Unsteady Interaction Research Articles

Effects of periodic wakes on the endwall secondary flow in high-lift low-pressure turbine cascades at low Reynolds numbers

Periodic wakes affect not only the surface boundary layer characteristics of low-pressure turbine blades and profile losses but also the vortex structures of the secondary flow and the corresponding losses. Thus, understanding the physical mechanisms of unsteady interactions and the potential to eliminate secondary losses is becoming increasingly important for improving the performance of high-lift low-pressure turbines. However, few studies have focused on the unsteady interaction mechanism between periodic wakes and endwall secondary flow in low-pressure turbines. This paper verified the accuracy of computational fluid dynamics by comparing experimental results and those of the numerical predictions by taking a high-lift low-pressure turbine cascade as the research object. Discussion was focused on the interaction mechanisms between the upstream wakes and secondary flow within the high-lift low-pressure turbine. The results indicated that upstream wakes have both positive and negative effects on the endwall flow, where the periodic wakes can decrease significantly the size of the separation bubble, prevent the formation of secondary vorticity structures at relatively high Reynolds numbers (100,000 and 150,000), and reduce the cross-passage pressure gradient of cascade. In addition, periodic wakes can improve the cascade incidence characteristic in terms of reducing the overturning and underturning of the secondary flow at downstream of the cascade all of which are beneficial for decreasing the endwall secondary losses, whereas more endwall boundary layer is involved in the main flow passage due to the wake transport, resulting in increased strength of the secondary flow at low Reynolds number of 25,000 and 50,000. Compared with the results without wakes, the total pressure loss for unsteady condition at the cascade exit decreases by 2.7% and 6.1% at high Reynolds number of 100,000 and 150,000, respectively. However, the secondary loss at unsteady flow conditions increases at low Reynolds number of 25,000 and 50,000.

Optimal Aerodynamic Design of a Transonic Centrifugal Turbine Stage for Organic Rankine Cycle Applications

This paper presents the results of the application of a shape-optimization technique to the design of the stator and the rotor of a centrifugal turbine conceived for Organic Rankine Cycle (ORC) applications. Centrifugal turbines have the potential to compete with axial or radial-inflow turbines in a relevant range of applications, and are now receiving scientific as well as industrial recognition. However, the non-conventional character of the centrifugal turbine layout, combined with the typical effects induced by the use of organic fluids, leads to challenging design difficulties. For this reason, the design of optimal blades for centrifugal ORC turbines demands the application of high-fidelity computational tools. In this work, the optimal aerodynamic design is achieved by applying a non-intrusive, gradient-free, CFD-based method implemented in the in-house software FORMA (Fluid-dynamic Opti-mizeR for turboMachinery Aerofoils), specifically developed for the shape optimization of turbomachinery profiles. FORMA was applied to optimize the shape of the stator and the rotor of a transonic centrifugal turbine stage, which exhibits a significant radial effect, high aerodynamic loading, and severe non-ideal gas effects. The optimization of the single blade rows allows improving considerably the stage performance, with respect to a baseline geometric configuration constructed with classical aerodynamic methods. Furthermore, time-resolved simulations of the coupled stator-rotor configuration shows that the optimization allows to reduce considerably the unsteady stator-rotor interaction and, thus, the aerodynamic forcing acting on the blades.

Adjoint-Based Sensitivity Analysis for Unsteady Bladerow Interaction Using Space–Time Gradient Method

Temporal variation of components' performance is becoming a crucial parameter in turbomachinery design process. The main physical mechanism driving the time-dependent behavior is the unsteady bladerow interaction as stator–rotor relative motion due to rotating frame of reference. However, so far unsteady effects have been ignored in design processes in common engineering practice. In fact, steady approach has been generally employed for computational fluid dynamics (CFD)-based turbomachinery design. Moreover, conventional blade design has been based on single operating point considerations. Taking into account multiple time-dependent phenomena, as the unsteady performance parameters variation, might be beneficial in making a further improvement on component performance. In quantitative terms, first of all it is important to investigate the relative effect of unsteady variation, compared to the standard steady approach, and to create a capability for calculating temporal sensitivity variation, while keeping a reasonable computing cost. This work investigates the unsteady variation of turbomachinery performance on quasi-three-dimensional (3D) geometries: single-stage turbine and single-stage compressor. Steady flow solutions using mixing plane method are compared to the unsteady flow solutions using a direct unsteady calculation, while assessing the introduction of the space–time gradient (STG) method. The results clearly show how the unsteady variation is a non-negligible effect in performance prediction and blade design. Then, a new computational technique to quantify temporal sensitivity variation is introduced, based on the STG method, with an extension to adjoint-based sensitivity analysis. The relation between time and space in multipassage-multirow domain, the fundamental assumption of the STG method, is applied within the adjoint operator formulation, which gives unsteady sensitivity information on a broad range of design parameters, at the cost of a single computation. Finally, the unsteady sensitivities are compared to the ones resulting from steady solution in the two quasi-3D cases. This work introduces a coherent and effective mathematical formulation for accounting deterministic unsteadiness on component design, while reducing computational cost compared to standard unsteady optimization techniques.

Numerical simulation and experimental verification on downwash air flow of six-rotor agricultural unmanned aerial vehicle in hover

Recently, multi-rotor unmanned aerial vehicle (UAV) becomes more and more significantly irreplaceable in the field of plant protection against diseases, pests and weeds of crops. The easy takeoff and landing performance, hover function and high spraying efficiency of UAV are urgently required to spray pesticide for crop timely and effectively, especially in dispersed plots and hilly mountains. In such situations, the current researches about UAV spray application mainly focus on studying the influence of the UAV spraying parameters on the droplet deposition, such as operation height, operation velocity and wind velocity. The deposition and distribution of pesticide droplets on crops which depends on installation position of nozzle and airflow distribution characteristics of UAV are directly related to the control effect of pesticide and crop growth in different growth periods. As a preliminary step, this study focuses on the dynamic development law and distribution characteristics of the downwash air flow for the SLK-5 six-rotor agricultural UAV. Based on compressible Reynolds-averaged Navier-Stokes (RANS) equations with an RNG k-e turbulence model and dynamic mesh technology, the efficient three-dimensional computational fluid dynamics (CFD) method was established to analyze the flow field distribution characteristics of UAV in hover. Then the unsteady interaction flow field of the wing was investigated in detail. The downwash wind speed of the marked points for the SLK-5 UAV in hover was also tested by weather tracker. It was found that the maximum velocity value of the downwash flow was close to 10 m/s; the z-direction velocity was the main body of the wind velocity in the downwash airflow, and the comparison of the wind velocity experiment test and simulation showed that the relative error was less than 12% between the experimental and simulated values of the z-direction velocity at the marked points. Then the flow characteristics of the longitudinal and cross section were analyzed in detail, the results obtained can be used as a reference for drift and sedimentation studies for multi-rotor unmanned aerial vehicle. Keywords: UAV, downwash air flow, numerical simulation, experimental verification, pesticide spray, wing interference DOI: 10.25165/j.ijabe.20171004.3077 Citation: Yang F B, Xue X Y, Zhang L, Sun Z. Numerical simulation and experimental verification on downwash air flow of six-rotor agricultural unmanned aerial vehicle in hover. Int J Agric & Biol Eng, 2017; 10(4): 41–53.

Filtering Mixing Planes for Low Reduced Frequency Analysis of Turbomachines

A class of problems in turbomachinery is characterized by unsteady interactions at low reduced frequencies. These interactions are often the result of perturbations with length-scale on the order of the machine circumference and examples include axial compressors operating with inlet distortion, fans with downstream pylons, and turbine rotors downstream of midframe struts. Typically, this unsteadiness is accompanied by higher frequency fluctuations caused by perturbations with a length-scale on the order of a blade pitch. Conventional numerical analysis of this class of problem requires computations with a time step governed by the high-frequency content but a greatly reduced run time could be achieved if the time step was dictated solely by the low reduced frequency, long length-scale, interaction of interest. In this paper, a filtering mixing plane technique is proposed that removes unwanted short length-scale perturbations at the interfaces between blade rows. This approach gives the user control over the amount of mixing that occurs at these interfaces with the limits being fully mixed-out to pitchwise uniformity (conventional mixing plane) or no mixing (conventional sliding plane). By choosing to retain only enough harmonics to resolve the low reduced frequency interaction of interest, an order of magnitude reduction in run time can be achieved.

Numerical simulation of unsteady propeller/rudder interaction

A numerical approach based on a potential flow method is developed to simulate the unsteady interaction between propeller and rudder. In this approach, a panel method is used to solve the flow around the rudder and a vortex lattice method is used to solve the flow around the propeller, respectively. An iterative procedure is adopted to solve the interaction between propeller and rudder. The effects of one component on the other are evaluated by using induced velocities due to the other component at every time step. A fully unsteady wake alignment algorithm is implemented into the vortex lattice method to simulate the unsteady propeller flow. The Rosenhead-Moore core model is employed during the wake alignment procedure to avoid the singularities and instability. The Lamb-Oseen vortex model is adopted in the present method to decay the vortex strength around the rudder and to eliminate unrealistically high induced velocity. The present methods are applied to predict the performance of a cavitating horn-type rudder in the presence of a 6-bladed propeller. The predicted cavity patterns compare well with those observed from the experiments.

On Turbulence Measurements and Analyses in a Two-Stage Two-Spool Turbine Rig

Since the experiment in turbulence research is of very high importance for evaluating turbulence hypothesis, turbulence measurements were carried out in a two-stage two-spool transonic turbine test rig at the Institute for Thermal Turbomachinery and Machine Dynamics in Graz in which the two rotors are counter-rotating with two different rotational speeds. For the current measurement campaign, triple hot-wire probes, which represent a very new measurement technique in this test rig, were used and their results validated with a fast response aerodynamic pressure probe (FRAPP). Based on the data measured with this device, turbulence intensities may be determined using a method called Fourier filtering. If the classical ensemble averaging procedure with only one trigger is applied, the periodic fluctuations of the other rotor will artificially increase the stochastic fluctuations. Therefore, the two trigger signals of the two rotors require a special analysis method, which was established at Graz University of Technology. The results from this method will be compared to the classical triple decomposition, which uses only one trigger signal. With this analysis tool, it is not only possible to evaluate unsteady signals triggered by one of the two rotors, but also the unsteady interactions of the rotors can be determined and investigated.

Structural insight, mutation and interactions in human Beta-catenin and SOX17 protein: A molecular-level outlook for organogenesis

Essential human proteins; SOX17-HMG domain and beta-catenin uphold a major responsibility for vertebrate gastrulation and embryonic development. Earlier experimental assays document their interaction and states that upon M76A and G103R mutation, their interaction varied. Till date, there was no computational analysis for either of proteins as well as their respective residues for the interaction. The present study extracted and analyzed the experimentally validated 3D models of SOX17-HMG domain and beta-catenin. After analysis of the evolutionarily conserved residues and the sequence-level alteration, the mutated SOX17-HMG protein was re-modeled, demonstrated and energy minimized. Molecular dynamics simulation was performed upon the docked complex of beta-catenin with wild-type and mutant-type protein, individually. Comparable analysis for interaction studies revealed reduction of predominant ionic interactions from 16 (wild-type) to 5 (mutant-type). Glu residues from wild-type protein played a pivotal role forming 50% of the ionic interactions alone. Fascinatingly, statistically significant deductions for several stability calculations deduced the mutant-type protein/complex to form unsteady interaction with beta-catenin. Again, helix-to-coil transition in mutant-type protein supported its weaker conformation. This probe depicts the paramount molecular-level detailed scrutiny for the essential human proteins and disclosure of the mutational analysis, which might tend to hinder the signal transduction. It instigates the future development for the pharmaceutical research.

Numerical and Experimental Investigation of Axial Gap Variation in High-Pressure Steam Turbine Stages

This work aims at investigating the impact of axial gap variation on aerodynamic performance of a high-pressure steam turbine stage. Numerical and experimental campaigns were conducted on a 1.5-stage of a reaction steam turbine. This low speed test rig was designed and operated in different operating conditions. Two different configurations were studied in which blades axial gap was varied in a range from 40% to 95% of the blade axial chord. Numerical analyses were carried out by means of three-dimensional, viscous, unsteady simulations, adopting measured inlet/outlet boundary conditions. Two sets of measurements were performed: steady measurements, from one hand, for global performance estimation of the whole turbine, such as efficiency, mass flow, and stage work; steady and unsteady measurements, on the other hand, were performed downstream of rotor row, in order to characterize the flow structures in this region. The fidelity of computational setup was proven by comparing numerical results to measurements. Main performance curves and spanwise distributions have shown a good agreement in terms of both shape of curves/distributions and absolute values. Moreover, the comparison of two-dimensional maps downstream of rotor row has shown similar structures of the flow field. Finally, a comprehensive study of the axial gap effect on stage aerodynamic performance was carried out for four blade spacings (10%, 25%, 40%, and 95% of S1 axial chord) and five aspect ratios (1.0, 1.6, 3, 4, and 5). The results pointed out how unsteady interaction between blade rows affects stage operation, in terms of pressure and flow angle distributions, as well as of secondary flows development. The combined effect of these aspects in determining the stage efficiency is investigated and discussed in detail.

Numerical method for unsteady fluid structure interaction problem

Numerical method for unsteady fluid structure interaction problem

A substructure-based numerical technique and experimental analysis of turbine blades damping with underplatform friction dampers

Friction dampers are commonly used in jet and turboprop engines to decrease vibration stresses of turbine blades by means of irreversible conversion of mechanical energy into heat. Effectiveness of such an energy transfer depends on design, material and operational conditions of dampers. Optimization of dampers design is a complex task usually associated with analysis of nonlinear contact problems and complicated experimental verification. It is also coupled with high time costs causing the engineering task to be modified into a complex research problem. Although it is necessary to understand that numerical modeling of damping of turbine blades represents a task that need significant computational resources and precise experimental verification. So, it was decided to create a finite element-model for calculations of unsteady blade-damper interaction based on a substructure reduction method. The dummy blades and dampers were used to simplify the task.The presented technique is based on the finite-element method with a numerical model reduction by Craig–Bampton and Guyan algorithms. The model consisted of dummy blades pair with a wedged damper between the platforms. This technique allowed considering three-dimensional shapes of parts, non-linear contact forces, friction, various operational loads and conditions. The model was verified by experiments performed on a special test rig based on a vibration shaker and a 3D laser vibrometer. A relationship between oscillation amplitude of blades and a centrifugal load on the damper was obtained in the range of centrifugal loads 0…700 N. Also, the effect of friction coefficient µ in the range 0.2 … 0.8 on resonant blades amplitudes was investigated. An optimal operational range with maximum damper efficiency was defined. An effect of so-called anti-phase and in-phase modes of adjacent blades on damper efficiency was investigated.

Explicit discontinuous spectral element method with entropy generation based artificial viscosity for shocked viscous flows

A spatio-temporal adaptive artificial viscosity (AV) based shock-capturing scheme is proposed for the solution of both inviscid and viscous compressible flows using a high-order parallel Discontinuous Spectral Element Method (DSEM). The artificial viscosity and artificial thermal conduction coefficients are proportional to the viscous and thermal entropy generating terms, respectively, in the viscous entropy conservation law. The magnitude of AV is limited based on the explicit stable CFL criterion, so that the stable artificial viscous time step size is greater than the convective stable time step size. To further ensure the stability of this explicit approach, an adaptive variable order exponential filter is applied, if necessary, in elements where the AV has been limited. In viscous flow computations a modified Jameson's sensor (Ducros et al., 1999 [61]) limits the AV to small values in viscous shear regions, so as to maintain a high-order resolution in smooth regions and an essentially non-oscillatory behavior near sharp gradients/shocks regions. We have performed a systematic and extensive validation of the algorithm with one-dimensional problems (inviscid moving shock and viscous shock-structure interaction), two-dimensional problems (inviscid steady and unsteady shocked flows and viscous shock-boundary layer interaction), and a three-dimensional supersonic turbulent flow over a ramped cavity. These examples demonstrate that the explicit DSEM scheme with adaptive artificial viscosity terms is stable, accurate and efficient.

Aerodynamic Effects of Unsteady Blade-Tower Interaction

In this study, a 2D model as the horizontal cross-sections for HAWT of NREL phase VI is investigated to figure out the flickering of aerodynamic force with six different geometries by pressure-based Navier-Stokes solver and k-ω SST turbulence model. All six cases presented have zero yaw angle and zero pitch angle. Computational domain is divided as sliding mesh and stagnation domains to simulate the blade motion. In this article the dynamic response of tower interference is performed by lateral force, lift force, pressure coefficient and velocity contour by locations of the blade. The aerodynamic response is arranged in an overshoot function for the lift force coefficient of the airfoil to account for the aerodynamic coupling with the tower. This work present in this study gives an insight into rotor structure aerodynamic and aeroelastic interaction.

N-pulse particle image velocimetry-accelerometry for unsteady flow-structure interaction

Flow-structure interaction experiments are a major area of application of instruments capable of simultaneously measuring instantaneous fields of velocity and acceleration. An N-pulse particle image velocimeter-accelerometer (N-P PIVA) employing bursts of N pulses, where N = 3 or 4, and operating in the high-image-density particle seeding mode is described and demonstrated in the context of a representative flow-structure interaction experiment. The instrument employs two double-pulsed lasers and a high-resolution, fast-framing camera to acquire successive particle images having time separations small enough to perform good interpolation or finite differencing. The interrogation procedure locates the same group of particles at each pulse time using multiple cross-correlations, and a predictor-corrector algorithm enhances the strength of the cross-correlations by centering the windows on the particle groups at each time. A flow-structure experiment was performed in liquid surrounding a horizontal cylinder suspended by two thin, flexible, vertical rods from a slider block driven horizontally and sinusoidally. The value of the Keulegan–Carpenter number is and the frequency parameter (or Stokes number) is . Data from 2-, 3- and 4-pulse systems are compared to assess their relative performance. Measurements from the 4-pulse method with interpolation have smaller mean bias errors than the 3-pulse method with interpolation or the 4-pulse method with least squares, but larger random error. To make measurements close to the surface of the cylinder, a method using near-wall transformation and correlation analysis on a transformed grid is developed. Image processing used to determine the position, velocity and acceleration of the center of the cylinder is described. These measurements, together with the N-P PIVA data allow complete evaluation of each term in the exact, stationary control surface formulation of the fluid force applied to the cylinder surface (Noca 1997 PhD Thesis California Institute of Technology, Noca et al 1997 J. Fluids Struct. 11 345–50, 1999 J. Fluids Struct. 13 551–78, Unal et al 1997 J. Fluids Struct. 11 965–71).

A field study of wind dominant single sided ventilation through a narrow slotted architectural louvre system

An increasingly popular solution for ventilation that facilitates strategies such as night cooling is the provision of purpose provided ventilation openings comprised of horizontal slotted architectural louvres. Often these are employed in single sided ventilation strategies where there exists an irregular unsteady interaction of wind and buoyancy forces. This paper presents results from full scale experimental measurements of the macroscopic Air Change Rate (ACR) for an opening utilising an architectural slotted louvre in zero2020/NBERT, a National Building Energy Retrofit Testbed in Cork, Ireland. 2 slot louvre cases and 3 plain opening cases were investigated with 44 tracer gas concentration decay tests completed in a single cell isolated office space. The findings show that, for similar boundary conditions, the spectral characteristics of the velocity in the opening are modified by the introduction of the slot louvre. A non-dimensional analysis highlights stronger wind dominant aeration for the louvre than a plain opening having comparable overall façade opening dimensions. On average across the various cases measured, the slot louvre ACR were 6.5% higher compared with the plain opening ACR with even greater increases when considering comparable free opening area cases specifically. A sensitivity analysis using stepwise multiple linear regression also demonstrated a high correlation between ACR, wind speed and wind direction for the slot louvre. A comparison of existing single sided correlations showed lower prediction error for the plain opening cases than for the slot louvre. When considering the dimensionless exchange rate parameter, Fr, the published values for plain openings was comparable to those in this study but were too low in general for the slot louvre. An alternative value for this is suggested based on the field study measurements.

Shock wave–boundary layer interaction in supersonic flow over a forward-facing step

We study in the present work a Mach 2.5 flow over a forward-facing step. The focus of the work is the flow ahead of the step, in particular, the unsteady interactions between the shock, the boundary layer and the separation bubble. The primary geometrical parameter in the problem is the ratio of the step height to the incoming boundary layer thickness,$h/\unicode[STIX]{x1D6FF}$, which is kept fixed at 2. Results are presented from detailed particle image velocimetry (PIV) measurements in two orthogonal planes to obtain a reasonable picture of the whole flow field. The mean velocity field in the central cross-stream or wall-normal ($x$–$y$) plane shows that the incoming boundary layer separates upstream of the step forming a large separation bubble ahead of the step, which can be relatively well resolved in PIV measurements compared to the compression ramp cases. Wall pressure fluctuation spectra close to the separation location show a dominant frequency ($f$) that is two orders of magnitude smaller than the characteristic frequency of the incoming boundary layer ($U_{\infty }/\unicode[STIX]{x1D6FF}$), consistent with low-frequency motions of the shock that have received a lot of recent attention ($U_{\infty }$ $=$ free-stream velocity,$\unicode[STIX]{x1D6FF}$ $=$ boundary layer thickness). PIV measurements in the wall-normal plane show large variations in shock position with time. The shock position measured from velocity data outside the boundary layer is found to be well correlated with the reverse flow area ahead of the step, and weakly correlated to structures in the incoming boundary layer. In contrast, the shock foot, determined from velocity data within the boundary layer, is found to be well correlated to the low- and high-speed streaks in the incoming boundary layer, in addition to the reverse flow area ahead of the step. Instantaneous velocity fields in the spanwise ($x$–$z$) plane parallel to the lower wall show that the shock is broadly two-dimensional with small spanwise ripples, while the recirculation region has very large spanwise variations. The spanwise-averaged shock location is found to be well correlated to the most upstream location of the recirculation region over a spanwise length ($x_{r,min}^{sp}$). Instantaneous velocity fields show that when some part of the recirculation region is far upstream, the corresponding nearly two-dimensional shock is also far upstream. On the other hand, when$x_{r,min}^{sp}$is relatively downstream, the resulting shock is also found to be downstream. Hence, the present results suggest that for the forward-facing step configuration, the large-scale streamwise motions of the shock are mainly correlated to the most upstream point of the recirculation region, which has large spanwise variations.

Interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex

This paper focuses on the nonlinear interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a sub-surface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in Kelvin–Helmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective “self”-energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs – termed “cooperative” and “adverse” shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive.

Interaction behavior of triple transitional round fountains in a homogeneous fluid

In this study, the PIV and flow visualization techniques and three-dimensional direct numerical simulation are used to investigate the behavior of triple transitional round fountains, which are aligned along a straight line, interacting with each other in a homogeneous fluid over the ranges of 1 ≤ Fr ≤ 10 and 100 ≤ Re ≤ 1000, at a fixed spacing of D/X0=6, where Re and Fr are the Reynolds and Froude numbers, D is the spacing between the two neighbouring fountain sources, and X0 is the radius of orifices at the fountain source, respectively. The results show that the interaction behavior of triple transitional round fountains, over the ranges of Re and Fr studied, is dominated by the bobbing and flapping motions, and is either steady, or unsteady weakly multi-modal, or unsteady strongly multi-modal. In a steady interaction, the bobbing-flapping motions are only present in its initial development stage and the interaction will attain a steady state in the later stage in which the bobbing-flapping motions are no longer present. In contrast, in an unsteady interaction, the interaction remains unsteady all the time and the bobbing-flapping motions are present at all stages. Among all cases considered, a steady interaction occurs at Re ≤ 300 with Fr=1 and at Re=100 with Fr ≤ 5; an unsteady weakly multi-modal interaction occurs at Re=100 with 6 ≤ Fr ≤ 10, at 200 ≤ Re ≤ 300 with 2 ≤ Fr ≤ 10, and at Re=400 with Fr=1; and an unsteady strongly multi-modal interaction occurs at 600 ≤ Re ≤ 1000 with Fr=1 and at 400 ≤ Re ≤ 1000 with 2 ≤ Fr ≤ 10. Such interaction behavior is found to be similar to that of twin transitional round fountains over comparable ranges of Re and Fr, as discovered by us in an earlier study. It is also found that the two interaction regions formed by the three fountains have essentially symmetrical behavior about the middle fountain for all cases considered. Furthermore, the maximum fountain penetration heights and the maximum thicknesses of the interaction regions of the triple transitional round fountains are quantified with the experimental and numerical results and compared to the available scalings for single fountains at comparable Fr and Re values. Several scaling relations are then developed for these parameters over the ranges of Fr and Re considered.

An Efficient Unsteady Adjoint Optimization System for Multistage Turbomachinery

Unsteady blade row interactions play an important role in the performance of multistage turbomachinery. However, most aerodynamic optimizations of multistage turbomachinery are based on mixing-plane steady flow simulations. To take into account the unsteady flow features in the optimization cycle, this paper develops an adjoint-based unsteady aerodynamic optimization system for multistage turbomachinery. To the authors' best knowledge, this is the first work in the literature conducting the unsteady adjoint aerodynamic optimization of multistage turbomachinery. The unsteady flow equations and the discrete adjoint equations are solved using a finite volume code, with the harmonic balance method adopted to reduce the cost of unsteady simulations. The system is applied to the unsteady aerodynamic optimization of a 1.5-stage compressor. Results show the efficiency and capability of the proposed framework for the unsteady aerodynamic optimization of multistage turbomachinery.

The Theoretical Research for the Rotor/Fuselage Unsteady Aerodynamic Interaction Problem

Based on coupled unsteady panel/free-wake method, a universal analysis model was established, which provides a good prediction for the rotor/fuselage unsteady aerodynamic interaction. Considering the deficiencies of the traditional time-marching rotor free-wake algorithms, notably on stability and efficiency, the CB3D algorithm with 3rd-order accuracy is proposed. For solving the problem that part of the wake vortices may penetrate the fuselage, a “material line” rectification method with 3rd-order accuracy is proposed. An analysis for the model accuracy was then conducted to validate the accuracy of the new model, and a comparison against the available experimental data is performed. The simulated results show a good agreement with these experimental data. With the new model, several simulations are conducted for the typical rotor/fuselage aerodynamic interaction, and the results are analyzed.