Two-layer Flow Model Research Articles

Numerical study on thermally driven smoke flow characteristics in long tunnels under natural ventilation

The paper focuses on the flow structures and mass flow rates of thermally driven smoke flows induced by fires in long transportation tunnels under natural ventilation. The important influencing factors including heat release rate (HRR), tunnel width and height, are taken into consideration. The mechanism of the smoke flow movement is explored. The results show that for a fire in a long naturally ventilated transportation tunnel, there exists a critical point which is dependent on HRR and tunnel geometry. This critical point is defined as the location where the smoke layer thickness and the outgoing mass flow rate increase towards it and decrease after it. Further, it is found that the critical point moves farther away from the fire source in a wider or higher tunnel, while it lies closer to the fire source for a higher HRR. A correlation is proposed to estimate the location of the critical point. The outgoing mass flow rates along the tunnel are calculated using the two-layer flow model and well-mixed flow model of thermally driven flows, and the results indicate that these models produce satisfactory predictions of the mass flow rates if the vertical temperature profile is known.

Unraveling the effect of a two-layer system on the mobility of rapid gravitational flows

Rapid gravitational flows such as debris avalanches and debris flows may entrain significant amounts of in situ material along their tracks, increasing their volume. Interactions between rapid gravitational flows and bed material are complicated. Especially, the physical mechanism of the fluidization has remained a mystery up to now. To gain a better understanding of the fluidization mechanism and influencing factors, we conducted flume experiments simulating the process of a flow overriding saturated bed material. Results showed that the overriding flow fluidized the bed material into a viscous state rather than liquefying saturated bed material. We also carried out a rheometer test on the saturated bed material. It revealed shear-thinning of the bed material. We deduced that shear thinning, and not liquefaction, was the principal mechanism for bed-material fluidization. Based on these results, a two-layer flow model was proposed using the classical depth-integrated approximation and the Saint Venant equation. It was assumed that both the dry rock avalanche and the impacted saturated bed material behaved as visco-plastic flows with different apparent viscosities. The model's two viscosity parameters were calibrated using the experimental run-out times and distances. We conclude from comparison of the tests and simulations, that our model well simulates the entrainment process.

Longitudinal dispersion coefficients of submerged vegetation flow under the effect of surface wind.

The longitudinal dispersion coefficient is an important index for contaminant transports in rivers. Investigating it by using an analytical approach is conducive to obtain its expression with physical meanings and wide application ranges. However, the analytical solutions are extremely complex for subsequent derivations when many influencing factors, such as benthic vegetation and surface wind, are considered. This study combines turbulent flow theory and Biot's theory for poroelasticity into a two-layer flow model and acquires the analytical solutions of velocity. A database is generated from the analytical solutions to search a more concise expression of velocity through genetic programming. A formula for longitudinal dispersion coefficients of submerged vegetation flow under the effect of surface wind is deduced on the basis of this expression. Calculated coefficients from the formula are compared with the experimental coefficients from the model and real vegetation to show its validity. The formula indicates that the longitudinal dispersion coefficients are mainly affected by turbulent effect, vegetation height, and surface wind. The growth of vegetation height can weaken the influence of surface wind on longitudinal dispersion coefficient.

A 1D shallow-flow model for two-layer flows based on FORCE scheme with wet–dry treatment

Abstract The two-layer problem is defined as the coexistence of two immiscible fluids, separated by an interface surface. Under the shallow-flow hypothesis, 1D models are based on a four equations system accounting for the mass and momentum conservation in each fluid layer. Mathematically, the system of conservation laws modelling 1D two-layer flows has the important drawback of loss of hyperbolicity, causing that numerical schemes based on the eigenvalues of the Jacobian become unstable. In this work, well-balanced FORCE scheme is proposed for 1D two-layer shallow flows. The FORCE scheme combines the first-order Lax–Friedrichs flux and the second-order Lax–Wendroff flux. The scheme is supplemented with a hydrostatic reconstruction procedure in order to ensure the well-balanced behaviour of the model for steady flows even under wet–dry conditions. Additionally, a method to obtain high-accuracy numerical solutions for two-layer steady flows including friction dissipation is proposed to design reference benchmark tests for model validation. The enhanced FORCE scheme is faced to lake-at-rest benchmarking tests and steady flow cases including friction, demonstrating its well-balanced character. Furthermore, the numerical results obtained for highly unsteady two-layer dambreaks are used to analyse the robustness and accuracy of the model under a wide range of flow conditions.

Modeling of a dispersive tsunami caused by a submarine landslide based on detailed bathymetry of the continental slope in the Nankai trough, southwest Japan

Tsunamis caused by submarine landslides are not accompanied by seismic waves and thus may appear at the coast without warning. In this study, detailed bathymetric surveys with a multi-narrow beam echo sounder were used to map submarine landslides on the continental shelf near Cape Muroto, in the Nankai trough off southwestern Japan. One of the surveyed submarine landslides was selected to supply dimensions for the simulation of a submarine mass movement by a two-layer flow model in which the upper and lower layers correspond to seawater and turbidity currents, respectively. The time series of seafloor deformation during this simulated landslide was used as the boundary condition to drive a tsunami simulation. The results showed strong directivity effects during tsunami generation in which pushing-dominant (positive) tsunami waves propagated seaward, in the direction of the submarine landslide, and pulling-dominant (negative) tsunami waves propagated landward. Both types of waves were strongly modified by frequency dispersion. For pulling-dominant waves, a tsunami simulation that included dispersion (Boussinesq) terms predicted greater maximum tsunami heights than a non-dispersive tsunami simulation. To avoid underestimation of tsunami heights, we recommend including dispersion terms when modeling tsunamis caused by submarine landslides for disaster planning purposes.

A (non-)hydrostatic free-surface numerical model for two-layer flows

A semi-implicit (non-)hydrostatic free-surface numerical model for two layer flows is derived from the Navier–Stokes equations by applying kinematic boundary conditions at moving interfaces and by decomposing the pressure into the hydrostatic and the hydrodynamic part. When the latter is ignored, the algorithm conveniently transforms into a solver for a hydrostatic flow. In addition, when the vertical grid spacing is larger than the layer depths, the algorithm naturally degenerates into a solver for the shallow water equations. In this paper, the presented numerical model is developed for the horizontal centrifugal casting, a metallurgical process, in which a liquid metal is poured into a horizontally rotating cylindrical mold. The centrifugal force pushes the liquid metal toward the mold wall resulting in a formation of a sleeve with a uniform thickness. The mold gradually extracts the sensible and the latent heat from the sleeve, which eventually becomes solid. Often a second layer of another material is introduced during the solidification of the first layer. The proposed free-surface model is therefore coupled with the heat advection-diffusion equation with a stiff latent heat source term representing the solidification. The numerical results show a good agreement with measurements of temperatures performed in the plant. A validation of the proposed model is also provided with the help of using other numerical techniques such as the approximate Riemann solver for the two layer shallow water equations and the volume of fluid method.

Application of a Special Technique for Controlling the Cutting Bed Height in Gas Drilling of Horizontal Wells

Sedimentation of cuttings limits application of gas drilling through a horizontal well section. We have constructed a theoretical model of two-layer flow as applied to flow of the gas and solid particles; we have developed a diffusion theory for gas drilling conditions for horizontal well sections. The calculations are performed using data from real wells. The calculations show that when drilling a horizontal section, a cutting bed will inevitably be formed and we need to control sedimentation of the cuttings by regulating the gas flow velocity. For low gas velocities, the resistance of the particles to motion is mainly created as a result of their collisions with the well wall in the cutting bed zone. For high gas flow velocities, the major resistance is created as a result of collisions of the particles with the well wall in the two-layer flow zone. Based on previous studies of two-layer flow and the cutting bed, it was established that gas injection should be done at the bottom of the well when gas drilling a horizontal section. The ascending gas flow velocity should be 1.5 times higher than the particle sedimentation rate. Only under such conditions is control of cutting bed formation possible.

The P1 and P2 approximations of the spherical harmonic method as applied to radiative heat transfer computations with allowance for strong blowing from the surface of a vehicle moving in the Jovian atmosphere

The spherical harmonics method in the P1 and P2 approximations is used to analyze radiative heat transfer for a space vehicle entering a planet’s atmosphere. Strong blowing of ablated materials from the vehicle surface is taken into account by using a two-layer flow model without allowance for the viscosity and thermal conduction of the gas. The heating and ablation of a multilayered thermal protection system are determined simultaneously with the vehicle’s flight trajectory, which is calculated taking into account the mass loss due to the ablation. The approach is illustrated by computing the flight of a space vehicle shaped as a spherical segment or a spherically blunted cone entering the Jovian atmosphere at a speed of 60 km/s and an entry angle of −5°.

A method for calculating intense injection from surfaces of blunt bodies entering planetary atmospheres at hypersonic velocities

Flow past blunt bodies entering planetary atmospheres at hypersonic velocities is studied. A method for calculating the flowfield near the body nose is developed which allows for radiative heat transfer in the P1 approximation of the spherical harmonics method but does not take gas viscosity and heat conduction into account. The solution is constructed on the basis of a two-layer flow model, with account for intense injection of ablation products from the body nose due to radiative heat fluxes from the shock layer. The advantages of the method are that the multi-dimensional character of the radiation field is taken into account and the general problem of radiation gasdynamics is solved on the basis of a unified algorithm. The flow past a spherical segment and a spherically-blunted cone re-entering the Earth’s atmosphere at a velocity of 20 km/s and an entry angle of −10° is calculated.

TWO-DIMENSIONAL NUMERICAL SIMULATION MODEL FOR UNIFYING DEBRIS FLOW AND SEDIMENT SHEET FLOW

The present study deals with deposition-erosion processes of debris flow with transition between fully dispersed debris flow and sediment sheet flow. A two-layer flow model proposed by the authors was applied to twodimensional numerical simulation of debris flows, and simple numerical experiments were carried out. It was indicated that a two-dimensional numerical simulation using the two-layer flow model can analyze phenomena in which velocity directions of upper-layers of water flows are different form that of lower layers of sediment-water mixture flow.

An Analysis of the Performance of Weir Type Oil Skimmers

A model of two-layer flow over a broad crested weir is used as the basis for comparing the performance of weir type skimmers. It is shown that the oil concentration of the mixture flowing over the weir can be described in terms of a single densimetric Froude number based on the weir flow and width, the slick thickness, and the density difference between the oil and the underlying water. Although all the data sets exhibit a large scatter, they broadly follow the trend of the model, and the analysis clearly demonstrates the superiority of the hydro-adjustable designs.

Effects of sedimentation of small red blood cell aggregates on blood flow in narrow horizontal tubes

The flow properties of aggregating red cell suspensions flowing at low flow rates through horizontal tubes are analyzed using a theoretical model. The effects of sedimentation of small aggregates, which will be formed at comparatively high flow rates, on the relative apparent viscosity are considered. In the case in which a large number of small aggregates are formed in a suspension flowing through a horizontal tube, it seems that red cells are transported as a concentrated suspension through the bottom part of the tube because of sedimentation of aggregates. A two-layer flow model is used for the distribution of red cells. It consists of plasma in the upper part and a concentrated red cell suspension in the bottom part of the tube divided by a smooth and horizontal interface. It is assumed that the suspension is a Newtonian fluid whose viscosity increases exponentially with hematocrit. The velocity distribution, the relative apparent viscosity and the flux of red cells are calculated as functions of width of plasma layer for a different discharge hematocrit. The theoretical results are compared with the results obtained from experimental data. The relative apparent viscosity increases rapidly with an increasing degree of sedimentation over a wide range of plasma layer widths.

Effects of Tip Clearance of Nozzle Vanes on Performance of Radial Turbine Rotor

In radial turbines with variable nozzles, the flow downstream of the nozzles could be distorted by the leakage flow through the tip clearance of the upstream nozzle vanes. To investigate the effects of flow distortion on the performance of turbine rotors, two rotors with different numbers of blades were tested for three types of distorted velocity distribution at the rotor inlet. In the case of the 20-blade rotor with moderate blade loading, the flow distortion at the rotor inlet had a negligible effect on the rotor characteristics, and the measured data on the turbine performances agreed well with prediction. Predictions were made with a conventional one-dimensional flow model applied to the rotor flow, while a two-layer flow model was applied to the flow in the nozzle with clearance. In the case of the 10-blade rotor with heavy blade loading, however, the rotor performance was found to be sensitive to the inlet flow distortion and was considerably lower than the prediction.

Performance deterioration of radial turbines due to tip clearance of nozzle blades.

To investigate the influence of tip clearance of a variable-area nozzle on the performance of a radial turbine, a series of experiments at the rated nozzle angle were pursued with various tip-clearance at various rotor speeds. The theory based on a two-layer flow model for nozzle with tip clearance, proposed in the preceeding paper, is applied to the prediction of turbine performance by combining the conventional prediction method for a turbine rotor. The predicted performances, such as the efficiency, the torque coefficient and the flow coefficient, agree well with the experimental data in practical application.

The effects of tip-clearance on the performance of nozzle blades of radial turbines. (2nd report Experiment and performance-prediction at three nozzle angles)

In the preceeding paper a two-layer flow model was proposed for analyzing the influence of tip-clearance on the turning angle and the pressure loss of turbine nozzles, and the prediction was compared with a series of experiments at the rated nozzle angle. In the present experiment, the nozzle angle was changed so that the throat area was 0.8 and 1.4 times the rated condition and similar experiments were repeated. Contour maps of total pressure loss and spanwise distributions of mean exit-flow angle are presented. The theory based on the two-layer flow model predicts the effects of tip clearance well, although it slightly underestimates the clearance effect at a lightly loaded condition. The reason for that and a way to correct it are discussed.

Measurement of Slip Velocity and True Flow Curve of Poly (vinyl chloride) Melts

PVC melts have viscoelastic properties. Moreover PVC melts have additional flow characteristics such as slippage on the wall of solid surfaces. The velocities on the wall of most polymer melts are usually zero, but those of PVC melts are not zero but finite. In the present paper, the slip velocities were measured by a simple method using some grooved nozzles, which can stop the slippage on the wall over a certain shear rate range. The measured values of the slip velocities were found to be from 10 to 60% of the average velocities. It was found that grooved nozzles should be suitably designed for various compounds, flow conditions, geometries, etc. The true flow curves, defined as those in which the effect of the slippage is removed, had almost the same property as the flow curves of the other polymer melts without slippage. A simple model of two-layer flow was introduced in order to predict the slip velocities and deepen understanding of the slippage mechanism. A very thin layer of a low molecular weight liquid is assumed to ooze out on the wall from a bulk flow layer of the PVC compound. The slip velocities could be predicted approximately from the model. It may be concluded that the very thin layer really exists, since the slip velocities had almost the same values regardless of the differences in the surface metals of the nozzles.

Determining the average flow characteristics of the carrier fluid in a turbulent gaseous suspension

The effect of solid particles on the thickness of the viscous sublayer in a stream of a gaseous suspension is analyzed on the basis of the two-layer flow model. The characteristics of the velocity profile of the carrier gas are determined, with collision interaction between solid particles and channel walls taken into account.