were partially suppressed by the use of plates with l/c = 0.2 and l/c = 0.3 by elongating the vortex formation length. Besides, two-point correlations of fluctuating velocity components revealed that the use of trailing edge plates of l/c > 0.1 is effective in decreasing the size and magnitude of turbulent structures. Consequently, the turbulent fluctuations were found to be reduced, and the vortex shedding frequency was attenuated in the near wake of the airfoil.

Experimental Study on Time Evolution of Shock Wave and Turbulent Boundary Layer Interactions

In this paper, a test system based on the Nano-tracer Planar Laser Scattering (NPLS) technique for studying time evolution of unsteady flow structures was finished. Based on this system, the experimental study on the interactions between the incident shock wave and the turbulent boundary layer of the incoming wall was performed. The experiments were performed in a Mach 3.4 supersonic low-noise wind tunnel at the unit Reynolds number of 6.30 × 106/m-1. For the first time, five frames of temporal-correlated fine structure images of transient flow field with shock wave and the turbulent boundary layer interactions (SWTBLI) were obtained under the experimental conditions, and the spatiotemporal evolution characteristics of the flow structure were analyzed. At the same time, the flow field characteristics of temporal-correlated images were studied when the density boundary layer thickness of incoming turbulent layer is δ1 = 0.55δ, δ2 = 0.72δ, δ3 = 0.87δ respectively. During the development of vortex structure in the boundary layer from turbulent boundary layer to separation bubble, the oscillation interval distribution law of induced shock wave was summarized, and the group velocity of vortex structure development in the boundary layer and the relationship between boundary layer thickness and physical space size growth law of separation bubble under different incoming turbulent boundary layer thicknesses were obtained. The results also show that with the increase of the incoming boundary layer thickness, the group velocity in the development process of vortex structure in the turbulent boundary layer does not change significantly. As the thickness of the boundary layer entering the separation bubble increases, the overall growth height of the separation bubble also increases.

Analysis of the Pressure Pulsation and Vibration in a Low-Specific-Speed Centrifugal Pump

Abstract Unsteady pressure pulsation and fluid force induced by flow instabilities in the centrifugal pump is an important cause of vibration, which is detrimental to the safe operation of the pump. In this study, we numerically investigated the pressure pulsation and radial force in a low-specific-speed centrifugal pump by using the detached-eddy simulation method. We also performed a vibration displacement experiment on the shaft of the centrifugal pump. The vortex identification method was introduced to clarify the internal correlation between unsteady flow structures with pressure pulsations. The results showed that the pressure pulsations at the impeller outlet were closely associated with the periodic vortex shedding from the blade pressure surface. The rotor–stator interaction between a relatively big trailing vortex core and volute tongue generated larger pressure pulsation and radial force in the pump at a low flow rate. Under a large flow rate, the trailing vortex core was easily broken and dispersed, and this resulted in smaller pressure pulsation and radial force compared with that at a low flow rate. Under the design flow rate, the pressure pulsation intensity and the radial force in the impeller were smaller than that under the off-design flow rate. Compared with the spectra between the radial force on the impeller and radial displacement on the shaft, they both presented higher amplitude at the shaft frequency. The vibration of the pump shaft was closely related to the radial force on the impeller.

Unsteady Flow Interactions Between a High- and Low-Pressure Turbine

Abstract This paper presents the unsteady flow interactions between an engine-representative high-pressure turbine (HPT) and low-pressure turbine (LPT) stage, connected by a turbine center frame (TCF) duct with nonturning struts. The setup was tested at the high-speed two-spool test turbine facility at the Institute for Thermal Turbomachinery and Machine Dynamics at Graz University of Technology and includes relevant purge and turbine rotor tip leakage flows. Due to the complexity of such a test, the unsteady component interactions in an HPT–TCF–LPT module have not received much attention in the past and require additional analysis to determine new approaches for further performance improvements on the system level. The flow downstream of an HPT is highly unsteady and dominated by stator–rotor interactions, which affect the flow behavior through the downstream TCF and LPT. To capture the unsteady flow structures, time-resolved aerodynamic measurements were carried out with a fast-response aerodynamic pressure probe (FRAPP) at three different measurement planes. In this paper, the time-resolved and phase-averaged flow fields with respect to the HPT and LPT trigger are studied. Since the two rotors are uncorrelated, the applied method allows the identification of the flow structures induced by either of them. Upstream of the LPT stage, the HPT flow structures evolving through the TCF duct dominate the flow fields. Downstream of the LPT stage, the flow is affected by both the HPT and the LPT secondary flow structures. The interactions between the various stator rows and the two rotors are detected by means of time-space plots and modal decomposition. To describe the fluctuations induced by both rotors, particularly the rotor–rotor interaction, the rotor synchronic averaging (RSA) is used to analyze the flow field downstream of the LPT. This paper highlights the need to account for the HPT-induced unsteady mechanisms in addition to the LPT flow structures and the interaction of both to arrive at improved LPT designs.

Active control of flow structure and unsteady aerodynamic force of box girder with leading-edge suction and trailing-edge jet

An experimental study was conducted to investigate the control effectiveness and underlying mechanism of the leading-edge suction and trailing-edge jet (LSTJ) for a box girder at a Reynolds number of 2.08×104. Four circular holes were machined in the leading edge and the trailing edge of the box girder to induce steady LSTJ flow. The strength of the LSTJ is described by a dimensionless suction/jet momentum coefficient. Pressure taps around the surface associated were used with a digital sensor array system to acquire the pressure distribution of the test model. The aerodynamic forces, which macroscopically represent the control abilities of the LSTJ, were calculated based on the surface pressure distribution. The pressure measurements indicate that the fluctuating pressure on the surface near the trailing edge was attenuated and the root-mean-square value of the lift, drag, and moment forces reduced with LSTJ control. In addition to the surface pressure measurements, particle image velocimetry (PIV) was used to obtain the flow fields of the box girder model with and without LSTJ control. Both the pressure measurement and PIV results show that a certain value of the suction/jet momentum coefficient can ensure optimum control effectiveness of the LSTJ. Moreover, the LSTJ was found to push the unsteady flow structure further downstream in the model wake. A data-processing method of dynamic mode decomposition was used to illustrate the LSTJ mechanism. The energy and Strouhal number of the main mode of the LSTJ controlled case were found to differ from the uncontrolled case. The topological structure of the main mode extracted from the flow field also showed a significant variation. Linear stability analysis of the wake flow field indicates that the control method of LSTJ changes the region of unstable flow notably. Moreover, the control effectiveness of the LSTJ at various wind angles of attack was confirmed in the present study.

A second-generation URANS model (STRUCT-ε) applied to simplified freight trains

An effective way to increase the volume of cargo transported by freight trains is to increase their operational speed. The complex flow generated by trains moving through air has attracted much attention from researchers aiming to further improve their performance. Unfortunately, wind tunnel tests do not fully represent the complex geometries and realistic flow conditions observed at full scale (wind gusts, atmospheric turbulence and relative motion of the train with respect to the ground). The availability of a reliable numerical model is therefore critical to analyze the influence of these conditions. Steady RANS models, although still in use in both industry and academia, have shown to be unsuitable, while LES solutions still involve an excessive computational cost. In this work a second-generation URANS closure (STRUCT−ε), proposed by Xu (2020) has been applied to the simulation of freight trains. The approach aims at advancing the robustness and applicability of hybrid turbulence models by relying on the efficiency of an extensively validated anisotropic k−ε method, while locally introducing the necessary resolution of complex unsteady flow structures. The proposed model does not leverage any grid dependent parameter, but triggers controlled resolution of turbulence only in regions of poor URANS applicability, while reverting to a URANS solution when rapidly varying structures are not identified. In the case considered in this work, the reduction of computational cost has been reached by increasing the cell size, while maintaining CFL numbers around 1.0. The work has demonstrated the LES-like capabilities of the STRUCT−ε approach on much coarser grids, which allows a reduction of the total computing time by a factor of 5, as an essential enabler for effective aerodynamic design applications, especially aerodynamics optimization, crosswind stability and slipstream studies.

Role of Transient Characteristics in Fish Trajectory Modeling

In this experiment, we analyzed live fish (silver carp) trajectories recorded in an experimental vertical-slot fishway. Combined with a numerical simulation, we demonstrated that randomness shown in fish trajectories might not merely be attributed to the fish’s random choices in its swimming, but could also be a consequence of adaption to the bulk unsteady turbulent flow structures. Simple superposition of a fish trajectory on the time-averaged flow field obtained either by interpolating on discrete point measurements or numerical simulation data is not an ideal method for description of fish movement. How to model the fish paths in transient flow and the necessity of simultaneous recording of the flow field and the fish locomotion are challenging topics. We also discussed the possible integration of currently existing methods to promote the development of fish trajectory modeling.

Hybrid remapping particle field reconstruction method for synthetic aperture particle image velocimetry.

The flow field velocity is an important parameter for completely characterizing the topologies of unsteady coherent flow structures. Synthetic aperture (SA)-based particle image velocimetry (SAPIV) has been used for three-dimensional flow measurements, owing to its wide range of acceptable tracer particle intensities and ability to view partially occluded fields. However, SAPIV typically suffers from poor reconstruction quality for nonuniformly illuminated particle volumes. In this paper, we propose a hybrid remapping particle field reconstruction method for SAPIV in a nonuniformly illuminated fluid flow. Both additive and minimum line-of-sight remapping are used to reconstruct the in-focus particles from the refocused image stacks. The structural similarity between the images projected by the reconstructed particle field and the images captured by the cameras are used to determine the reconstruction quality. This method was verified by both synthetic simulation and an experimental implementation. The performance of the proposed technique was compared with existing methods. The proposed method has the best reconstruction quality and computational speed among the considered methods.

The aerodynamic performance of passive wing pitch in hovering flight

Insect wings can passively maintain a high angle of attack during each flapping stroke without the aid of the active pitching motion due to the torsional flexibility of the wing basal region. However, there is no clear understanding of how torsional wing flexibility should be designed for achieving optimal aerodynamic performance. In this work, a computational study was conducted to investigate the passive pitching mechanism of a fruit fly wing in hovering flight using a torsional spring model. The torsional wing stiffness was characterized by the Cauchy number, a ratio between the aerodynamic force and the structural elastic force. Different flapping patterns including zero-deviation, figure-8, and oval-shaped flapping trajectories were evaluated along a horizontal stroke plane. The aerodynamic forces and associated unsteady flow structures were simulated using an in-house immersed-boundary-method based computational fluid dynamics solver. A parametric study on the Cauchy number was performed with a Reynolds number of 300. According to the analysis of the aerodynamic performance, we found that a balance of high lift and high lift-to-power ratio can be achieved in a particular range of Cauchy numbers (0.15–0.30) for all different flapping trajectories. This range is consistent with the Cauchy number calculated based on the experimental measurements of a fruit fly in the literature. In addition, 3D wake structures generated by the passive flapping wings were analyzed in detail. The findings of this work could provide important implications for designing more efficient flapping-wing micro-air vehicles.

Modeling gaseous non-reactive flow in a lean direct injection gas turbine combustor through an advanced mesh control strategy

Fuel efficiency improvement and harmful emissions reduction are the main motivations for the development of gas turbine combustors. Numerical computational fluid dynamics (CFD) simulations of these devices are usually computationally expensive since they imply a multi-scale problem. In this work, gaseous non-reactive unsteady Reynolds-Averaged Navier–Stokes and large eddy simulations of a gaseous-fueled radial-swirled lean direct injection combustor have been carried out through CONVERGE™ CFD code by solving the complete inlet flow path through the swirl vanes and the combustor. The geometry considered is the gaseous configuration of the CORIA lean direct injection combustor, for which detailed measurements are available. The emphasis of the work is placed on the demonstration of the CONVERGE™ applicability to the multi-scale gas turbine engines field and the determination of an optimal mesh strategy through several grid control tools (i.e., local refinement, adaptive mesh refinement) allowing the exploitation of its automatic mesh generation against traditional fixed mesh approaches. For this purpose, the normalized mean square error has been adopted to quantify the accuracy of turbulent numerical statistics regarding the agreement with the experimental database. Furthermore, the focus of the work is to study the behavior when coupling several large eddy simulation sub-grid scale models (i.e., Smagorinsky, Dynamic Smagorinsky, and Dynamic Structure) with the adaptive mesh refinement algorithm through the evaluation of its specific performances and predictive capabilities in resolving the spatial-temporal scales and the intrinsically unsteady flow structures generated within the combustor. This investigation on the main non-reacting swirling flow characteristics inside the combustor provides a suitable background for further studies on combustion instability mechanisms.

Physical aspects of shear thinning/thickening behavior in radiative flow of magnetite Carreau nanofluid with nanoparticle mass flux conditions

The development of ground-breaking solar power technologies is considered to be one of the critical clarifications towards satisfying an increasing demand of energy worldwide. The use of solar energy had a remarkable benefit in current span. Furthermore, in numerous utilizations, there is a sympathetic requirement for augmenting the poor thermal conductivity of standard materials so as to develop effective heat transfer fluids. Nanofluids are fluid disturbances of nanoparticles and extensive analysis has been presented on nanofluid application in heat transfer developments. The crucial objective of this article is to scrutinize numerically the structure of unsteady 3D radiative flow of magneto-Carreau nanofluid. The Buongiorno’s relation is utilized to visualize the effects of thermophoresis and Brownian motion on the Carreau nanoliquid. The convective heated surface is ponder for heat transfer mechanisms. Additionally, zero nanoparticle mass flux condition on the surface of the boundary is accounted. An appropriate conversion is used to alter the PDEs into ODEs and then elucidated numerically via bvp4c tactic. The impact of distinct parameters for shear thinning/thickening liquids on velocity component, nanoliquid temperature and concentration of Carreau fluid are reported graphically. It is deceptive that the temperature of the Carreau nanoliquid declines as the Prandtl number Pr augment. Additionally, it is reported from these plots that the concentration of Carreau nanoliquid decay as the Brownian motion parameter boost up and opposite performance is being acknowledged for thermophoresis parameter.

Unsteady Flow Structures Induced by Single Microsecond-Pulsed Plasma Actuator

The unsteady flowfield around a single microsecond-pulsed dialectic barrier discharge plasma actuator in quiescent air is investigated using particle image velocimetry, Schlieren visualization, and a pressure-field microphone. A single microsecond pulse with a rising time of and a decaying time of is employed. It is the first time that a series of planar-type pressure waves which is induced by the microsecond-pulsed dialectic barrier discharge plasma actuator and propagates outward in the rising period is observed. It is likely that the streamer discharge which occurs in the rising stage and conduces to numerous current pulses with energy release could play an important role in generating these pressure waves. During the plateau of the constant voltage of 10 kV, a wall jet that has a deflection angle of 60 deg is formed, and the maximum velocity is approximately , while a new type of arched jet is observed during the plateau of the constant voltage of 0 kV. These wall jets provide favorable conditions for creating some perturbations and promoting mixing between the mainstream flow and the boundary flow.

Large eddy simulation of unsteady turbulent flow structures and film-cooling effectiveness in a laidback fan-shaped hole

Large eddy simulation (LES) is used to predict the turbulent flow structures and film-cooling characteristics of the unsteady jet/cross-flow interactions in a fan-shaped hole. The coolant hole is located on a flat plate surface with a 35 degree angle with respect to the main flow stream at a constant film density ratio DR=2 and two different blowing ratios M=1 and 2. The computational results under the different blowing ratios are validated by measurements data for the laterally-averaged and time-averaged film-cooling effectiveness. In addition, two different hybrid RANS/LES turbulence models, SAS (scale-adaptive simulation) and DES (detached-eddy simulation), are employed to show the influence of the turbulence model on the film-cooling effectiveness. The results reveal that the LES model is the only turbulence model that can calculate the film-cooling performance with an acceptable accuracy as compared to the experimental results. Comprehensive analyses are performed on the time-averaged and instantaneous turbulent flows within the cooling hole and mainstream channel, and the results show that the cooling jet flow structures and forest of hairpin vortices on the flat plate are significantly changed due to the blowing ratio. It is also observed that a pulsating behavior exists within the coolant hole, which is convected toward the hole exit. The interaction between the cooling hole flow and channel mainstream flow leads to unsteadiness at the interface mixing region (Kelvin-Helmholtz instability). In addition, velocity disturbances with various convective velocities are observed in the time-series flow fields at different blowing ratios. The evaluation of pressure fluctuation signals in the time and frequency domains show that the dominant frequency of the fan-shaped hole is shifted by changing the blowing ratio, and increasing the blowing ratio leads to the generation of more periodic vortical structures as well as improved film-cooling performance.

Turbulence modeling approaches on unsteady flow structures around a semi-circular cylinder

This paper presents the flow field around a Semi-Circular Cylinder (SCC), a basic geometry for fluid mechanics, obtained numerically by Computational Fluid Dynamics (CFD) at Reynolds number of 3.2 × 104. Time-averaged flow characteristics such as vorticity, velocity fields with streamline patterns, Reynolds stress correlations, Turbulence Kinetic Energy (TKE), pressure and drag coefficients have been examined by using Reynolds-averaged Navier-Stokes (RANS), Detached Eddy Simulation (DES) and Large Eddy Simulations (LES) turbulence models. Several RANS approaches with turbulence modeling including SST k-ω, k-ε and their derivatives were used, while in the LES simulations, the dynamic Smagorinsky subgrid-scale model was employed. The obtained results of the present study have been compared with an experimental study from the open literature. The results of the investigation showed that when numerical findings are compared to experimental ones, the results of LES and DES turbulence models were found to be more consistent than those obtained by using k-ε and SST k-ω models. Time-averaged flow patterns have been found to be considerably symmetric with respect to the axis passing through the end of the curved surface of the SCC. The deviation of LES and DES results, and experimental results was less than 7% in terms of the drag coefficient.

DDES analysis of unsteady flow evolution and pressure pulsation at off-design condition of a centrifugal pump

In the present paper, to investigate unsteady flow structures and pressure pulsations at off-design conditions, a low specific speed centrifugal pump is investigated by the DDES (Delayed Detached Eddy Simulation) method. Emphasis is laid on the unsteady evolution of flow structure and pressure pulsation at the stalled condition. Results show that the jet-wake flow pattern could be captured by the current numerical simulation method, and it shows a high calculation precision for the jet flow. Relative velocity decreases rapidly in the wake region towards the blade suction side. Significant inflection point exists between the jet and wake flow regions, and it almost keeps unchanged at the identical impeller-volute position under various flow rates. At the stalled status, the inflection point moves towards the blade pressure side with the blade passing the volute tongue, and evident non-uniform flow distributions are formed in the blade channels characterized by the multiple vortices. The blade channel is gradually blocked by the corresponding stall cell when the blade approaches the volute tongue, and it indicates that the volute tongue has a significant effect on the evolution process of the stall structure. By combination analysis of the unsteady evolution of the stall structure and pressure spectrum, the stall frequency at 0.25fn (being fn the impeller rotating frequency) is captured for the current model pump.

Stator–rotor interaction in the tip leakage flow of an inlet vaned low-speed axial fan

Purpose The purpose of the paper is to quantify the impact of the non-uniform flow generated by the upstream stator on the generation and convection of the tip leakage flow (TLF) structures in the passages of the rotor blades in a low-speed axial fan. Design/methodology/approach A full three dimensional (3D)-viscous unsteady Reynolds-averaged Navier-stokes (RANS) (URANS) simulation of the flow within a periodic domain of the axial stage has been performed at three different flow rate coefficients (φ = 0.38, 0.32, 0.27) using ReNormalization Group k-ε turbulence modelling. A typical tip clearance of 2.3 per cent of the blade span has been modelled on a reduced domain comprising a three-vaned stator and a two-bladed rotor with circumferential periodicity. A non-conformal grid with hybrid meshing, locally refined O-meshes on both blades and vanes walls with (100 × 25 × 80) elements, a 15-node meshed tip gap and circumferential interfaces for sliding mesh computations were also implemented. The unsteady motion of the rotor has been covered with 60 time steps per blade event. The simulations were validated with experimental measurements of the static pressure in the shroud of the blade tip region. Findings It has been observed that both TLF and intensities of the tip leakage vortex (TLV) are significantly influenced by upstream stator wakes, especially at nominal and partial load conditions. In particular, the leakage flow, which represents 12.4 per cent and 11.3 per cent of the working flow rate, respectively, has shown a clear periodic fluctuation clocked with the vane passing period in the relative domain. The periodic fluctuation of the TLF is in the range of 2.8-3.4 per cent of the mean value. In addition, the trajectory of the tip vortex is also notably perturbed, with root-mean squared fluctuations reaching up to 18 per cent and 6 per cent in the regions of maximum interaction at 50 per cent and 25 per cent of the blade chord for nominal and partial load conditions, respectively. On the contrary, the massive flow separation observed in the tip region of the blades for near-stall conditions prevents the formation of TLV structures and neglects any further interaction with the upstream vanes. Research limitations/implications Despite the increasing use of large eddy simulation modelling in turbomachinery environments, which requires extremely high computational costs, URANS modelling is still revealed as a useful technique to describe highly complex viscous mechanisms in 3D swirl flows, such as unsteady tip flow structures, with reasonable accuracy. Originality/value The paper presents a validated numerical model that simulates the unsteady response of the TLF to upstream perturbations in an axial fan stage. It also provides levels of instabilities in the TLV derived from the deterministic non-uniformities associated to the vane wakes.

The flow regime and hydrodynamic performance for a pitching hydrofoil

The objective of this paper is to study the flow regime and hydrodynamic performance for a pitching Clark-Y hydrofoil. The aims are to (1) improve the understanding of the interplay between the hydrodynamic performance, unsteady flow structures and dynamic motion of the hydrofoil, (2) study the influence of the pitching rate on the transition of different flow regimes. The experimental investigations were conducted in the looped cavitation tunnel, and the dynamic moment measurement system was applied to obtain the hydrodynamic forces. The pitching hydrofoil is controlled to rotate from α+ = 10° to α+ = 15° firstly, then goes from α+ = 15° to α− = 5°, finally goes back to α+ = 10° from α− = 5°. The pitching rate is varying with the Reynolds number Re = 4.4 × 105. The numerical investigations were performed by solving the incompressible URANS equations using the coupled k-ω SST turbulence model and γ-Reθ transition model. The numerical results agree well with the experimental measurements. The pitching motion affects the turbulence kinetic energy distribution around the hydrofoil, leading to the delay or acceleration of the transition between different flow patterns. During the pitching process, higher level of turbulence kinetic energy distribution causes earlier transition from laminar to turbulence. Moreover, hysteresis effect of the hydrodynamic force is observed. For the upstroke stage, the higher pitching rate promotes the laminar separation slightly and intensifies the delay of turbulence separation. For the downstroke stage, the higher pitching rate promotes the turbulence separation extensively. The first leading edge vortex (LEV) and anticlockwise trailing edge vortex (TEV) are delayed with the increase of pitching rate, which is responsible to the delay of dynamic stall. The lower pitching rate shrinks the hysteresis loops and intensifies the fluctuation of the dynamic force.

Retrieval, reporting and methodological characteristics for systematic reviews/meta-analyses of animal models: a metaepidemiological study

Free convection inside an attic enclosure in which sinusoidal heat flux applied on the inclined walls and a constant temperature applied on the base wall has been investigated numerically to demonstrate the primary flow characteristics and heat transfer within the attic enclosure over daily routine cycles. To solve the governing equations, the finite volume technique has been utilized. After performing the grid independency and time step size tests, the roles of Rayleigh number (Ra) and the attic aspect ratio (AR) on the unsteady flow structure and heat transfer phenomenon are explained for a constant Prandtl number (0.72) for the air. Results are illustrated as a form of stream function and isotherms. Moreover, heat transfer is calculated in terms of Nusselt number. The numerical simulations reveal stratified flow within the enclosure during the daytime nonlinear heating stage. However, during night-time, nonlinear cooling stage the flow turns into unstable as the forms of rising and sinking plumes for sufficiently higher Rayleigh number.

Cellular automata ray tracing in two-dimensional aero-optical flow fields

<sec>For the supersonic flow field with large density fluctuation produced by the unsteady flow and turbulent large-scale structures, an effective method to obtain the beam path is to solve the ray equation. Then the optical path difference (OPD), Strehl ratio (SR), optical transmission function (OTF), etc. can be obtained to analyze the optical distortion, and the correction of aero optics effects can be realized to improve the optical system performance. Generally, when the refractive index distribution is arbitrary, the ray equation analytic solution is difficult to obtain.</sec> <sec>Cellular automata (CA) ray tracing algorithm is proposed in this paper for aero-optical calculation in the 2D discrete flow fields. Unlike numerically solving the ray equation (NSRE), the coordinate value and the offset angle are calculated according to the position and direction transformation rules in CA algorithm. The position transformation rule is used to obtain the end point of the beam vector and determine whether the offset angle needs calculating at each iteration, the direction transformation rule is to calculate the offset angles. Then the refractive index field is integrated along the beam path to obtain the optical path length (OPL). The OPD is calculated from OPL. In this paper, aero-optical calculation is based on two types of flow fields. The supersonic shear layer including supersonic mixing layer and boundary layer 2D density distribution is measured by the nano-tracer-based planar laser scattering (NPLS) technique. The supersonic flow field surrounding the optical dome is simulated based on detached-eddy simulation (DES).</sec><sec>The OPD<sub>rms</sub> and program running time quantitatively verify the calculation accuracy and high efficiency of CA. The results show that for the 2D supersonic NPLS flow field and the 2D supersonic flow field surrounding the optical dome, the calculation accuracy of CA is approximately equal to NSRE. Moreover, we find that the program running time of NSRE is about four times that of the CA algorithm, so the efficiency of ray tracing is effectively improved. Thus, the CA algorithm provides a new scheme for aero-optical calculation in the 2D supersonic flow field. Meanwhile, it also provides a guideline for the research on the ray tracing in 3D discrete aero-optical flow field.</sec>

Study of Unforced Unsteadiness in Centrifugal Pump at Partial Flow Rates

In order to explore the unforced unsteadiness of centrifugal pumps, a 2-D frequency domain imaging display technology was used to study the development of these unsteady flow structures at partial flow conditions. The results showed that, the unsteady flow field was not only affected by rotor and stator interaction, but also appeared an unforced unsteadiness with fundamental frequency of St≈0.23 around the impeller throat area. Moreover, as the flow rates decreased, this unsteady flow structure gradually weakened and disappeared. When the flow rate was reduced to 0.6 times of design flow rate, another two unforced unsteady flow structures with characteristic frequencies of St≈0.0714 and St≈0.12 began to appear in the same area. Therefore, with the operating condition smaller than design flow rate, the internal flow became more and more complex. In addition to the forced unsteadiness, the unforced unsteadiness which is not connected with the blade passage frequency became more and more obvious.