Quasi-steady Flow Research Articles

One-dimensional model for microscale shock tube flow

A one-dimensional model for the numerical simulation of transport effects in small-scale, i.e., low Reynolds number, shock tubes is presented. The conservation equations have been integrated in the lateral directions and three-dimensional effects have been introduced as carefully controlled sources of mass, momentum and energy, into the axial conservation equations. The unsteady flow of gas behind the shock wave is reduced to a quasi-steady flow by choosing a coordinate system attached to the shock. The boundary layer problem is thereby reduced to a laminar solution, similar to the Blasius solution, with the exception that the wall velocity can be nonzero. The resulting one-dimensional equations are then solved numerically using a two-step Lax-Wendroff/ MacCormack scheme with flux correction transport. For validation purposes, comparisons are performed against previously published shock structure and low Reynolds number shock tube experiments; good agreement is observed. The model has been used to predict the performance of a 10µm shock tube and the result of this simulation shows the possibility of shock wave disappearance at lower pressure ratios for a micro-scale shock tube.

MODIFICATION OF ANGULAR VELOCITY BY INHOMOGENEOUS MAGNETOROTATIONAL INSTABILITY GROWTH IN PROTOPLANETARY DISKS

We have investigated evolution of magneto-rotational instability (MRI) in protoplanetary disks that have radially non-uniform magnetic field such that stable and unstable regions coexist initially, and found that a zone in which the disk gas rotates with a super-Keplerian velocity emerges as a result of the non-uniformly growing MRI turbulence. We have carried out two-dimensional resistive MHD simulations with a shearing box model. We found that if the spatially averaged magnetic Reynolds number, which is determined by widths of the stable and unstable regions in the initial conditions and values of the resistivity, is smaller than unity, the original Keplerian shear flow is transformed to the quasi-steady flow such that more flattened (rigid-rotation in extreme cases) velocity profile emerges locally and the outer part of the profile tends to be super-Keplerian. Angular momentum and mass transfer due to temporally generated MRI turbulence in the initially unstable region is responsible for the transformation. In the local super-Keplerian region, migrations due to aerodynamic gas drag and tidal interaction with disk gas are reversed. The simulation setting corresponds to the regions near the outer and inner edges of a global MRI dead zone in a disk. Therefore, the outer edge of dead zone, as well as the inner edge, would be a favorable site to accumulate dust particles to form planetesimals and retain planetary embryos against type I migration.

NUMERICAL SIMULATION OF SHOCK WAVE AND TURBULENCE INTERACTION OVER A CIRCULAR CYLINDER

The interaction of shock wave and turbulence for transonic flow over a circular cylinder is investigated using detached-eddy simulation (DES). Several typical cases are calculated for free-stream Mach number M∞ from 0.85 to 0.95, and the physical mechanisms relevant to the shock wave and turbulence interaction are discussed. Results show that there exist two flow states. One is unsteady flow state with moving shock waves interacting with turbulent flow for M∞ < 0.9 approximately, and the other is quasi-steady flow with stationary shocks standing over the wake of the cylinder for M∞ > 0.9, suppressing the vortex shedding from the cylinder. Moreover, local supersonic zones are identified in the wake of the cylinder and generated by two processes, i.e., reverse flow and shock wave distortion induced the supersonic zone. Turbulent shear layer instabilities are revealed and associated with moving shock wave and traveling pressure wave.

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.

Laboratory and well-history based predictions of productivity decline due to oilfield scaling—analytical modelling and field study

Sulphate scaling may develop during offshore waterflood projects where mixing of injected and formation waters causes salt precipitation. Salt deposition results in permeability decline and, consequently, in impairment of well productivity. The problem has been widely presented in the literature for the North Sea, Campos Basin and the Gulf of Mexico. Recently several oil companies have reported several field cases of oilfield scaling in Australia. In this paper, methods are summarised for forecasting productivity decline from the history of well productivity index decline, produced water composition, and also from laboratory corefloods. The methods account for chemical reactions based on exact analytical solutions of inverse and forward modelling of quasi steady state oil-water flow towards producing wells. The main result obtained from the analytical model is a measure of the decline in productivity index with time for either linear flow in the case of a coreflood or the radial flow towards well. The analytical model has been used to predict further productivity decline in scaled-up producers of the deepwater offshore field X (Campos Basin, Brazil). Laboratory corefloods were carried out for field X cores and waters, and the model coefficients were determined. The productivity losses due to barium sulphate scaling have been noticed during several years of seawater flooding. The values obtained for reaction kinetics and formation damage coefficients are similar to those obtained from corefloods.

Occurrence Mechanism and Oscillation Characteristics of Pulsation Phenomenon Arising in Cavitation Surge in Cascade

In this study, numerical analysis of cavitating three-blade cyclic flat-plate cascade is performed with paying attention to cavitation surge which is a type of cavitation instabilities. A numerical method employing “locally homogeneous model for compressible gas-liquid two-phase medium” is applied to solve the unsteady cavitating flowfield. From results of numerical analysis, few typical tendency of cavitation surge which is well known in experiments was reproduced numericaly, that frequency of cavitation surge decreases with lowering σ, and that cavitation surge is easy to occur at low flow rate condition. Additionaly, mechanism of pulsation phenomenon of cavitation surge in flat-plate cascade was clarified, that collapse pressure of cloud cavity in downstream of cascade propagates upstream on contact with re-entrant jet which is flowing backward inside a sheet cavity and causes oscillation in upstream pressure, also that negative angle of attack and choking of cascade throat are considered to cause of oscillation in flow rate. About dynamic transfer function of cavitation, certain degree of possibility is confirmed in quasi-steady mass flow gain factor Mquasi and cavitation compliance Kquasi for prediction of occurrence limit of cavitation instabilities. Additionally, for prediction of frequency of cavitation surge, it was confirmed that local cavitation compliance Klocal is more available than quasi-steady one.

Unsteady film cooling with imposed nonuniform pulsations of the main flow

Effects of the main flow pulsations on the unsteady adiabatic film cooling efficiency were investigated. The possibility of using the critical value of the modified Strouhal number for the single-row perforation to identify the quasi-steady flow in the double-row perforation was proved. The penetration of disturbances into the perforation channels due to “plunger” effect was observed. The influence of the imposed pulsations on the adiabatic film cooling efficiency was shown to be weaker for the double-row perforation as compared to the single-row perforation.

Alternative method to evaluate discharge coefficients. Part 2: Case study

The purpose of this article is to apply an alternative method whereby discharge coefficients can be estimated for the flow through a poppet valve at various lifts. Presented is the development of an operational quasi-steady flow rig. An engine cylinder head poppet valve was used as the case study. The requirement to directly measure mass flowrates using a standard conventional steady flow apparatus has been eliminated. Transient mass flowrates, pressures and temperatures of air during an inflow test for a poppet valve at various lifts were measured. Mass flowrates were also calculated from measured cylinder gas pressures and corrected for heat transfer. Using both methods to determine the mass flowrates, isentropic discharge coefficients were calculated and shown to compare within>4.0 per cent of steady flow data. A computational fluid dynamics (CFD) validation of the quasi-steady flow rig is also presented.

Structure and mixing of a transient flow of helium injected into an established flow of nitrogen: two dimensional measurement and simulation

The transient injection and mixing between nitrogen and helium in a confined chamber at atmospheric pressure is studied experimentally. The 2D injector and mixing chamber contained a middle injection slot for nitrogen flanked by a pair of outer slots for helium. Experiments were conducted by introducing the helium streams into a previously established quasi-steady flow of nitrogen. The nitrogen stream was seeded with nitric oxide (NO) that served as a source for quantitative, planar laser-induced fluorescence (PLIF) imaging of the transient mixing process. PLIF images were acquired by triggering an Nd:YAG laser system at selected times following helium valve actuation. The observed flow structures and extent of mixing between the two streams proved to be highly unsteady and irregular with the helium/nitrogen jets frequently deviating from the centerline toward the confining walls. Representative unsteady CFD solutions also show this same absence of symmetry and the same general flow structures as the measurements, however, they predict somewhat higher helium concentration in recirculation regions than were observed in the measurements.

Unsteady Phenomena in the Double-Diffusive Convection Flows at High Rayleigh Number

A two-dimensional dual-mesh hybrid numerical method is used to investigate some small scale phenomena in double-diffusive convection flows at high Rayleigh number. With a horizontal temperature gradient, the interface of the two-layer stratified system becomes tilted and wavy, resulting in two typical flow patterns. The quasi-steady flow pattern is scattered with abundant salt fingers and hook-like plumes, which agree well with experimental data available in the literature qualitatively. It is found that three-dimensional modeling should be carried out in order to have better agreement with experimental data. In addition, the stratified system is found to be sensitive to the buoyancy ratio.

Eigenmodes of a Counter-Rotating Vortex Dipole

Highly resolved solutions of the two-dimensional incompressible Navier-Stokes and continuity equations describing the evolution of a counter-rotating pair of vortices have been obtained accurately and efficiently by spectral-collocation methods and an eigenvalue decomposition algorithm. Such solutions have formed the basic state for subsequent three-dimensional biglobal-eigenvalue-problem linear-instability analyses, which monitor the modal response of these vortical systems to small-amplitude perturbations, periodic along the homogeneous axial spatial direction, without the need to invoke an assumption of azimuthal spatial homogeneity. A finite element methodology (Gonzalez, L. M., Theofilis, V., and Gomez-Blanco, R., Finite Element Numerical Methods for Incompressible Biglobal Linear Instability Analysis on Unstructured Meshes, AIAA Journal, Vol. 45, No. 4,2007, pp. 840-855) has been adapted to study the instability of vortical flows and has been validated on the Batchelor vortex (Mayer, E. W., and Powell, K. G., Viscous and Inviscid Instabilities of a Trailing Vortex, Journal of Fluid Mechanics, Vol. 245, 1992, pp. 91-114). Subsequently, the instability of the counter-rotating dipole has been analyzed; aspects monitored have been the dependence of the results on the Reynolds number, the value of the (nonzero) axial velocity considered, and the time at which the quasi-steady basic flow has been monitored. Essential to the success of the analysis has been the appropriate design of a calculation mesh, as well as exploitation of the symmetries of the basic state. The spatial structure of the amplitude functions of all unstable eigenmodes reflects the inhomogeneity of the basic state in the azimuthal spatial direction, thus providing a posteriori justification for the use of the biglobal-eigenvalue-problem concept.

The Effects of Mesoscale Surface Heterogeneity on the Fair-Weather Convective Atmospheric Boundary Layer

Large-eddy simulation (LES) is used to examine the impact of heterogeneity in the surface energy balance on the mesoscale and microscale structure of the convective atmospheric boundary layer (ABL). A long (16 or 32 km) and narrow (5 km) domain of the convective ABL is forced with an imposed surface heat flux consisting of a constant background flux of 0.20 K m s−1 (250 W m−2) added to a sinusoidal perturbation of 16 or 32 km and whose amplitude varies from 0.02 to 0.20 K m s−1 (25–250 W m−2). The output is analyzed using a spatial filter, spectral analyses, and a wave-cutoff filter to show how the mesoscale and microscale components of the ABL respond to surface heterogeneity. The ABL response is divided by amplitude of heterogeneity into oscillatory and nonoscillatory mesoscale flows, with amplitudes of 0.08 K m s−1 (100 W m−2) and greater being oscillatory. Although mean ABL structure is disturbed relative to the homogeneous case for all heterogeneous cases, the microscale structure of the ABL in the quasi-steady flows retains characteristics of mixed-layer similarity. The vertical sensible heat flux is dominated in all cases by the microscale flux, with an interscale term becoming significant for high-amplitude cases and the mesoscale flux remaining small in all cases. Prior observations of ABLs over heterogeneous surfaces are consistent with the lower-amplitude cases. These results contradict past studies that suggest that heterogeneous surfaces lead to large mesoscale fluxes. The interscale flux and oscillatory microscale structures raise questions about the ability of mesoscale models to properly simulate the ABL in high-amplitude heterogeneity.

Flow of a dispersed phase in the Laval nozzle and in the test section of a two-phase hypersonic shock tunnel

An unsteady gas-particle flow in a hypersonic shock tunnel is studied numerically. The study is performed in the period from the instant when the diaphragm between the high-pressure and low-pressure chambers is opened until the end of the transition to a quasi-steady flow in the test section. The dispersed phase concentration is extremely low, and the collisions between the particles and their effect on the carrier gas flow are ignored. The particle size is varied. The time evolution of the particle concentration in the test section is obtained. Patterns of the quasi-steady flow of the dispersed phase in the throat of the Laval nozzle and the flow around a model (sphere) are presented. Particle concentration and particle velocity lag profiles at the test-section entrance are obtained. The particle-phase flow structure and the time needed for it to reach a quasi-steady regime are found to depend substantially on the particle size.

Thermodynamic analysis of a gamma type Stirling engine in non-ideal adiabatic conditions

In this study, a thermodynamic analysis of a gamma type Stirling engine is performed by using a quasi steady flow model based on Urieli and Berchowitz's works. The Stirling engine analysis is performed for five principal fields: compression room, expansion room, cooler, heater and regenerator. The conservation law of the mass and the energy equations are derived for the related sections. A FORTRAN code is developed to solve the derived equations for all process parameters like pressure, temperature, mass flow, dissipation and convection losses for the different spaces (compression space, cooler, regenerator, heater and expansion space) as a function of the crank angle. The developed model gave more precise results for the pressure profile than the models available in the literature.

A Theoretical and Numerical Study of Urban Heat Island–Induced Circulation and Convection

Abstract Urban heat island–induced circulation and convection in three dimensions are investigated theoretically and numerically in the context of the response of a stably stratified uniform flow to specified low-level heating that represents an urban heat island. In a linear, theoretical part of the investigation, an analytic solution for the perturbation vertical velocity in a three-dimensional, time-dependent, hydrostatic, nonrotating, inviscid, Boussinesq airflow system is obtained. The solution reveals a typical internal gravity wave field, including low-level upward motion downwind of the heating center. Precipitation enhancement observed downwind of urban areas may be partly due to this downwind upward motion. The comparison of two- and three-dimensional flow fields indicates that the dispersion of gravity wave energy into an additional dimension results in a faster approach to a quasi-steady state and a weaker quasi-steady flow well above the concentrated heating region in three dimensions. In a nonlinear, numerical modeling part of the investigation, extensive dry and moist simulations using a nonhydrostatic, compressible model with advanced physical parameterizations [Advanced Regional Prediction System (ARPS)] are performed. While the maximum perturbation vertical velocity in the linear internal gravity wave field exists in the downwind region close to the heating center, the maximum updraft in three-dimensional dry simulations propagates downwind and then becomes quasi stationary. In three-dimensional moist simulations, it is demonstrated that the downwind upward motion induced by an urban heat island can initiate moist convection and result in downwind precipitation. The cloud induced by the downwind upward motion grows rapidly to become deep convective clouds. Heavy rainfalls are localized in a region not far from the heating center by a convective precipitating system that is nearly stationary. The differences in results between two and three dimensions are explained by the presence of (moist) convergence in an additional dimension. The numerical simulation results indicate that the intensity and horizontal structure of the urban heat island affect those of circulation and convection and hence the distribution of surface precipitation.

Non-linear higher-order boundary value problems describing thin viscous flows near edges

Two boundary value problems for non-linear higher-order ordinary differential equations are analyzed, which have been recently proposed in the modeling of steady and quasi-steady thin viscous flows over a bounded solid substrate. The first problem concerns steady states and consists of a third-order ODE for the height of the liquid; the ODE contains an unknown parameter, the flux, and the boundary conditions relate, near the edges of the substrate, the height and its second derivative to the flux itself. For this problem, (non-)existence and non-uniqueness results are proved depending on the behavior, as the flux approaches zero, of the “height-function” (the function which relates the height to the flux near the edge out of which the liquid flows). The second problem concerns quasi-steady states and consists of a fourth-order ODE for the (suitably scaled) height of the liquid; non-linear boundary conditions relate the height to the flux near the edges of the substrate. For this problem, the existence of a solution is proved for a suitable class of height-functions.

Characteristic Velocity of Stream Bed Movement

Assuming quasi-steady flow, the characteristic velocity of stream bed movement and the relation between the depth of the moving gravel layer and the water depth are derived for both diffusion wave and kinematic wave approximations. The characteristic velocity relation is verified using field data and is compared with the relation derived by Weir in 1983.

Skin-Friction Measurements and Flow Establishment Within a Long Duct at Superorbital Speeds

The successful operation of an acceleration-compensated skin-friction transducer in test times and at total enthalpies offered by the X3 superorbital expansion tube was demonstrated. Localized measurements of skin friction and heat flux along the centerline of an inner wall of a 1-m-long rectangular diverging duct were reported. The laminar measurements were obtained in air with a freestream Mach number of 10 and stagnation enthalpy of 40 MJ/kg. Steady heat flux and skin-friction levels confirmed the establishment of quasi-steady flow periods of 350 μs along the length of the duct. Experimental results were shown to be in excellent agreement with computational fluid dynamics estimates. The measured Reynolds analogy factor was shown to be slightly higher than theoretical flat-plate predictions and computational fluid dynamics estimates, though agreement was to within experimental uncertainty. Estimates of the gas-phase and surface Damkohler numbers suggested that although the boundary layer was likely to be chemically frozen, recombination at the surface may be occurring. The experimental data and computational fluid dynamics results for a thermochemical nonequilibrium gas and catalytic and noncatalytic walls indicated that the effects of gas-phase and surface chemical reactions were negligible.

An overview of a Lagrangian method for analysis of animal wake dynamics

The fluid dynamic analysis of animal wakes is becoming increasingly popular in studies of animal swimming and flying, due in part to the development of quantitative flow visualization techniques such as digital particle imaging velocimetry (DPIV). In most studies, quasi-steady flow is assumed and the flow analysis is based on velocity and/or vorticity fields measured at a single time instant during the stroke cycle. The assumption of quasi-steady flow leads to neglect of unsteady (time-dependent) wake vortex added-mass effects, which can contribute significantly to the instantaneous locomotive forces. In this paper we review a Lagrangian approach recently introduced to determine unsteady wake vortex structure by tracking the trajectories of individual fluid particles in the flow, rather than by analyzing the velocity/vorticity fields at fixed locations and single instants in time as in the Eulerian perspective. Once the momentum of the wake vortex and its added mass are determined, the corresponding unsteady locomotive forces can be quantified. Unlike previous studies that estimated the time-averaged forces over the stroke cycle, this approach enables study of how instantaneous locomotive forces evolve over time. The utility of this method for analyses of DPIV velocity measurements is explored, with the goal of demonstrating its applicability to data that are typically available to investigators studying animal swimming and flying. The methods are equally applicable to computational fluid dynamics studies where velocity field calculations are available.

Sedimentary fill of submarine canyons and channels using a Cellular Automata process-based model

Understanding the deposition processes in submarine canyons and channels has significant implications for petroleum exploration. A numerical model has been established to simulate the sedimentary fill of canyons and channel-levee complexes present in turbiditic environments. The model is based on a Cellular Automata (CA) approach. Depositional processes which control the evolution of the system are described by the rules established either empirically from observations or from simplified physical laws. Sedimentary systems are described by a meshed domain and are built with a series of unitary events. Two versions have been developed and couple the impact of flow effects on the nature and architecture of deposits. The first model allows a dynamic description of seabed evolution under the activity of gravity flows. For a single event simulation, both the morphology of the seabed and sediment distribution is estimated at each time step. The model was calibrated by the application to the turbulent surge that occurred during the 1999 storm in Capbreton canyon (France) using core control. The second model simulates deposit architecture accumulated by a succession of steady state flows. A possible way to average physical processes over time is to then consider geological events such as successive quasi-steady state flows for which sediment transport has permanent values. The CA paradigm is an efficient approach to quickly obtain such stationary states. Results obtained for the first sequence of the Pab channel complex (Indo-Pakistani margin) provides the first step towards the quantitative understanding of external parameters on catastrophic gravity flow dynamics and on the organisation of subsequent deposits.