Unsteady Non-uniform Flow Research Articles

Experimental and numerical investigation of the gap flow between a pusher and a barge in deep and shallow water

The flow in the gap between a pusher boat and a barge of a conventional inland waterway convoy was experimentally and numerically investigated to gain insight into the complex flow pattern and to provide benchmark data for validation of an adequate turbulence model. Two water depths were considered, corresponding to deep water and moderately shallow water conditions. Both cases highlighted the extremely unsteady non-uniform flow pattern in the gap. The collected data were subsequently used to assess a numerical method based on solving the Reynolds-averaged Navier–Stokes (RANS) equations and the Improved Delayed Detached Eddy Simulation (IDDES) technique. Generally, our numerical predictions compared favorably to the experimental data; however, the IDDES method proved to be more accurate, especially in the prediction of the velocity field in the gap region. The IDDES technique was then used to analyze the flow in water depth to draft ratios h/T of 2.14, 1.5, and 1.2. At h/T=1.2, comparatively larger recirculation zones and a massive increase in resistance were observed. Additionally, to quantify the influence of the gap between pusher and barge on resistance in shallow waters, we modified our model by simply covering the gap and then analyzing this modified model by carrying out an additional simulation at h/T=1.2. Covering the gap reduced the overall longitudinal hydrodynamic force acting on the convoy by about 6.5 %.

Unsteady Non-Uniform Flow of Molten Metals in Rectangular Open Channels

In the metallurgical industries, it is very important to characterize the flow of molten metals in open channels given that they are transported through these devices to different plant sections. However, unlike the flow of water which has been studied since ancient times, the flow of molten metals in open channels has received little attention. The unsteady non-uniform flow of blast furnace molten pig iron in a rectangular open channel is analyzed in this work by numerical solution of the Saint-Venant equations. The influence of mesh size on the convergence of molten metal height is studied to determine the proper mesh and time step sizes. A sinusoidal inflow pulse is imposed at the entrance of the channel in order to analyze the propagation of the resulting wave. The influence of the angle of inclination of the channel and the roughness coefficient of the walls on the amplitude and the dynamic behavior of the height of the molten metal are analyzed. Phase portraits of the channel state variables are constructed and interpreted. Numerical simulations show that as the angle of inclination of the channel increases, the amplitude of the formed wave decreases. From 10 degrees onwards, the peak of the wave descends even below the initial height. On the other hand, the roughness coefficient affects the molten pig iron height profiles in an inverse way than the angle of inclination. The amplitude of the formed wave increases as the roughness coefficient increases.

Прогнозирование объема каверн на вращающихся лопастях и масштабные эффекты

Object and purpose of research. Pressure pulsations induced by cavitating blades substantially contribute to flowinduced loads and amplify structural vibration. These pulsations depend on oscillation of the volume of cavities over blades. Prediction of them usually involves model tests and there are three kinds of scale effects influencing the cavity volumes. The first one is associated with the non-uniform inflows. The second one is associated with the combined influence of the blade boundary layer and surface tension on the cavity surface. The third one is associated with the cavity buoyancy. Materials and methods. Because of complexity of blade flows, a qualitative analysis of similar unsteady non-uniform flows around 3D hydrofoils is useful. This paper presents such an analysis for a hydrofoil with the sections copied from a marine propeller blade. The inflows correspond to the wakes of a ship and of her model. Computations carried out using an analysis of viscous-inviscid interaction. Main results. The qualitative explanation of observed trends and scale effects is obtained due to this analysis. In particular, the role of pressure side cavitation in full scale conditions is pointed out. Conclusion. The difference of model and ship wakes results in the substantial difference in blade section angles of attack at the same blade loading. Therefore, in model tests the suction side cavitation is more extensive, whereas the pressure side cavitation may not appear, though it exists on full-scale ship propeller blade. This substantial scale effect has been usually out of previous considerations.

Overland Flow Characteristics Using Kinematic Wave Formulation.(Dept.C)

The characteristics of overland flow resulting from a uniform rainfall intensity on an impervious sloping plane are investigated. The characteristic solution of the one dimensional unsteady nonuniform flow equations with the kinematic wave approximation applied to the momentum equation is used. The influence of the different overland flow parameters on the synthesized hydrograph, the peak runoff discharge, and the time taken to reach equilibrium is studied for the case of turbulent flow. The overland flow parameters include the slope and the length of the plane, the surface resistance, and the uniform rainfall intensity. A dimensionless peak runoff hydrograph is determined and compared with both Izzard's experimental dimensionless hydrograph and the dimensionless hydrograph determined by the finite difference solution of the full dynamic form of the momentum equation.

A Dual-VENC Four-Dimensional Flow MRI Framework for Analysis of Subject-Specific Heterogeneous Nonlinear Vessel Deformation.

Advancement of subject-specific in silico medicine requires new imaging protocols tailored to specific anatomical features, paired with new constitutive model development based on structure/function relationships. In this study, we develop a new dual-velocity encoding coefficient (VENC) 4D flow MRI protocol that provides unprecedented spatial and temporal resolution of in vivo aortic deformation. All previous dual-VENC 4D flow MRI studies in the literature focus on an isolated segment of the aorta, which fail to capture the full spectrum of aortic heterogeneity that exists along the vessel length. The imaging protocol developed provides high sensitivity to all blood flow velocities throughout the entire cardiac cycle, overcoming the challenge of accurately measuring the highly unsteady nonuniform flow field in the aorta. Cross-sectional area change, volumetric flow rate, and compliance are observed to decrease with distance from the heart, while pulse wave velocity (PWV) is observed to increase. A nonlinear aortic lumen pressure-area relationship is observed throughout the aorta such that a high vessel compliance occurs during diastole, and a low vessel compliance occurs during systole. This suggests that a single value of compliance may not accurately represent vessel behavior during a cardiac cycle in vivo. This high-resolution MRI data provide key information on the spatial variation in nonlinear aortic compliance, which can significantly advance the state-of-the-art of in-silico diagnostic techniques for the human aorta.

Biomechanically driven unsteady non-uniform flow of Copper water and Silver water nanofluids through finite length channel

Background and objectivesThis paper aims to investigate the unsteady flow of two types of nanofluids i.e Copper water nanofluids and Silver water nanofluids) through finite length non-uniform channel driven by peristaltic sinusoidal wave propagations. MethodsThe governing equations are reduced in linear form using dimensional analysis and considering the low Reynolds number and large wavelength approximations. The time dependent temperature field, axial velocity, transverse velocity and pressure difference are obtained analytically in closed form solution. Trapping phenomenon is also discussed with the help of contour plots of stream function. A comparative study of pure water (Newtonian fluid), Copper water nanofluids and Silver water nanofluids under the influence of relevant physical parameters is made in graphical form and also discussed. The effects of absorption parameter and Grashof number on velocity profiles, temperature profiles and pressure distribution along the length of channel are examined. Results conclusionsThe computational results reveal that the velocity profile is maximum for Silver water nanofluids however, it is least for Copper water nanofluids. It is also concluded the temperature profile is more for pure water in comparison to Silver water and Copper water nanofluids. This model is applicable to design, micro-peristaltic pumps which help in Nanoparticle-based targeted drug delivery and to transport the sensitive or corrosive fluids, sanitary fluids, slurries and noxious fluids in nuclear industry.

Perbandingan Hasil Pemodelan Aliran Satu Dimensi Unsteady Flow dan Steady Flow pada Banjir Kota

One dimensional flow is often used as a flood simulation for the planning capacity of the river. Flood is a type of unsteady non-uniform flow, that can be simulated using HEC-RAS. HEC-RAS software is often used for flood modeling with a one-dimensional flow method. Unsteady flow modeling results in HEC-RAS sometimes refer to error and warning due to unstable analysis program. The stability program among others influenced bend in the river flow, the steep slope of the river bottom, and changes in cross-section shape. Because the flood handling required maximum discharge and maximum flood water level, then a steady flow is often used as an alternative to simulate the flood flow. This study aimed to determine the advantages and disadvantages of modeling unsteady non-uniform and steady non-uniform flow. The research location in the Kanal Banjir Barat, in the Semarang City. Hydraulics modeling uses HEC-RAS 4.1 and for discharge the plan is obtained from the HEC-HMS 3.5. Results of the comparison modeling hydraulics the modeling of steady non-uniform flow has a tendency water level is higher and modeling of unsteady non-uniform flow takes longer to analyze. Results of the comparison the average flood water level maximun is less than 15% (± 0,3 meters), that is 0.27 meters (13.16%) for Q50, 0.25 meters (11.56%) for Q100, dan 0.16 meters (4.73%) for Q200. So the modeling steady non-uniform flow can still be used as a companion version the modeling unsteady non-uniform flow.

Forecasting river temperatures in real time using a stochastic dynamics approach

[1] We address the growing need for accurate water temperature predictions in regulated rivers to inform decision support systems and protect aquatic habitats. Although many suitable river temperature models exist, few simultaneously model water temperature dynamics while considering uncertainty of predictions and assimilating observations. Here, we employ a stochastic dynamics approach to water temperature modeling that estimates both the water temperature state and its uncertainty by propagating error through a physically based dynamical system. This method involves converting the governing hydrodynamic and heat transport equations into a state space form and assimilating observations via the Kalman Filter. This model, called the River Assessment for Forecasting Temperature (RAFT), closes the heat budget by tracking heat movement using a robust semi-Lagrangian numerical scheme. RAFT considers key thermodynamic processes, including advection, longitudinal dispersion, atmospheric heat fluxes, lateral inflows, streambed heat exchange, and unsteady nonuniform flow. Inputs include gridded meteorological forecasts from a numerical weather prediction model, bathymetric cross-sectional geometry, and temperature and flow measurements at the upstream boundary and tributaries. We applied RAFT to an ∼100 km portion of the Sacramento River in California, downstream of Keswick Dam (a regulatory dam below Shasta Dam), at a spatial resolution of 2 km and a temporal resolution of 15 min. Model prediction error over a 6 month calibration period was on the order of 0.5°C. When temperature and flow gage data were assimilated, the mean prediction error was significantly less (0.25°C). The model accurately predicts the magnitude and timing of diel temperature fluctuations and can provide 72 h water temperature forecasts when linked with meteorological forecasts and real-time flow/temperature monitoring networks. RAFT is potentially scalable to model and forecast fine-grained one-dimensional temperature dynamics covering a broad extent in a variety of regulated rivers provided that adequate input data are available.

Velocity Deformation Model for Unsteady Open-Channel Flows over Smooth and Rough Beds

AbstractA one-dimensional depth-averaged velocity deformation model is developed to study the characteristics of the unsteady flows in open channels. The vertical profile of the streamwise velocity is expressed in a power series, and the coefficients of the velocity are evaluated by using the unsteady equation of motion. A concise form of the friction velocity for unsteady nonuniform flow is then proposed by utilizing the coefficients of the power series. The applicability of the model is validated with experimental data, producing reasonably good agreement between the model results and the observed data. Finally, the deformation of velocity at the surface is assured by comparing velocity distribution of numerical model with the computational results from a previous model.

Identification of Water Quality Model Parameter Based on Finite Difference and Monte Carlo

Identification results of water quality model parameter directly affect the accuracy of water quality numerical simulation. To overcome the difficulty of parameter identification caused by the measurement’s uncertainty, a new method which is the coupling of Finite Difference Method and Markov Chain Monte Carlo is developed to identify the parameters of water quality model in this paper. Taking a certain long distance open channel as an example, the effects to the results of parameters identification with different noise are discussed under steady and un-steady non-uniform flow scenarios. And also this proposed method is compared with finite difference method and Nelder Mead Simplex. The results show that it can give better results by the new method. It has good noise resistance and provides a new way to identify water quality model parameters.

Mathematical modeling and simulation of biologically inspired hair receptor arrays in laminar unsteady flow separation

Bats possess arrays of distributed flow-sensitive hair-like mechanoreceptors on their dorsal and ventral wing surfaces. Bat wing hair receptors are known to play a significant role in flight maneuverability and are directionally most sensitive to reversed flow over the wing. In this work, we consider the mechanics of flexible hair-like structures for the time accurate detection and visualization of hydrodynamic images associated with unsteady near surface flow phenomena. A nonlinear viscoelastic model of a hair-like structure coupled to an unsteady nonuniform flow is proposed. Writing the hair model in nondimensional form, we identify five dimensionless groups that govern hair behavior. An order of magnitude analysis of the physical forces involved in the fluid–structure hair response is performed. Through the choice of hair material properties, we show how a local measure of near surface flow velocity may be obtained from hair tip displacement and resultant moment. When hair structures are placed into an array, time and space accurate hydrodynamic images may be obtained. We illustrate the imaging of reversed flow that occurs during a laminar unsteady flow separation with an array of hair-like structures.

Developing a model for analysis of uncertainties in prediction of floods

A realistic new sediment–laden water prediction computer model was developed. In this model unsteady non-uniform flow computations were incorporated. Using this model, flooding flow–sediments were simulated and compared to earlier research including hydrologic engineering centre (HEC-series) computer models. Uncertain value of parameters and errors in flow–sediment transport equation in existing coupled flow–sediment models were studied. Sensitive nonlinear flow–sediment terms simplified in linear models and state of non-uniform sediment laden flooding flows in loosed boundaries were considered. The new applied modeling of flooding sediment–water transport simulation was tested with data of three rivers and relative merits of the various techniques involved in full phases of flow–sediment in loosed boundaries for real river situations were discussed. Uncertain values of sensitive parameters were investigated through sensitivity analysis of flow–sediment parameters in three hydrologic catchments. Results of numerical analysis were compared to field observations relying on the accuracy of the developed model. Uncertainties and errors involved in; numerical scheme, hydraulic-sediment parameters, the out-reach output, flooding sediment–laden water characteristics, peak outflow, time increments, depth, speed of floods were found rather sensitive to the solution of problems. Computed grid size intervals and the peak outflows increased with space step and decreased with time step. Errors of in-reach parameters, the peak inflow hydrograph and roughness coefficient highlighted out-reach output.

Numerical Modeling of the Tee Thermal Diffuser in Coastal Regions

Mixing of the heated water discharged from a tee thermal diffuser is analyzed using the three-dimensional grid-based numerical model. The discharge momentum flux is incorporated properly into the model by adopting the concept of the numerical slot diffuser with the multiple jet theory. A line patch is introduced to impose the discharge momentum flux, which plays an important role in the mixing of the heated water discharged from the multiport diffuser in the near field. Experiments are conducted which deal with discharging heated water by the tee diffuser in shallow ambient water with crossflow and the results are compared with numerical results. The agreement of the numerical results and the experimental data is reasonably good. The proposed coastal circulation model is applied to the virtual multiport diffuser in order to investigate the applicability of the model in simulating seawater flow fields and mixing of the heated water in a real site. The results show that the proposed model predicts the mixing characteristics of the heated water reasonably well in consideration of a real bottom topography and the condition of unsteady nonuniform flow.

The force exerted on a body in inviscid unsteady non-uniform rotational flow

A general expression is derived for the fluid force on a body of simple shape moving with a velocity v through inviscid fluid in which there is an unsteady non-uniform rotational velocity field u0(x,t) in two or three dimensions. It is assumed that the radius is small compared with the scale over which the strain rate changes, though for the sphere it is also assumed that the changes in the ambient velocity field over the scale of the sphere are small compared with the velocity of the body relative to the flow. Given these approximations it is shown that the effects of the rate of change of the vorticity of the ambient flow is of second order and can be neglected. However the rate of change of the irrotational straining motion is included in the analysis. It is shown that the inertial forces derived by many authors for irrotational flow can be simply added to a generalization of the lift force derived by Auton (1987) in a companion paper. It is shown how this lift force is made up of a rotational and an inertial or added-mass component. For three-dimensional bluff bodies the latter is generally larger (by a factor of three for a sphere), and can be simply calculated from the added-mass coefficient. For illustration, the general expression is used to derive formulae for (i) the motion of a spherical bubble in a steady non-uniform flow to contrast with the motion in an unsteady flow, and (ii) the motion of rigid volumes of neutral density across an inviscid shear flow. These results show how added-mass (and lift) forces lead to different motions for a sphere and a cylinder. The general expression is useful in two-phase flow calculations, and for indicating the forces and motions of ‘lumps of fluid’ in turbulent flows.

Largescale ripples of the lower Wabash River

ABSTRACTLargescale ripples in the meandering lower Wabash River of Illinois and Indiana, U.S.A., include scroll bars and three dunelike bed forms (dunes, sand waves, and transverse bars). Scroll bars are lobate crested, asymmetrical in stream‐wise vertical profile, usually solitary, and oriented approximately normal to local channel strike. They form by passive flow expansion downchannel from locally emergent topographic highs, face and lie near inner banks of meander bends, enjoy a high preservation potential as leveelike ridges of ridge‐and‐swale topography, and migrate only during relatively low stream discharges, when water depth over bar crests is less than 0·5 m.Dunes correspond to dunes of the flow‐regime classification and rarely are solitary or superimposed. Sand waves may be symmetrical or asymmetrical, are always superimposed by dunes, occur in depths greater than 4 m and in bed material coarser than 1 mm mean size, and develop at bankfull and flood flows. Transverse bars migrate in depths less than 5 m in straight reaches and near inner banks of bends, display crestal dunes, and correspond to the bars of Costello (1974) and to the sand waves of Boothroyd (1969). Hydrodynamic regimes of scroll bars and transverse bars differ from that of dunes. The omnipresence of dunes upon stoss‐sides of sand waves confirms the existence of an equilibrium superimposition of dunelike largescale ripples.Depth‐velocity‐size diagrams appear to be a valid representation of empirical stability fields of dunelike largescale ripples in deep unsteady nonuniform aqueous flows. Stability fields of dunes and sand waves overlap greatly. Velocity profiles demonstrate an absence of leeside flow separation over dunes and an appearance (rare) over transverse bars only when the ratio of trough depth to crest depth exceeds two.Dune stratification displays (1) largescale trough cross‐strata, (2) thinning of sets as bed‐material size increases, and (3) an orientation within 20° of local channel strike. Transverse bars show avalanche sets up to 2 m thick, with reactivation surfaces. Scroll bars display thick avalanche sets separated by reactivation structures consisting of erratically oriented smallscale trough cross‐strata. Avalanche sets of scroll bars and of transverse bars are oriented 50–150° from and within 50° of, respectively, local channel strike.

State variable model of overland flow

The state variable approach to systems analysis and synthesis is used to develop a lumped mathematical model of overland flow. The model describes the unsteady nonuniform flow in terms of a set of first order ordinary differential equations and a set of arithmetic equations. Conceptually the model consists of a series of interacting reaches with unsteady uniform flow subjected to impulse inputs. The change in hydraulic roughness due to the rainfall impact effect is accounted for. The regeneration performance of the model is tested by comparison with experimental hydrographs of overland flow from a laboratory catchment. Close agreement between experimental and calculated hydrographs is obtained for both uniformly distributed as well as temporally and spatially varied rainfall inputs. The state variable approach is not limited to overland flow; it provides a comprehensive mathematical framework for a general hydrologic model.

Unsteady Nonuniform Flow in the Entrance of a Pipe

The laminar incompressible flow started from rest in the entrance of a pipe is analyzed using the integral form of the equations of continuity, momentum, and energy, together with a similarity hypothesis for the velocity profiles across the boundary layer. A first-order partial-differential equation for the growth of the boundary-layer thickness is obtained and solved by the method of characteristics. The flow is shown to depend critically on a dimensionless parameter which can be interpreted as the ratio of a characteristic time of the variation of the discharge to a time characteristic of the diffusion of viscous effects.

Rheology of concentrated mixtures of fluid with small particles, parameters of phase interaction: PMM vol. 36, n≗3, 1972, pp. 480–493

The combined motion of fluid and solid, fluid, or gaseous particles suspended in it is considered. Particles are assumed to be small and to be distributed in space at random, hence the Reynolds numbers of flows past particles of various dimensions are small, and we can neglect any random (“quasi-turbulent”) pulsations of the two phases. Parameters defining phase interaction under conditions of unsteady nonuniform flow are calculated. Disperse systems consisting of a fluid and particles suspended in it may be arbitrarily separated into two categories. In “soft” systems which belong to the first category the particles and the fluid are in regular and defined motion; random pulsations of phases are weak and do not appreciably affect the system behavior, so that in the majority of cases these may be neglected. Systems of the second category (“rigid” systems) are, on the other hand, subject to intensive chaotic pulsation of particles and fluid, which have a decisive effect on the Theological properties and distinctive features of the transport process in such systems. A consistent hydromechanical theory of “soft” systems has been developed only for fairly small concentrations of the disperse system, so that we can either neglect particle interaction altogether, or make an approximate allowance for pairinteraction between these [1]. The theory of random quasi-turbulent motion of phases and of its effect on the rheology of “rigid” systems is presented in [3]. However the neglect in the latter of phase pulsations made it necessary to specify a priori certain important parameters which determine the behavior of a disperse system. Hence the development of the theory for highly concentrated soft systems is of considerable interest, also in the analysis of processes in rigid disperse systems. The problem of constrained motion of fluid in concentrated cloud of random distributed particles and of resulting phase interaction was considered earlier on various assumptions [4 – 6]. A stricter treatment of the problem of steady flow through a lattice of solid particles was given by Tam [7] who used the approximation of “point” forces whereby perturbations generated by point forces applied to the fluid at the centers of particles are substituted for perturbations introduced in the stream by particles. This method, which is free of arbitrary empirical assumptions, was extended to unsteady flows in [8]. Below we formulate a method of successive approximations in which the pointforce approximation proposed in [7, 8] is taken as a reasonable “zero” approximation, thus providing in principle the possibility of improving the accuracy of results derived with the use of this approximation. Results obtained in [7, 8] are extended to streams of fluid which not only are unstable but also nonuniform and the particles are not necessarily solid or stationary.

Sediment Dispersion in Flow with Moving Boundaries

The longitudinal dispersion equation for sediment in unsteady nonuniform flow with moving boundaries is formulated from the three-dimensional instantaneous diffusion equation for movement of sediment by means of the time- and space-averaging processes. The equation is then studied for its applicability and validity in the sediment problem. The analytical expressions of the longitudinal dispersion coefficient for sediment in flow with moving boundaries are obtained for both turbulent and laminar flow. The effect of moving boundaries in turbulent flow on the value of the longitudinal dispersion coefficient has theoretically been shown to be negligible, but may be significant at a place where a sand or water wave breaks, causing an infinite gradient of bed or flow profile. The longitudinal dispersion equation that may often be called the suspended-load equation is shown to play an important role in the mathematical modeling of an alluvial channel where the suspended bed-material discharge is greater than the contact-bed discharge.