Unsteady Velocity Research Articles

Instantaneous pressure determination from unsteady velocity fields using adjoint-based sequential data assimilation

A sequential data assimilation (DA) method is developed for pressure determination of turbulent velocity fields measured by particle image velocimetry (PIV), based on the unsteady adjoint formulation. A forcing term F, which is optimized using the adjoint system, is added to the primary Navier–Stokes (N–S) equations to drive the assimilated flow toward the observations at each time step. Compared with the conventional unsteady adjoint method, which requires the forward integration of the primary system and the backward integration of the adjoint system, the present approach integrates the primary-adjoint system all the way forward, discarding the requirement of data storage at every time step, being less computationally resource-consuming, and saving space. The pressure determination method of integration from eight paths [J. O. Dabiri et al., “An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements,” J. Exp. Biol. 217, 331 (2014)] is also evaluated for comparison. Using synthetic PIV data of a turbulent jet as the observational data, the present DA method is able to determine the instantaneous pressure field precisely using the three-dimensional velocity fields, regardless of the observational noise. For the two-dimensional three-component (3C) or two-component (2C) velocity fields, which are not sufficient for pressure determination by the integration method due to the lack of off-plane derivatives, the present DA method is able to reproduce pressure fields whose statistics agree reasonably well with those of the referential results. The 3C and 2C velocity fields yield quite similar results, indicating the possibility of pressure determination from only planar-PIV measurements in turbulent flows. The tomography PIV measurements are also used as observational data, and a clear pressure pattern is obtained with the present DA method.

Experimental study of swirling flow from conical diffusers using the water jet control method

The actual requirements of the energy market enforce the hydraulic turbine to operate far from the best efficiency point. When hydraulic turbines operate at partial discharge, downstream of the runner (in the conical diffuser), the decelerated swirling flow becomes highly unstable. In these conditions a spiral vortex breakdown occurs, also known in engineering literature as the precessing vortex rope. The flow unsteadiness produced by the vortex rope results in severe pressure fluctuations that hinder the turbine operation or may cause accidents. We propose the water jet method for decelerated swirling flow with vortex rope from conical diffuser to mitigate the unsteadiness. The method involves injecting water at the inlet of the conical diffuser. Initial experimental investigations of the unsteady pressure field at conical diffuser wall reveal that the water injection method mitigates the pressure pulsations associated to the precessing vortex rope. In this paper, we investigate experimental measurements of the unsteady velocity field in a conical diffuser using LDA (Laser Doppler Anemometry). The main goal of the paper is to show how different water-jet discharge rates change the velocity field and the characteristics of the vortex rope in the wake.

Vortex dynamics and scalar transport in the wake of a flat-plate controlled by a vibrating trailing-edge flap

We investigate the onset and development of vortical flow disturbances introduced into the wake of a horizontally fixed flat-plate by means of the controlled motion of a trailing edge flap. The vibrating mechanics of the flap allows for the introduction of both impulsive and harmonic weak amplitude velocity disturbances which are propagated downstream into the wake flow of the flat-plate. Quantitative experimental and numerical predictions of both steady and unsteady wake flow velocity resulting from different flapping frequencies are made at low Reynolds numbers (Re < 104). Frequency response tests of the wake confirmed the existence of two dominant frequencies where the wake flow organises with a particular arrangement of downstream moving vortex structures. Numerical predictions of steady (unforced) and forced wake velocity profiles and kinetic energy profiles are in good agreement with the experimental results. In order to understand practical implications of the dominant vortex structures in scalar transport, we have extended the numerical part of the study solving for the concentration equation of a passive scalar being injected in particular regions of the physical domain. A spatial correlation between the trajectory of vortex structures and the scalar concentration downstream the wake is observed. Moreover, the onset of tip vortex structures produced during the forcing cycle seems to be responsible of a local increase of scalar concentration near the span wise flap ends.

A numerical investigation on the unidirectional unsteady oscillatory wind flow over a fixed isolated downsized barchan dune.

Turbulent wind patterns over a two-dimensional isolated downsized barchan dune under the influence of sinusoidal inflow with different amplitudes and periods are simulated. The evolution rules of wind velocity over time at different positions are revealed. The flow reattachment distance and turbulence intensity distribution are also compared. The results show that wind velocities at different positions of the dune whose similar evolvement process of going from short-term fast adjustment transition to long-term stable sinusoidal fluctuation, can be reasonably estimated by the present simulation. It is found that, for the leeward toe of a dune with complex reversed flow, the balance position value of the sinusoidal wind velocity fluctuation is no longer close to the value of the steady wind velocity but shows a velocity deviation of about 0.40m/s. The flow reattachment distances under different unsteady inflows ultimately show a sinusoidal fluctuation with time, and their values are all larger than that of the steady flow. These synthetically predict that the unsteady flow has a stronger shaping effect on the leeward side of the dune body by enhancing sand transport. In addition, the predicted distribution comparison between unsteady wind velocity and turbulence intensity indicates that the unsteady wind velocity has a dominant effect on the turbulence intensity.

Uncertainty in finite-time Lyapunov exponent computations

The Finite-Time Lyapunov Exponent (FTLE) is a well-established numerical tool for assessing stretching rates of initial parcels of fluid, which are advected according to a given time-varying velocity field (which is often available only as data). When viewed as a field over initial conditions, the FTLE's spatial structure is often used to infer the nonhomogeneous transport. Given the measurement and resolution errors inevitably present in the unsteady velocity data, the computed FTLE field should in reality be treated only as an approximation. A method which, for the first time, is able for attribute spatially-varying errors to the FTLE field is developed. The formulation is, however, confined to two-dimensional flows. Knowledge of the errors prevent reaching erroneous conclusions based only on the FTLE field. Moreover, it is established that increasing the spatial resolution does not improve the accuracy of the FTLE field in the presence of velocity uncertainties, and indeed has the opposite effect. Stochastic simulations are used to validate and exemplify these results, and demonstrate the computability of the error field.

Flow Behaviour in the calciner of cement production

Calciner was one of the cement production unit that used momentum, heat, mass distribution and chemical reaction to change calcium carbonate into calcium oxide. One of the important processes was fluid flow. Thus, the computational fluid dynamic was used to predict the flow behavior in the calciner. Regarding gas hydrodynamics, the Navier-Stokes equations were applied along with all practical operating conditions. The simulation results showed that both sides of calciner had the same velocity. High velocity was originated from decreasing of flow area. The velocity in the conjunction zone between TAD and Kiln had high unsteady velocity distribution but, in the higher level, the velocity approached a steady state. This simulation model could be used as a preliminary data in order to predict the temperature distribution.

Lagrangian Analysis of Flame Dynamics in the Flow Field of a Bluff Body-Stabilized Combustor

Abstract Experiments are performed in a partially premixed bluff body-stabilized turbulent combustor by varying the mean flow velocity. Simultaneous measurements obtained for unsteady pressure, velocity, and heat release rate are used to investigate the dynamic regimes of intermittency (10.1 m/s) and thermoacoustic instability (12.3 m/s). Using wavelet analysis, we show that during intermittency, modulation of heat release rate occurring at the acoustic frequency fa by the heat release rate occurring at the hydrodynamic frequency fh results in epochs of heat release rate fluctuations where the heat release rate is phase locked with the acoustic pressure. We also show that the flame position during intermittency and thermoacoustic instability are essentially dictated by saddle point dynamics in the dump plane and the leading edge of the bluff body.

Efficient numerical representation of the impacts of flexible plant reconfiguration on canopy posture and hydrodynamic drag

This study considered a new approach for representing flexible canopies within large-eddy simulation that captures the impacts of reconfiguration on both the canopy posture and the canopy drag. The unsteady change in plant posture in response to the passage of turbulence structures (monami) was assessed using established steady-reconfiguration models responding to the unsteady velocity at the top of the canopy. The new drag and plant posture models improved the modelling of highly flexible canopies by more accurately capturing the observed vertical distribution of peak Reynolds stress. When compared to models that do not consider reconfiguration, or that represent it only through a velocity-dependent drag coefficient, the addition of a velocity-dependent canopy posture (unsteady reconfiguration) achieved up to a 56% reduction of the root mean square error for mean horizontal flow velocity and Reynolds stress profiles over the canopy. The RMSE for turbulence intensities and skewness were reduced up to 48% and 56%, respectively.

On unsteady velocity measurements and profiling in compression waves in an asymmetrical trapezoidal channel

A compression wave is a highly-unsteady rapidly-varied free-surface flow associated with a sudden rise in water surface elevation and may travel over very long distances along flat prismatic canals. New experiments were conducted to investigate the unsteady turbulent characteristics of compression waves, in a large-size channel. The focus was on the effects of the asymmetrical trapezoidal shape of the channel cross-section on the transient turbulence characteristics of the three-dimensional compression wave. The measurements showed a complicated unsteady motion down the transverse slope, underneath the leading edge of the compression wave. A marked increase in free-surface elevation was observed during the surge passage. A three-dimensional transient motion was observed. An intense transient recirculation was seen next to the invert at the base of the transverse slope and in the shallow flow zones. Visual observations and velocity measurements showed some recirculation primarily in the shallow water region. The results highlighted strong secondary currents on the transverse slope, albeit for short, transient periods.

On an analytical explanation of the phenomena observed in accelerated turbulent pipe flow

This research presents a new theory that explains analytically the behaviour of any fully developed incompressible turbulent pipe flow, steady or unsteady. We propose the name of theory of underlying laminar flow (TULF), because its main consequence is the description of any turbulent pipe flow as the sum of two components: the underlying laminar flow (ULF) and the purely turbulent component (PTC). We use the framework of the TULF to explain analytically most of the important and interesting phenomena reported in He &amp; Jackson (J. Fluid Mech., vol. 408, 2000, pp. 1–38). To do so, we develop a simple model for the pressure gradient and Reynolds shear stress that could be applied to the linearly accelerated pipe flow described by He &amp; Jackson (2000). The following features of the unsteady flow are explained: the deformation undergone by the mean velocity profiles during the transient, the velocity overshoot observed in the more rapid excursions, the dual deformation of mean velocity profiles when overshoots are present, the laminarisation effects described during acceleration, the rapid decrease of the Reynolds shear stress upon approaching the wall that brings forth the laminar sublayer, and some other minor effects. A new field is defined to characterise the degree of turbulence within the flow, directly calculable from the theory itself. Arguably, this new field would describe the degree of turbulence in a pipe flow more accurately than the familiar turbulence intensity parameter. Finally, a paradox is found in the deformation of the unsteady mean velocity profiles with respect to equal-Reynolds-number steady profiles, which is duly explained. The research also predicts the occurrence of mean velocity undershoots if the flow is decreased rapidly enough.

Synchronization of dual diffusion flame in co-flow

In this study, the interaction of two adjacent diffusion flames (dual flame) were experimentally investigated using the direct imaging method and particle image velocimetry (PIV) measurements for varied distances between the two flames under the influence of the co-flow. The direct imaging method indicates the presence of various synchronization modes, such as merging, in-phase synchronization, amplitude death, anti-phase synchronization, and desynchronization, as the distance between the flames was increased. The dual flame synchronization was characterized using an image analysis of the time-series variation of flame heights summarized by the mean flame height, root-mean-square of the flame height, Strouhal number, and the cross-correlation coefficient of flame heights against the burner distance. Furthermore, the unsteady velocity fields of the synchronized flames were measured using PIV combined with the proper orthogonal decomposition (POD) analysis to extract the flow structure of the dual flame. The experimental results indicated that the in-phase mode is characterized by the formation of symmetrical vortices, whereas the anti-phase mode features the formation of asymmetrical vortices inside and outside of the flame. The POD analysis demonstrated higher fluctuating energy in the anti-phase mode than in the in-phase mode, which suggested the formation of a highly organized flame structure in the anti-phase mode.

The flow of nano-liquid film in the presence of operative Prandtl number model through an unsteady stretchable disc

This paper examines the impact of magnetohydrodynamic (MHD) over a thin film of variable thickness. A scattering of nano-liquid through a radially extending disc with unsteady stretchable velocity is considered. In the boundary layer flow, the contribution of nano-liquid is more efficient to improve the thermal and convective heat transport. Prandtl number model of dynamic viscosity and thermal conductivity is examined using the preliminary result of nanofluid flow. In this scenario, nano-element like water base Alumina (γAl2O3−H2O) and ethylene glycol base Alumina (γAl2O3−C2H6O2) are working nanofluids. Make use of appropriate self-similar conversion, the system of model partial differential equations (PDEs) with strong nonlinearity is converted into a non-dimensional set of couple ODEs (Ordinary Differential Equations). Consequently, the system of these transformed equations is analytically explained by implementing Optimal Homotopy Analysis Method (OHAM). The effects of embedded parameters such as magnetic parameter (M), nanofluid volume fraction and Eckert number (Ec)) on involved distributions are interpreted graphically to examine the mass and heat transport features for both sorts of nanoparticles. Moreover, the (Cf) skin friction along with the (Nu) heat transport rate (Nusselt number) is formulated for different values of relevant variables.

Turbulence Amplitude Amplification in an Externally Forced, Subsonic Turbulent Boundary Layer

Experimental studies of the changes in turbulence characteristics inside a boundary layer due to external forcing were performed using hot-wire anemometry. The forcing was created by a periodically forced shear layer that was external to a compressible subsonic turbulent boundary layer. The convecting coherent structures in the shear layer create a concomitant unsteady pressure and velocity field and provide an external disturbance for the turbulent boundary layer on the wall of the tunnel close to the forced shear layer. Both the pressure and velocity fluctuations inside the boundary layer were simultaneously measured along with the forcing signal, and a phase-locked analysis was performed. Regions of amplified turbulence inside the boundary layer were observed. Near the wall, the region of amplified turbulence was slightly upstream or lagging of the external forcing and away from the wall it was downstream or leading the forcing signal. Analysis of the convective speeds in the region of amplified turbulence supported the existence of the critical layer inside the wake region of the boundary layer, and the critical layer is believed to be responsible for the amplified levels of the turbulence in the wake region. Various modulation and amplification correlation coefficients were computed and analyzed, and the results also indicated the presence of the critical layer. Examination of the phase-locked turbulence revealed similarities between the turbulence amplitude amplification results due to these externally forced experiments and modulation response of an internally forced, subsonic boundary layer in the literature.

A generalized non-reflecting inlet boundary condition for steady and forced compressible flows with injection of vortical and acoustic waves

This paper describes a new boundary condition for subsonic inlets in compressible flow solvers. The method uses characteristic analysis based on wave decomposition and the paper discusses how to specify the amplitude of incoming waves to inject simultaneously three-dimensional turbulence and one-dimensional acoustic waves while still being non-reflecting for outgoing acoustic waves. The non-reflecting property is ensured by using developments proposed by Polifke et al. [1, 2]. They are combined with a novel formulation to inject turbulence and acoustic waves simultaneously at an inlet. The paper discusses the compromise which must be sought by the boundary condition formulation between conflicting objectives: respecting target unsteady inlet velocities (for turbulence and acoustics), avoiding a drift of the mean inlet velocities and ensuring non-reflecting performances for waves reaching the inlet from the computational domain. This well-known limit of classical formulations is improved by the new approach which ensures that the mean inlet velocities do not drift, that the unsteady components of velocity (turbulence and acoustics) are correctly introduced into the domain and that the inlet remains non-reflecting. These properties are crucial for forced unsteady flows but the same formulation is also useful for unforced cases where it allows to reach convergence faster. The method is presented by focusing on the expression of the ingoing waves and comparing it with the classical NSCBC approach [3]. Four tests are then described: (1) the injection of acoustic waves through a non reflecting inlet, (2) the compressible flow establishment in a nozzle, (3) the simultaneous injection of turbulence and ingoing acoustic waves into a duct terminated by a reflecting outlet and (4) a turbulent, acoustically forced Bunsen-type premixed flame.

Leveraging LDV techniques for the investigation of unsteady turbomachinery flows

ABSTRACTSteps required for proper acquisition and processing of laser Doppler velocimetry data for turbomachinery research applications are addressed. Turbomachinery applications are difficult due to the small internal passages, high-frequency fluctuations, large turbulence intensities, and strong secondary flows resulting in low overall signal-to-noise ratios and narrowband noise sources that cannot be removed by simple band-pass filters. Special aspects that must be considered for successful and accurate laser Doppler velocimetry studies to be conducted in turbomachinery are discussed. Specifically, the design of the measurement volume size, reflection mitigation, engineering of seed particle size and injection schema, and alignment of the traverse mechanism are addressed in terms of their importance (from literature sources) and the solutions implemented by the authors. These techniques have been applied to successfully obtain three-component, unsteady velocity data in a high-speed centrifugal compressor for aeroengine application. Processing techniques are also presented including a novel mixture-model-based statistical method for narrowband noise isolation developed by the authors. The method, validation steps, and example results are presented, showing the successful rejection of noise with high accuracy, a low failure rate, and a significant reduction in required manual inspection. This newly developed method elucidated flow features that were not clear prior to the noise removal.

The effect of an unsteady flow incident on an array of circular cylinders

In this paper we investigate the effect of an inhomogeneous and unsteady velocity field incident on an array of rigid circular cylinders arranged within a circular perimeter (diameter $D_{G}$) of varying solid fraction $\unicode[STIX]{x1D719}$, where the unsteady flow is generated by placing a cylinder (diameter $D_{G}$) upwind of the array. Unsteady two-dimensional viscous simulations at a moderate Reynolds number ($Re=2100$) and also, as a means of extrapolating to a flow with a very high Reynolds number, inviscid rapid distortion theory (RDT) calculations were carried out. These novel RDT calculations required the circulation around each cylinder to be zero which was enforced using an iterative method. The two main differences which were highlighted was that the RDT calculations indicated that the tangential velocity component is amplified, both, at the front and sides of the array. For the unsteady viscous simulations this result did not occur as the two-dimensional vortices (of similar size to the array) are deflected away from the boundary and do not penetrate into the boundary layer. Secondly, the amplification is greater for the RDT calculations as for the unsteady finite Reynolds number calculations. For the two highest solid fraction arrays, the mean flow field has two recirculation regions in the near wake of the array, with closed streamlines that penetrate into the array which will have important implications for scalar transport. The increased bleed through the array at the lower solid fraction results in this recirculation region being displaced further downstream. The effect of inviscid blocking and viscous drag on the upstream streamwise velocity and strain field is investigated as it directly influences the ability of the large coherent structures to penetrate into the array and the subsequent forces exerted on the cylinders in the array. The average total force on the array was found to increase monotonically with increasing solid fraction. For high solid fraction $\unicode[STIX]{x1D719}$, although the fluctuating forces on the individual cylinders is lower than for low $\unicode[STIX]{x1D719}$, these forces are more correlated due to the proximity of the cylinders. The result is that for mid to high solid fraction arrays the fluctuating force on the array is insensitive to $\unicode[STIX]{x1D719}$. For low $\unicode[STIX]{x1D719}$, where the interaction of the cylinders is weak, the force statistics on the individual cylinders can be accurately estimated from the local slip velocity that occurs if the cylinders were removed.

Unsteady measurement of core penetration flow caused by rotating geometric non-axisymmetry in a turbine rotor-stator disc cavity

The existence and causes of the deep ingress into the core region of a turbine rotor-stator disc cavity, or core penetration flow, generated by a rotating non-axisymmetric geometry have been investigated experimentally. In a low-speed, low-expansion ratio, single-stage, cold turbine test facility, time-resolved tangential and radial velocities in the cavity have been measured with 2-D hot-wire anemometers. In addition, time-resolved static pressures on the stator disc have been measured with fast response pressure transducers, and unsteady cavity velocity field in the absolute frame has been measured using Particle Image Velocimetry (PIV). Rotating geometric non-axisymmetry leads to an unsteady radial pressure gradient in the disc cavity. A time lag in the tangential velocity adjustment to the variation in the radial pressure gradient results in a net radial force, causing core penetration flow. A first-harmonic rotating geometric non-axisymmetry makes the core penetration flow to occur three times per revolution (twice when the cavity exit pressure increases and once when the cavity exit pressure decreases) and to revolve at the disc’s rotational speed. Core penetration flow due to the rotating geometric asymmetry is not affected by variations in the annulus flow coefficient or rotational Reynolds number but is weakened by increasing purge air flow rate.

Characterizing hydrogen-fuelled pulsating combustion on thermodynamic properties of a combustor

Unlike hydrocarbon fuel, hydrogen is ‘green’ and attracting more and more attentions in energy and propulsion sectors due to the zero emission of CO and CO2. By applying numerical simulations, we explore the physics of how a hydrogen-burnt flame can sustain pulsating combustion and its impact on the thermodynamic properties of a standing-wave combustor. We also explain how implementing a heat exchanger can mitigate such pulsating combustion. The dynamic interactions of the unsteady flow-flame-acoustics-heater are examined by varying the mass flow rate ṁH2 and the heating bands’ surface temperature TH. The frequency and amplitude of the pulsating combustion are shown to depend strongly on ṁH2. In addition, varying TH is shown to lead to not only the molar fraction of the combustion species being changed but also the flame-sustained pulsating oscillations being mitigated somehow. Finally, nonlinearity is observed and identified in the unsteady flow velocity and the two heat sources.

Vorticoacoustic Stability of Solid Rocket Motors: A Numerical Study

This work presents highly resolved Navier–Stokes simulations in a cylindrical solid rocket motor. The study focuses on the vorticoacoustic interactions and their role on motor stability. This paper proposes comparisons between simulations and available theories on unsteady axial velocity but also radial velocity, pressure, temperature, and entropy. Overall, the agreement is excellent except for pressure, which is found to be purely acoustic in simulations (i.e., no vortical pressure). The role of radial velocity is further investigated because it gives rise to the rotational correction term in stability integrals. This paper shows that this term strongly depends on the definition of the propellant admittance, and it can actually be viewed as a part of the classical propellant pressure-coupled response. This study has also estimated damping terms directly by studying the decay of pressure perturbations in simulations and has compared them to classical stability integrals from theory. In keeping with the aforementioned results, the agreement is much better when rotational correction and vortical pressure terms are dropped.

High resolution LDA measurements in transitional oblique shock wave boundary layer interaction

Spatial development of a transitional Oblique Shock Wave Interaction at Mach 1.68 is presented. This type of flow is characterised by very small length scales (boundary layer thickness is smaller than 1mm), high velocities, reverse flows and a wide range of velocity fluctuations along the transition process. Unsteady velocity fields have been obtained using a high spatial resolution Laser Doppler Anemometry system, allowing quantitative measurements of the velocity fluctuations down to $$y/\delta =0.1$$ . A model to take into account the finite size of the probe volume on the mean and RMS velocity measurements is used and applied to the present measurements. Finally, the amplification of the velocity fluctuations along the transitional separated shear layer is described.