Unsteady Interaction Research Articles

Analysis of Near-Wall CO due to Unsteady Flame-Cooling Air Interaction

The interaction of a stoichiometric, laminar premixed methane/air flame with a coolant jet is investigated using two-dimensional fully resolved simulations (FRSs). The flame is forced at the inlet with velocity modulation and the coolant is injected from a cooling hole located on the wall at the same temperature as the premixture. FRS cases featuring a combination of blowing ratios, forcing frequencies, position of the cooling hole and the coolant type (air and $$N_2$$ ) are studied to understand the effects of these parameters on flame dynamics and CO emissions. The results show a negligible impact of the forcing frequency on the exhaust CO emissions. However, increasing the blowing ratio and the cooling hole streamwise location both increase the exhaust CO emissions. Using air instead of nitrogen as the coolant reduces the CO emission by providing additional oxygen and therefore enhancing CO oxidation. Furthermore, analysis of the CO mass fraction in the near-wall, post-cooling hole region shows a strong dependence on the local temperature and the mixture fraction used as a measure of dilution. CO mass fraction—temperature ( $$Y_{CO} - T$$ ) scatter plots reveal the same trends as those of one-dimensional (1D) freely-propagating flames at different equivalence ratios up to a limit, identified using a progress variable based on the $$CO_2$$ mass fraction. The results of this work highlight the potential pathways for modelling the near-wall CO mass fraction in effusion cooled combustors.

Close to a Century of Popular Music Practices and Experiences in Nigeria (1922–2020) and a Brief History of Their Socio-political Background

For 98 years (1922–2020), the entire corpus of popular music practices and experiences in Nigeria evolved and thrived almost uninterrupted until the great disruption caused when the World Health Organization (WHO) declared Severe Acute Respiratory Syndrome Coronavirus 2 (COVID-19) a global pandemic on 11 March 2020. Between 1922 and 2020, there have been hazy and unsteady creative attempts, incipient interactions and interruptions, generational changes and exchanges, and ideological shifts which have marked the evolution of Nigerian popular music. Based on a historical-analytical approach, this article reports on a study that aimed to recollect and explore the remarkable socio-political developments, transformations and perceptions that have consistently underpinned these 98 years of popular music practices/experiences in Nigeria. As part of the study findings, these years were divided into the following four periods: the foggy years (1922–1944); the interactive-budding period (1945–1969); the liberal period (1970–1999); and the mononationalist period (2000–2020). In part, the methodology relied on the oral accounts of some elderly and middle-aged Nigerian popular music artists, entrepreneurs, enthusiasts and analysts, as well as archival resources (print and audio-visual), and the extant literature on popular music in and social history of Nigeria. The findings also revealed transnational heritages and memorial continuities that partly and presently characterise these periods.

Influence of rotor speed, discharge pressure, and clearance size on the unsteady flow dynamics and heat interaction of roots blower

The geometry of the 2-lobe rotors of a roots blower is proposed by the combination of three arcs and is parameterized by two independent variables. By considering a standard combination of these variables, attempts are made to grasp the unsteady interior flow phenomena and thermal interaction in the blower as well as to comprehend the effect of main influencing factors on the performance of the blower using a transient finite volume-based dynamic-mesh-rearrangement method. A grid-independent test is conducted, and the adopted methodology is validated. At first, an endeavor is made to realize the transient internal flow field and heat interaction within the roots blower. Then, individual efforts are made to apprehend the effect of rotor speed, discharge pressure, and clearance size (provided in between the rotors or in between the rotors and casing) on the said transient flow dynamics and heat interaction. Time variation of the discharge velocity, mass flowrate, and discharge temperature are found to be fluctuating in nature. Pressure, velocity, and temperature distributions in the blower, as well as the leakages, backflow, vortices in the blower, etc., at different moments, are found to be strongly dependent on the rotor speed, discharge pressure, clearance size between the rotors or between the rotor and housing. The nature and amplitude of the time variation of exhaust velocity, discharge mass flowrate, outlet-temperature, and the blower performance are also found to be very much sensitive to the chosen rotor speed, discharge pressure, and clearance size.

An experimental study of rotor-stator wake unsteadiness in a multistage axial compressor

The flow in a multistage axial compressor is highly unsteady, three-dimensional and turbulent. The interaction between compressor blade rows results in rotor/stator wake unsteadiness, which is not typically considered in the computational fluid dynamics (CFD) models. To gain depth and insight into the inner flow mechanism in multistage compressors, specifically the wake variability driven by the rotor/stator and stator/stator interactions, a compound total-pressure pneumatic probe with both high and low response-frequency were designed and manufactured. Unsteady rotor and stator wake measurements between blade rows for the third stage were carried out with this probe installing on a 3-DOF displacement mechanism, to deepen the knowledge of unsteady interactions in the embedded stages of a four-stage low-speed axial compressor. By performing frequency spectrum analysis and ensemble-average methods, higher spectral magnitude of the blade passing frequency (fBPF) and higher root mean square values of total pressure (PtRMS) at both sides of the stator wake region caused by the shedding of upstream boundary layer are revealed. In addition, the high-order harmonics are strengthened by the stator/stator interactions, especially near the blade tip. The individual contributions of rotor geometry variations/interactions of the upstream rotor wakes and the effects of downstream stator potential modulation to the wake variations can be understood.

Three-dimensional unsteady stator-rotor interactions in high-expansion organic Rankine cycle turbines

Organic Rankine cycle (ORC) systems are a readily available technology to convert thermal energy from renewable- and waste heat sources into electricity. However, their thermal performance is relatively low due to the low temperature of the available heat sources, but more importantly, due to the low efficiency of the employed expander. Designing the turboexpander is exceptionally challenging, because the flow field is highly supersonic and unsteady, and since the expansion takes place in the highly non-ideal dense-vapor region. In this work, we perform unprecedented three-dimensional unsteady simulations of several high-expansion cantilever ORC turbines to highlight distinctive loss mechanisms. The simulations indicate strong unsteady effects in the rotor blade passage, as a result of unsteady propagating shock waves interacting with viscous wakes and boundary layers. Moreover, the flow field in the rotor blade passage is strongly affected by three-dimensional secondary flow features and a sharp expansion in the shroud region at the inlet of the rotor blade. These span-wise mechanisms and unsteady flow interactions introduce irreversible losses which must be taken into account for designing highly efficient ORC expanders.

The Investigation of a Sliding Mesh Model for Hydrodynamic Analysis of a SUBOFF Model in Turbulent Flow Fields

A computational fluid dynamics (CFD)-based simulation using a finite volume code for a full-appendage DARPA (Defense Advanced Research Projects Agency) SUBOFF model was investigated with a sliding mesh model in a multi-zone fluid domain. Unsteady Reynolds Averaged Navier–Stokes (URANS) equations were coupled with a Menter’s shear stress transport (SST) k-ω turbulence closure based on the Boussinesq approximation. In order to simulate unsteady motions and capture unsteady interactions, the sliding mesh model was employed to simulate flows in the fluid domain that contains multiple moving zones. The pressure-based solver, semi-implicit method for the pressure linked equations-consistent (SIMPLEC) algorithm was employed for incompressible flows based on the predictor-corrector approach in a segregated manner. After the grid independence test, the numerical simulation was validated by comparison with the published experimental data and other numerical results. In this study, the capability of the CFD simulation with the sliding mesh model was well demonstrated to conduct the straight-line towing tests by analyzing hydrodynamic characteristics, viz. resistance, vorticity, frictional coefficients, and pressure coefficients.

Aerodynamically induced noise of a lift-offset coaxial rotor with pitch attitude in high-speed forward flight

This paper investigates both acoustics and performance of a lift-offset coaxial rotor based on a first-principles and high-fidelity CFD (Computational Fluid Dynamics) and CSD (Computational Structural Dynamics) loose coupling approach in high-speed forward flight at different vehicle pitch attitudes. The pitch attitudes selected for this research are −5∘, 0∘, and 5∘. Detailed aerodynamic analyses are performed at two flight speeds: 150 (278 km hr−1) and 200 knots (370 km hr−1). A total of six major unsteady aerodynamic interactions are identified: 1) hub-wake interaction, 2) self-BVI (blade-vortex interaction), 3) parallel rotor-to-rotor BVI, 4) blade-crossover events, 5) root-induced BVI, and 6) reversed-flow-edge-vortex interactions. The strength of these interactions is found to be dependent on vehicle pitch attitude. The cases with a negative pitch attitude show significantly stronger impulsive pressure pulses, which is found to be induced by parallel rotor-to-rotor BVIs of the lower rotor. It is shown that the positive and zero pitch attitude cases tend to dominate the acoustic region on the starboard side of the coaxial rotor, whereas the negative pitch attitude case shows higher acoustic pressure peaks on the port side. Overall, the high-speed case with a positive pitch attitude shows significant improvement in rotor aerodynamic efficiency, rotor acoustics, and vehicle power performance at high speed. The hemispherical acoustic simulation results also show that the noise is less likely to propagate in the forward direction at a positive pitch attitude in high-speed forward flight.

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.

Tower shadow excitation of a downwind rotor blade of a turbine with a tubular tower

The downwind configuration of wind turbines offers benefits regarding the blade-tower clearance, as during operation the blade primarily bends away from the tower. Consequently, the blades can be designed with lower stiffness. For tubular towers, however, a significant deficit of the wind speed in the tower wake occurs, resulting in fatigue-inducing vibrations. For this reason, full-height lattice towers are considered the preferred support structures for wind turbines with a downwind rotor. This work estimates the tower shadow excitation of a downwind rotor blade from a tubular tower. To this end, the blade of a commercial 6 MW downwind turbine is modelled with finite-elements. The tower wake is described on the basis of Madsen’s model and for the unsteady aerodynamic interaction Küssner’s function is adopted. At below- and above-rated wind conditions, the tower wake-induced vibrations are compared with the response of a blade of an equivalent upwind rotor, considering both the tip deflections and the root moments, the latter on the basis of damage-equivalent moments, to obtain an indication of the expected difference in fatigue damage. The downwind blade experiences vibrations with considerable larger amplitudes, especially in the out-of-plane direction. From the damage-equivalent moments it can be inferred that the blades of the downwind rotor encounter a much faster accumulation of fatigue damage.

Complete liquid-solid momentum coupling for unresolved CFD-DEM simulations

Liquid-solid systems are frequently encountered in industrial processes and it is broadly recognised that numerical simulations are a useful tool for gaining insight in these processes. In this study, the unresolved CFD-DEM approach is extended with a complete momentum coupling for liquid-solid flows. Established correlations are used for the drag and lift forces, while new implementations are introduced for the unsteady interaction forces. A virtual mass force model based on the work of Felderhof (Felderhof 1991) is introduced, which accounts for the local particle volume fraction and the liquid-solid density ratio. The Basset history force, which is usually neglected due to computational difficulties related to its implementation, is evaluated according to the approach proposed by Parmar et al. A liquid fluidised bed is used as a demonstration case for the extended model. In this work, it is shown that with appropriate stabilisation measures, the Basset history force is approximated accurately (within 5%), while computational efficiency is maintained ( < 30% increase in computational time). Furthermore, the relevance of the complete momentum coupling is demonstrated by analysis of the solids mixing in the liquid fluidised bed. It is shown that when accounting for the complete interaction force, solids mixing is up to 20% slower compared to simulations with the drag-only approach.

Method for solving plane unsteady contact problems for rigid stamp and elastic half-space with a cavity of arbitrary geometry and location

In the work, the process of unsteady contact interaction of rigid stamp and elastic half-space having a recessed cavity of arbitrary geometry and location with a smooth boundary was investigated. Three variants of contact conditions are considered: free slip, rigid coupling, and bonded contact. The method for solving the problem is constructed using boundary integral equations. To obtain boundary integral equations, the dynamic reciprocal work theorem is used. The kernels of integral operators are bulk Green functions for the elastic plane. Because of straight-line approximations of the domain boundaries with respect to the spatial variable and straight-line approximations of the boundary values of the desired functions with respect to time, the problem is reduced to solving a system of algebraic equations with respect to the pivotal values of the desired displacements and stresses at each time interval. One of the axes is directed along the regular boundary of half-space, the second - deep into half-space.

Experimental Investigation of Vortex-Tube Streamwise-Vorticity Characteristics and Interaction Effects with a Finite-Aspect-Ratio Wing

An experimental study is conducted to analyze a streamwise-oriented vortex and investigate the unsteady interaction with a finite-aspect-ratio wing. A pressurized vortex tube is used to generate streamwise vortices in a wind tunnel and the resulting flow behavior is analyzed. The vortex tube, operated at various pressures, yields flows that evolve downstream under several freestream wind tunnel speeds. Flow measurements are performed using two- and three- dimensional (2D and 3D) particle image velocimetry to observe vortices and their freestream interactions from which velocity and vorticity data are comparatively analyzed. Results indicate that vortex velocity greater than freestream flow velocity is a primary factor in maintaining vortex structures further downstream, while increased supply pressure and reduced freestream velocity also reduce vortex dissipation rate. The generated streamwise-oriented vortex is also impinged on a finite-aspect-ratio airfoil wing with a cross-section of standard NACA0012 airfoil. The wingtip-aligned vortex is shown to investigate the interaction of the streamwise vortex and the wingtip vortex region. The results indicate that the vorticity at the high vortex-tube pressure has a significant effect on the boundary layer of airfoil.

Effects of Bionic Volute Tongue on Aerodynamic Performance and Noise Characteristics of Centrifugal Fan Used in the Air-conditioner

The aerodynamic noise generated by the centrifugal fan used in the air conditioner is related to the comfort of human living and working, which can be controlled by using the bionic design and optimization of key components of centrifugal fan. Inspired by the non-smooth leading edge of long-eared owl wing, eight kinds of volute tongues are proposed to reduce the aerodynamic noise of a centrifugal fan. The flow and sound characteristics are numerically investigated by incorporating computational fluid dynamics and computational aero-acoustics. The optimal result exhibits a noise reduction of up to 1.5 dB with a slight increase in mass flow rate. The acoustic characteristics, with respect to the sound pressure level, power spectral density, and sound directivity are discussed. The time-domain, frequency-domain, and root mean square values of pressure fluctuation are monitored and analyzed to assess the unsteady flow interaction between the volute tongue and impeller. The intensity and scale of vortices in the centrifugal fan are suppressed in the upstream and downstream of the bionic volute tongue, and the turbulence effect on the surface of the volute tongue becomes even and weak.

Effects of unsteady interaction on the performance of an ultra-high-pressure-ratio centrifugal compressor

A numerical investigation of an ultra-high-pressure-ratio centrifugal compressor is presented, mainly focusing on the unsteady impeller-diffuser interaction. The compressor is characterized by a high total pressure ratio of about 11.5 and a small radial gap between the impeller and diffuser, whose radius ratio is 1.067. The unsteady effect is stringently assessed by comparing the results of steady and unsteady Reynolds-averaged Navier–Stokes simulations. Within the impeller, the unsteady perturbation, dominated by the blade passing frequency of the diffuser, can only propagate to 20% of the normalized streamwise length from the impeller outlet. The velocity component distribution at the impeller outlet is affected by the unsteadiness, resulting in a variation of the impeller efficiency. In contrast with the impeller, the unsteady perturbation is present inside the whole diffuser passage. The circumferential flow angle variation at the diffuser inlet induces the unsteady formation and shedding of the diffuser leading edge vortex, increasing the flow loss correspondingly. However, the smaller incidence angle at the diffuser inlet makes for better diffusion inside the diffuser passage. The positive and negative effects of the unsteadiness counteract each other. Therefore, both the stage and component performances change slightly, although the flow field changes significantly due to the unsteadiness.

Unsteady fluid-structure interactions in a soft-walled microchannel: A one-dimensional lubrication model for finite Reynolds number

We develop a one-dimensional model for the unsteady fluid--structure interaction (FSI) between a soft-walled microchannel and viscous fluid flow within it. A beam equation, which accounts for both transverse bending rigidity and nonlinear axial tension, is coupled to a one-dimensional fluid model obtained from depth-averaging the two-dimensional incompressible Navier--Stokes equations across the channel height. Specifically, the Navier--Stokes equations are scaled in the viscous lubrication limit relevant to microfluidics. The resulting set of coupled nonlinear partial differential equations is solved numerically through a segregated approach employing fully-implicit time stepping. We explore both the static and dynamic FSI behavior of this example microchannel system by varying a reduced Reynolds number $Re$, which necessarily changes the Strouhal number $St$, while we keep the geometry and a modified dimensionless Young's modulus $\Sigma$ fixed. At steady state, an order-of-magnitude analysis (balancing argument) shows that the axially-averaged pressure in the flow, $\langle P\rangle$, exhibits two different scaling regimes, while the maximum deformation of the top wall of the channel, $H_{\mathrm{max}}$, can fall into four different regimes, depending on the magnitudes of $Re$ and $\Sigma$. These regimes are physically explained as resulting from the competition between the inertial and viscous forces in the fluid flow as well as the bending resistance and tension in the elastic wall. Finally, the linear stability of the steady inflated microchannel shape is assessed via a modal analysis, showing the existence of many highly oscillatory but stable modes, which further highlights the computational challenge of simulating unsteady FSIs.

Vortex sound interaction in acoustic resonance of a flow duct containing a plate

Acoustic resonance induced by vortex shedding from a flat plate in a flow duct has been widely concerned in a variety of engineering applications. However, the unsteady vortex sound interaction is still an open issue. A nonlinear physical model is established based on three meshless sub-models, including the discrete vortex method (DVM) for vortex shedding, the vortex sound theory for sound radiation and the time-domain boundary element method (TDBEM) for sound propagation within the duct. Then, the feedback effect of sound wave is considered by adding acoustic particle velocity onto the potential flow of vortex shedding, which makes the coupling process bidirectional. Both the flow field, sound field and their unsteady interaction are obtained simultaneously. The predicted resonant frequency and amplitude results are in accordance with the previous experiment data, especially, the lock-in phenomenon is reasonably captured. By comparing the numerical results with and without acoustic feedback, it reveals that the feedback sound plays a significant role in the onset of lock-in phenomenon, including enhancing the strength and modulating the frequency of vortex shedding. It helps to get a more detailed insight into the underlying physical process of vortex sound interaction for studying control strategy.

Flow-induced vibration of one-fixed-one-free tandem arrangement cylinders with different mass-damping ratios using wind tunnel experiment

Flow-induced vibration (FIV) of an elastically mounted circular cylinder with four different mass-damping parameters m∗ζ (= 0.184, 0.288, 0.407, 0.719) placed in the wake of a fixed one has been studied in a wind channel at Reynolds number Re= 4000–48000. The spacing ratios S/D are from 1.1 to 8.0 (where S is the center-to-center spacing and D is the cylinder diameter). Two initial conditions, ‘from rest’ and ‘increasing velocity’, are used in the test. The vibration amplitude responses, oscillation frequency and vortex shedding frequency are analyzed and discussed. Based on the m∗ζ, S/D and initial conditions, results indicate that, for both ‘from rest’ and ‘increasing velocity’ cases, the downstream cylinder exhibits three regimes of vibration responses: pure VR (vortex resonance), separated VR and wake-induced galloping (WIG), and combined VR and WIG. However, the S/D for the occurrence of each regime will be changed depending on m∗ζ and initial conditions. Vortex resonance, gap flow and the unsteady vortex-structure interactions can contribute to the vibrations. When the spacing is small, an obvious hysteresis phenomenon can be observed for ‘from rest’ and ‘increasing velocity’. As S/D increases, the hysteresis can be negligible and the vibration characteristics are nearly the same for various initial conditions. By comparing with the results between high m∗ζ performed in wind tunnel at present and low m∗ζ in water tunnel, it can be found that, with the increasing of m∗ζ, the vibration amplitude and region are gradually decreasing. And the vibration regime, oscillation frequency and vortex shedding frequency are significantly different.

Dynamics of unsteady asymmetric shock interactions

The response of asymmetric and planar shock interactions to a continuous excitation of the lower incident shock is investigated numerically. Incident shock waves and centred expansion fans are generated by two wedges asymmetrically deflecting the inviscid free stream flow at Mach 3. The excitations mechanisms considered are (i)Â pitching of the lower wedge traversing the steady-state dual-solution domain (DSD) of regular interaction (RI) and Mach interaction (MI), (ii) a periodic (sinusoidal) oscillation of the lower wedge deflection with a mean value both within and outside of the steady-state DSD and (iii) a periodic (sinusoidal) streamwise oscillation of the lower wedge location with fixed wedge deflection. A detailed analysis of characteristic unsteady flow features, including the Mach stem growth, pressure evolution across the shock system and corresponding flow deflections and entropy rise, is presented with a focus on the bi-directional RIMI transition process. For fast pitching conditions, the MI pattern is maintained far inside the steady-state RI domain. The observed transition limit as the rotational velocity decreases does not fully match steady-state theory, however. This is attributed to geometry-related effects. In the opposite case, transition, good agreement with steady-state theoretical predictions is obtained for slow rotations, and a shock polar analysis applied in the (moving) frame of reference of the shock interaction location improves the agreement with fast pitching numerical data significantly. Furthermore, the MI pattern is found to be more robust against periodic perturbations than the corresponding RI configuration for mean flow conditions inside the steady-state DSD, which appears to be a consequence of the dynamics of the Mach stem during a period of excitation. This is not the case for mean flow conditions outside the steady-state DSD in the RI domain for which a periodic alternation occurs instead.

Analysis of shape optimization problems for unsteady fluid-structure interaction

Shape optimization via the method of mappings is investigated for unsteady fluid-structure interaction (FSI) problems that couple the Navier–Stokes equations and the Lamé system. Building on recent existence and regularity theory we prove Fréchet differentiability results for the state with respect to domain variations. These results form an analytical foundation for optimization und inverse problems governed by FSI systems. Our analysis develops a general framework for deriving local-in-time continuity and differentiability results for parameter dependent nonlinear systems of partial differential equations. The main part of the paper is devoted to conducting this analysis for the FSI problem, transformed to a shape reference domain. The underlying shape transformation—actually we work with the corresponding shape displacement instead—represents the shape and the main result proves the Fréchet differentiability of the solution of the FSI system with respect to the shape transformation.

Discussion on “Review of CFD studies on axial-flow self-rectifying turbines for OWC wave energy conversion” by Cui, Y., Liu, Z., Zhang, X. and Xu, C.

This discussion is based on the paper by Cui et al. (2019) (hereafter identified as “the original authors” or “the original paper”). The original authors present a review on the application of CFD in the analysis of self-rectifying turbines for OWC wave energy conversion devices. We feel that this review is incomplete, as it overlooks a number of papers published in recent years that gave a new explanation for a phenomenon largely studied in the last two decades and discussed in the original paper: the hysteresis in Wells turbine performance. In addition, the original authors, in their conclusions, envisage a larger use of CFD in the coming years, especially for the unsteady analysis of the chamber-turbine interaction, probably ignoring that several CFD studies focusing on this aspect have already been published. In fact, it is through three-dimensional time-dependent CFD studies of the unsteady interaction between chamber and turbine that the explanation of the cause of the hysteresis was found. The objective of this discussion is to clarify two important aspects: the chamber-turbine interaction and the turbine hysteresis, that in our opinion were not correctly analyzed in the original review paper by Cui et al.