Unsteady Region Research Articles

Numerical investigation on characteristic flow regions for three staggered stationary circular cylinders

In this work, the characteristic flow regions for three stationary circular cylinders were numerically investigated by the multiple-relaxation-time (MRT) based lattice Boltzmann method (LBM). The immersed boundary method (IBM) was employed to handle the solid boundary of cylinders to account for the fluid–solid interaction. The cylinders were arranged in a staggered configuration, which means that one cylinder was placed in front of the others with side-by-side arrangement. The calculations were carried out at different spacing ratios T/D (varying from 1 to 10) and fixed spacing ratio S/D=3 with a constant Reynolds number Re=200, which represents a typical unsteady laminar flow. Here, D is the diameter of the cylinders, T is the spacing between the centers of two downstream cylinders, and S is the distance between the centers of the upstream cylinder and downstream cylinders. The experiments based on the laser-induced fluorescence (LIF) flow visualization were performed to verify the reliability of simulation results. The results indicated that the spacing ratio T/D has a significant influence on the wake structures. Two different characteristic steady and unsteady flow regions behind the upstream cylinder were observed. The characteristic steady flow occurs at the regions of 1≤T/D≤1.2 and 2.5≤T/D≤3.1, and the characteristic unsteady flow happens at the regions of 1.3≤T/D≤2.4 and 3.2≤T/D≤10. The present results would be helpful for designing multiple piers in the practical application.

Experimental study of transient air distribution of a jet collision region in an aircraft cabin mock-up

In commercial airliner, the mixing air distribution system in which air enters the cabin from the multi-slot diffusers underneath the luggage compartments and exhausted near the floor are most commonly used for air circulation, which result in two-jet collision regions with strong uncertainty and unsteady characteristics in cabin. In such unsteady regions, previous time-averaged data may miss much valuable information for studying thermal comfort, researching contaminant transport and verifying unsteady simulation modes. In this study, to experimentally explore more unsteady characteristics in cabin, we focused on this two-jet collision region in the middle of the aisle in the cabin, and a long time series of velocity fields was measured by particle image velocimetry (PIV) with a sampling frequency of 3Hz under both isothermal and cooling conditions. Through the measured data, the fluctuation characteristics of four typical points were discussed and compared under two operating conditions. By observing the long time series of the measured transient flow field, three typical instantaneous airflow fields were identified under each of the two conditions. Then, POD analysis was utilized to mathematically reveal the coherent structure from the various instantaneous flow fields. These high-quality experimental data of instantaneous flow fields are also valuable for validating transient simulation models.

Investigation of unsteady behaviors of forward and opposed flow combustion of solid fuel

We theoretically examine the characteristics of a combustion wave of solid fuel in a porous medium. We consider two problems (i) a sample is ignited at one of the either ends and (ii) a sample is ignited around the middle. Depending on the ignition process, forward and opposed modes of a combustion wave are found in the first problem while they simultaneously occurred in the second problem. Firstly, we make a comparative study between forward and opposed modes and secondly, we investigate the combined effects of these modes. Analytical expressions of combustion characters, namely, the moving speed of the reaction front and the spatial temperature and species profiles of the solid combustible, are obtained employing large activation energy asymptotics. It is found that the reaction fronts of both forward and opposed flows demonstrate unsteady behaviors for a higher thermal conductivity porous medium, a lower initial mass fraction of oxidizer and a lower gas flow velocity. The response of the moving speed of the reaction front of the forward mode to an increasing heat transfer coefficient is completely opposite to that of the opposed mode. In particular, the reaction front of the forward (opposed) flow becomes unsteady for lower (higher) heat transfer coefficient. However, for the middle ignition of a sample, the moving speed of the reaction front of the forward mode is found to monotonically increase with an increase of heat transfer coefficient, while in opposed mode it first increases and then decreases. The results also provide a remarkable finding that an “unsteady solution region” occurs in between the critical heat transfer coefficients of forward and opposed modes where the reaction fronts of both modes become unsteady. Moreover, the present solutions have been compared with previous numerical and experimental observations that show a qualitative agreement.

Assessment of Unsteady Pressure Measurement Uncertainty—Part II: Virtual Three-Hole Probe

With the advancements in miniaturization and temperature capabilities of piezoresistive pressure sensors, pneumatic probes—which are the long established standard for flow-path pressure measurements in gas turbine environments—are being replaced with unsteady pressure probes. On the other hand, any measured quantity is by definition inherently different from the “true” value, requiring the estimation of the associated errors for determining the validity of the results and establishing respective confidence intervals. In the context of pressure measurements, the calibration uncertainty values, which differ from measurement uncertainties, are typically provided. Even then, the lack of a standard methodology is evident as uncertainties are often reported without appropriate confidence intervals. Moreover, no time-resolved measurement uncertainty analysis has come to the attention of the authors. The objective of this paper is to present a standard method for the estimation of the uncertainties related to measurements performed using single sensor unsteady pressure probes, with the help of measurements obtained in a one and a half stage low pressure high speed axial compressor test rig as an example. The methodology presented is also valid for similar applications involving the use of steady or unsteady sensors and instruments. The static calibration uncertainty, steady measurement uncertainties, and unsteady measurement uncertainties based on phase-locked average (PLA) and ensemble average are presented by the authors in Dell'Era et al. (2016, “Assessment of Unsteady Pressure Measurement Uncertainty—Part 1: Single Sensor Probe,” ASME J. Eng. Gas Turbines Power, 138(4), p. 041601). Depending on the number of points used for the averaging, different values for uncertainty have been observed, underlining the importance of having greater number of samples. For unsteady flows, higher uncertainties have been observed at regions of higher unsteadiness such as tip leakage vortices, hub-corner vortices, and blade wakes. Unfortunately, the state of the art in single sensor miniature unsteady pressure probes is comparable to multihole pneumatic probes in size, preventing the use of multihole unsteady probes in turbomachinery environments. However, the angular calibration properties of a single sensor probe obtained via an aerodynamic calibration may further be exploited as if a three-hole directional probe is employed, yielding corrected total pressure, unsteady yaw angle, static pressure and Mach number distributions based on the PLAs with the expense of losing the time-correlation between the virtual ports. The aerodynamic calibration and derivation process are presented together with the assessment of the uncertainties associated to these derived quantities in this contribution. In the virtual three-hole mode, similar to that of a single sensor probe, higher uncertainty values are observed at regions of higher unsteadiness.

Assessment of Unsteady Pressure Measurement Uncertainty—Part I: Single Sensor Probe

With the advancements in miniaturization and temperature capabilities of piezoresistive pressure sensors, pneumatic probes—which are the long established standard for flow-path pressure measurements in gas turbine environments—are being replaced with unsteady pressure probes. Any measured quantity is by definition inherently different from the “true” value, requiring the estimation of the associated errors for determining the validity of the results and establishing respective confidence intervals. In the context of pressure measurements, the calibration uncertainty values, which differ from measurement uncertainties, are typically provided. Even then, the lack of a standard methodology is evident as uncertainties are often reported without appropriate confidence intervals. Moreover, no time-resolved measurement uncertainty analysis has come to the attention of the authors. The objective of this paper is to present a standard method for the estimation of the uncertainties related to measurements performed using single sensor unsteady pressure probes, with the help of measurements obtained in a one and a half stage low pressure (LP) high speed axial compressor test rig as an example. The methodology presented is also valid for similar applications involving the use of steady or unsteady sensors and instruments. The static calibration uncertainty, steady measurement uncertainties, and unsteady measurement uncertainties based on phase-locked average (PLA) and ensemble average are presented in this contribution. Depending on the number of points used for the averaging, different values for uncertainty have been observed, underlining the importance of having greater number of samples. For unsteady flows, higher uncertainties have been observed at regions of higher unsteadiness such as tip leakage vortices, hub corner vortices, and blade wakes. Unfortunately, the state of the art in single sensor miniature unsteady pressure probes is comparable to multihole pneumatic probes in size, preventing the use of multihole unsteady probes in turbomachinery environments. However, the angular calibration properties of a single sensor probe obtained via an aerodynamic calibration may further be exploited as if a three-hole directional probe is employed, yielding corrected total pressure, unsteady yaw angle, static pressure, and Mach number distributions based on the PLAs with the expense of losing the time-correlation between the virtual ports. The aerodynamic calibration and derivation process are presented together with the assessment of the uncertainties associated to these derived quantities by the authors in Dell'Era et al. (2016, “Assessment of Unsteady Pressure Measurement Uncertainty—Part II: Virtual Three Hole Probe,” ASME J. Eng. Gas Turbines Power, 138(4), p. 041602). In the virtual three-hole mode, similar to that of a single sensor probe, higher uncertainty values are observed at regions of higher unsteadiness.

Numerical simulations of the near wake of a sphere moving in a steady, horizontal motion through a linearly stratified fluid at Re = 1000

A numerical investigation of the near wake of a sphere moving horizontally through a linearly stratified fluid is presented. Simulations are first performed on a flow with Reynolds number Re = 200 for a range of internal Froude number, 0.1 ≤ Fr ≤ ∞. The simulations capture buoyant characteristic behavior, the presence of vortex shedding at low Fr, and lee waves. Simulations at higher Reynolds number, Re = 1000, for 1 ≤ Fr ≤ ∞ provide a description and parametrization of the near wake, including the density field. At Re = 1000, the effects of utilizing two different averaging techniques in the unsteady near wake region are discussed. Perturbation quantities in the stratified near wake are anisotropic, and based on the oscillations of the centerline vertical perturbation velocity, the Fr at which the stratified near wake may be considered indistinguishable from the uniform density near wake is suggested to be O(100). Parametrization of the near wake is accomplished using the parameterized vertical wake height, downstream distance from the sphere, and Fr as parameters.

Influence of Prandtl number on the instability of natural convection flows within a square enclosure containing an embedded heated cylinder at moderate Rayleigh number

Influence of Prandtl number (0.07 ≤ Pr ≤ 7) on the buoyancy induced flow within a square domain containing an embedded heated cylinder is investigated numerically at moderate Rayleigh number (2 × 105 − 2 × 106). In general, reduction of Prandtl number thickens the thermal boundary layer, and hence, the decrease of predicted Nusselt number is observed. However, the dynamic boundary layer becomes thin and this leads to the increase of internal counter rotating vortex pairs and further to the breakdown of vortex symmetry and hence the eventual instability. In the unsteady regime, the Nusselt number oscillation frequency is as expected twice of other flow variables and increases with the reduction of Prandtl number. For the Rayleigh number investigated, the unsteady-regime is dominated by the growth of thermal boundary layer and hence the averaged Nusselt number decreases accordingly. Also, different scaling laws for the Nusselt number exist due to the change of vortex structures in the steady and unsteady regions. Rayleigh number and Boussinesq number are the proper scaling parameters in the respective steady and unsteady regions with higher and lower Prandtl numbers.

Turbulent ‘stopping plumes’ and plume pinch-off in uniform surroundings

Observations of turbulent convection in the environment are of variously sustained plume-like flows or intermittent thermal-like flows. At different times of the day the prevailing conditions may change and consequently the observed flow regimes may change. Understanding the link between these flows is of practical importance meteorologically, and here we focus our interest upon plume-like regimes that break up to form thermal-like regimes. It has been shown that when a plume rises from a boundary with low conductivity, such as arable land, the inability to maintain a rapid enough supply of buoyancy to the plume source can result in the turbulent base of the plume separating and rising away from the source. This plume ‘pinch-off’ marks the onset of the intermittent thermal-like behavior. The dynamics of turbulent plumes in a uniform environment are explored in order to investigate the phenomenon of plume pinch-off. The special case of a turbulent plume having its source completely removed, a ‘stopping plume’, is considered in particular. The effects of forcing a plume to pinch-off, by rapidly reducing the source buoyancy flux to zero, are shown experimentally. We release saline solution into a tank filled with fresh water generating downward propagating steady turbulent plumes. By rapidly closing the plume nozzle, the plumes are forced to pinch-off. The plumes are then observed to detach from the source and descend into the ambient. The unsteady buoyant region produced after pinch-off, cannot be described by the power-law behavior of either classical plumes or thermals, and so the terminology ‘stopping plume’ (analogous to a ‘starting plume’) is adopted for this type of flow. The propagation of the stopping plume is shown to be approximately linearly dependent on time, and we speculate therefore that the closure of the nozzle introduces some vorticity into the ambient, that may roll up to form a vortex ring dominating the dynamics of the base of a stopping plume.

Calculation of the Unstable Mixing Region in Zn_{1-x}Cd_xO Ternary Alloys

The Zn1−xCdxO ternary alloys with a narrow band gap, which are useful for light emitters in the visible wavelengths, are studied with respect to the unsteady region in mixing. This unstable region in mixing is calculated from the free energy of mixing using the strictly regular solution model. The interaction parameter used in this calculation is obtained by means of the valence-forceeld model. An in uence of the strain energy induced by substrate on the region of the spinodal decomposition for the Zn1−xCdxO system is studied and discussed.

Subtropical Western Boundary Currents over Slopes Detaching from Coasts with Inshore Pool Regions: An Indication to the Kuroshio Nearshore Path

Abstract The dynamics of subtropical western boundary currents over slopes detaching from coasts with inshore pool regions, where the water of the subtropical gyre does not enter and the velocity is small, are investigated. This study is intended to understand the dynamics of the nearshore path of the Kuroshio, which has a distinct boundary between the boundary current and the coastal water. Numerical experiments under idealized conditions are made. The results show flow patterns with pool regions similar to the Kuroshio under simple conditions. A deep countercurrent is present on the lower bottom slope, which represents observed deep currents. This is part of a deep cyclonic recirculation north of the jet, which extends to the lower bottom slope despite steep topography. This extension can be explained by the geostrophic contours. In this region, the upper boundary current feels the bottom slope and the westward intensification is blocked. In the other region, where the bottom-layer velocity is very small, the upper boundary current is free from the bottom slope and westward intensification occurs at the coast. The sensitivity to the volume transport of the boundary current is investigated by case studies. The pool regions are broken in cases with large volume transports. It is indicated that these unsteady inshore regions are produced by instability caused by an outcrop of the upper isopycnal, which is led by a large baroclinic volume transport.

Application of Particle Image Velocimetry and Reference Image Topography to jet shock cells using the hydraulic analogy

This paper examines the shock cell structure, vorticity and velocity field at the exit of an underexpanded jet nozzle using a hydraulic analogy and the Reference Image Topography technique. Understanding the flow in this region is important for the mitigation of screech, an aeroacoustic problem harmful to aircraft structures. Experiments are conducted on a water table, allowing detailed quantitative investigation of this important flow regime at a greatly reduced expense. Conventional Particle Image Velocimetry is employed to determine the velocity and vorticity fields of the nozzle exit region. Applying Reference Image Topography, the wavy water surface is reconstructed and when combined with the hydraulic analogy, provides a pressure map of the region. With this approach subtraction of surfaces is used to highlight the unsteady regions of the flow, which is not as convenient or quantitative with conventional Schlieren techniques. This allows a detailed analysis of the shock cell structures and their interaction with flow instabilities in the shear layer that are the underlying cause of jet screech.

Turbulent kinetic energy balance of an oscillatory boundary layer in the transition to the fully turbulent regime

The sinusoidal oscillation of a fluid in the vicinity of a rigid smooth wall is studied using the results of direct numerical simulation of the Navier–Stokes equations. Simulations are performed at a wave Reynolds number Rew =U max A/ν=1.41×106 in the turbulent regime. The computed statistics are compared with great success with the available experimental results reported in the literature for U max =1.02 m/s the maximum orbital velocity, A=1.58 m the amplitude of the water excursion, and ν=1.14×10−6 m2/s the kinematic viscosity of the fluid (Rew =U max A/ν=1.41×106). The simulation results allow to identify the development of an unsteady shear layer and regions of zero and negative turbulent kinetic energy (TKE) production. The TKE balance is studied in detail, analyzing the role of each of the terms in the balance equation and the relative relevance of different TKE transport mechanisms. It is found that the local derivative of the TKE is particularly important in the shear layer region. The present results provide an accurate and detailed dataset that could be used for validation of both analytical and numerical models of oscillatory boundary layer flows.

A comparative study of sharp and round-edge tools in machining with built-up edge formation: cutting forces, cutting vibrations, and neural network modeling

The tool edge radius significantly affects material deformation and flow, tool–chip friction, and a variety of machining performance measures (such as the cutting forces and tool wear) in mechanical micro/meso-scale machining. The tool edge-related research, either theoretically or experimentally, has been only focused in machining cases in which no built-up edge (BUE) is generated. To close this research gap, a comparative study of sharp and round-edge tools in orthogonal machining with BUE formation is conducted, including both experimental investigations and theoretical modeling. The experimental results show that the variations of the cutting forces are more stable in machining with a sharp tool than those in machining with a round-edge tool. A round-edge tool produces higher vibration magnitudes than does a sharp tool. The cutting vibrations do not necessarily have the same varying pattern as that of the cutting forces in machining with either a sharp tool or a round-edge tool. A neural network-based theoretical model is developed to predict three distinct regions of BUE formation (namely BUE Initiation Region, Steady BUE Region, and Unsteady BUE Region) in machining with a round-edge tool. The developed neural network model has been proven valid using a separate set of cutting experiments under different cutting conditions from those used for network training and testing.

Effect of the position of a circular cylinder in a square enclosure on natural convection at Rayleigh number of 107

Numerical calculations are carried out for the natural convection induced by temperature difference between a cold outer square cylinder and a hot inner circular cylinder for Rayleigh number of Ra=107. This study investigates the effect of the inner cylinder location on the heat transfer and fluid flow. The location of inner circular cylinder (δ) is changed vertically along the centerline of square enclosure. The natural convection bifurcates from unsteady to steady state according to δ. Two critical positions of δC,L and δC,U as a lower bound and an upper bound are δC,L=0.05 and δC,U=0.18, respectively. Within the defined bounds, the thermal and flow fields are steady state. In the unsteady region, the natural convection shows a single frequency and multiple frequency periodic patterns alternately according to δ. When the inner cylinder locates at δ≥δC,U, the space between the upper surface of inner cylinder and the top surface of the enclosure forms a relatively shallow layer where the natural convection characterized as the pure Rayleigh–Benard convection forms alternately the upwelling and downwelling plums. As a result a series of cells known as Benard cells is derived. The changes in heat transfer quantities have also been presented.

Wind tunnel tests for a flapping wing model with a changeable camber using macro-fibercomposite actuators

In the present study, a biomimetic flexible flapping wing was developed on areal ornithopter scale by using macro-fiber composite (MFC) actuators. Withthe actuators, the maximum camber of the wing can be linearly changed from−2.6% to+4.4% of the maximum chord length. Aerodynamic tests were carried out in a low-speed windtunnel to investigate the aerodynamic characteristics, particularly the camber effect, thechordwise flexibility effect and the unsteady effect. Although the chordwise wing flexibilityreduces the effective angle of attack, the maximum lift coefficient can be increased by theMFC actuators up to 24.4% in a static condition. Note also that the mean values of theperpendicular force coefficient rise to a value of considerably more than 3 in an unsteadyaerodynamic flow region. Additionally, particle image velocimetry (PIV) tests wereperformed in static and dynamic test conditions to validate the flexibility and unsteadyeffects. The static PIV results confirm that the effective angle of attack is reduced by thecoupling of the chordwise flexibility and the aerodynamic force, resulting in adelay in the stall phenomena. In contrast to the quasi-steady flow condition of arelatively high advance ratio, the unsteady aerodynamic effect due to a leading edgevortex can be found along the wing span in a low advance ratio region. The overallresults show that the chordwise wing flexibility can produce a positive effect onflapping aerodynamic characteristics in quasi-steady and unsteady flow regions; thus,wing flexibility should be considered in the design of efficient flapping wings.

Hydrodynamic Characterization of a Nozzle Check Valve by Numerical Simulation

The ability to obtain correct estimates of the hydraulic characteristics of a nozzle check valve by finite-volume numerical simulation is discussed. The evaluation of the numerical results is performed by comparison of the computed pressure drops inside the valve with experimental measurements obtained on an industrial check valve. It is shown that, even with high mesh refinement, the obtained result is highly dependent on the choice of the turbulence model. The renormalization group theory (RNG) k-ε model proves to be the more accurate to describe the flow inside the valve, which is characterized by repeated flow decelerations and accelerations and by boundary layer development under adverse pressure gradient. Pressure-drop and flow coefficients computed by adopting the RNG model agree well with the experimental values at different positions of the plug. The opening transient of the valve is also analyzed by an unsteady flow simulation where the motion of the plug is taken into account. The characteristic curve of the valve obtained in steady flow conditions is finally compared with the transient opening characteristic, highlighting a temporary increase in the pressure drop, which occurs because of a large unsteady separation region downstream of the plug.

Application of the SAS turbulence model to predict the unsteady flow field behaviour in a forward centrifugal fan

In the current study, the unsteady flow in a centrifugal fan is carried out using Computational Fluid Dynamics calculation based on the Scale Adaptive Simulation (SAS) approach to model the turbulence phenomenon. The SAS concept is based on the introduction of the von Karman length scale into the turbulence scale equation. The information provided by the von Karman length scale allows SAS models to dynamically adjust to resolved structures in an Unsteady Reynolds-Averaged Navier–Stokes (URANS) simulation, which results in a Large Eddy Simulation-like behaviour in unsteady regions of the flow field. At the same time, the model provides standard RANS capabilities in stable flow regions. The introduction of the von Karman length scale is based on the reformulation of Rottas's equation for the integral length scale. To validate the numerical results, the overall performances of the fan and the wall pressure fluctuations computed upon the volute casing surface are compared with the unsteady measured data.

Height and stability of laminar plane fountains in a homogeneous fluid

The behaviour of plane fountains, resulting from the injection of a denser fluid upwards into a large body of a lighter homogeneous fluid, is investigated numerically. The transient behaviour of fountains with a uniform inlet velocity, Reynolds number Re = 100, Prandtl number Pr = 7, and Froude number 0.25 ⩽ Fr ⩽ 10.0 is studied numerically. In the present case, the density variation is as a result of temperature difference between the fountain and the ambient fluids. Three distinct regimes are identified; steady and symmetric fountains for 0.25 ⩽ Fr ⩽ 2.0, unsteady fountains with periodic lateral oscillation for 2.25 ⩽ Fr ⩽ 3.0, and unsteady fountains with aperiodic lateral oscillations for Fr ⩾ 4.0. It is found empirically that the non-dimensional fountain height, z m , scales differently with Froude number in each of these regimes; in the steady and symmetric region z m ∼ Fr , in the unsteady and periodic lateral oscillation region z m ∼ Fr 1.15 and in the unsteady and aperiodic lateral oscillation region z m ∼ Fr 4 / 3 . The results are compared with previous numerical and experimental results, where available and are consistent.

A numerical investigation on the fluid flow and heat transfer in the confined impinging slot jet in the low Reynolds number region for different channel heights

The numerical solution is obtained for unsteady two-dimensional fluid flow and heat transfer in a confined impinging slot jet using the finite volume method. In order to consider the effect of Reynolds number and height ratio on the flow and temperature fields in the channel, the numerical simulations were performed for different Reynolds numbers of 50–500 and different height ratios of 2–5. The critical Reynolds number, beyond which the flow and thermal fields change their state from steady to unsteady, depends on the Reynolds number and height ratio. The unsteadiness gives a big impact on the flow and temperature fields and as a result the pressure coefficient, skin friction coefficient and Nusselt number in the unsteady region show different characteristics from those in the steady region.

Bifurcation behaviors of catalytic combustion in a micro-channel

Bifurcation analysis of ignition and extinction of catalytic combustion in a short micro-channel is carried out with the laminar flow model incorporated as the flow model. The square of transverse Thiele modulus and the residence time are used as bifurcation parameters. The influences of different parameters on ignition and extinction behavior are investigated. It is shown that all these parameters have great effects on the bifurcation behaviors of ignition and extinction in the short micro-channel. The effects of flow models on bifurcation behaviors of combustion are also analyzed. The results show that in comparison with the flat velocity profile model, for the case of the laminar flow model, the temperatures of ignition and extinction of combustion are higher and the unsteady multiple solution region is larger.