Axisymmetric Turbulent Flow Research Articles

Parallel solution-adaptive method for two-dimensional non-premixed combusting flows

A parallel Adaptive Mesh Refinement (AMR) algorithm is proposed and applied to the predictions of both laminar and turbulent steady non-premixed compressible combusting flows. The parallel solution-adaptive algorithm solves the system of partial-differential equations governing two-dimensional axisymmetric laminar and turbulent compressible flows for reactive thermally perfect gaseous mixtures using a fully coupled finite-volume formulation on body-fitted multi-block quadrilateral mesh. Numerical results for co-flow laminar and turbulent diffusion flames are described and compared to available experimental data. The numerical results demonstrate the validity and potential of the parallel AMR approach for predicting both fine-scale features of laminar and complex turbulent non-premixed flames.

Relaminarization of Axisymmetric Turbulent Flow With Combined Axial Jet and Side Injection in a Pipe

The effect of side mass injection on turbulent flow with axial entry to a circular duct in the form of centrally confined jet has been investigated. A standard κ-ε model modified for streamline curvature has been used for detailed analysis following a comparison with a κ-ω model for some test cases. Results show that flow stabilization and relaminarization could occur due to the side injection. The predicted recirculation zone, friction factor, total turbulent energy, turbulent shear stress, Taylor scale Reynolds number, and turbulent energy flux show gradual reduction with increase in the side injection velocity.

Analysis and Prevention of Vortex Breakdown in the Simplified Discharge Cone of a Francis Turbine

We perform a numerical analysis of the decelerated swirling flow into the discharge cone of a model Francis turbine operated at variable discharge and constant head, using an axisymmetric turbulent swirling flow model and a corresponding simplified computational domain. Inlet boundary conditions correspond to velocity and turbulent kinetic energy profiles measured downstream the Francis runner. Our numerical results are validated against experimental data on a survey section further downstream in the cone, showing that the Reynolds stress turbulence model with a quadratic pressure-strain term correctly captures the flow field. It is shown that the diffuser performance quickly deteriorates as the turbine discharge decreases, due to the occurrence and development of vortex breakdown, with a central quasistagnant region. We investigate a novel flow control technique, which uses a water jet injected from the runner crown tip along the axis. It is shown that the jet discharge can be optimized for minimum overall losses, while the vortex breakdown is eliminated. This flow control method is useful for mitigating the Francis turbine flow instabilities when operating at partial discharge.

Pressure recovery studies on a supersonic COIL with central ejector configuration

A chemical oxygen–iodine laser (COIL) is an electronic transition, low pressure, high throughput system. The field use of this laser demands the development of suitable pressure recovery systems. Ejector based pressure recovery systems form a potent alternative for open cycle COIL operation. The two possible configurations of motive gas injection in ejectors are peripheral and central. The present paper focuses on the investigation of a central injection low pressure ejector operated with a small scale supersonic COIL (SCOIL). The ejector handles a motive flow of nearly 120 g s −1 and an entrained laser flow of nearly 3 g s −1. The predicted geometry using integral methods has been validated numerically by employing Fluent 6.1 software in a 2-d axisymmetric viscous turbulent flow formulation. The numerical predictions have been experimentally validated, which indicate a pressure recovery of 63 Torr at design conditions. The results also show that the recovered pressure improves to 75 Torr for an off-design condition of higher motive flow rate.

Investigation of the Cross-beam Correlation Algorithm to Reconstruct Local Field Statistics from Line-of-sight Measurements in Turbulent Flows

Optical techniques such as speckle photography and rainbow schlieren deflectometry yield path integrated measurements of deflection angle instead of the local field variable such as density, temperature and/or species concentration. Thus, a reconstruction algorithm is employed to obtain the local properties from the path-integrated measurements. Cross-beam correlation (CBC) algorithm provides the link between path-integrated and local field statistics in time-averaged axisymmetric turbulent flows. Path-integrated statistics are obtained using orthogonal light rays crossing within the turbulent flow. The algorithm assumes local isotropy and negligible correlation between points on orthogonal beams, which is valid strictly in fully turbulent flows. In this study, noise-free synthetic scalar turbulence data are generated and used to determine how different assumptions in the CBC algorithm affect the reconstruction accuracy. Results show that the reconstruction accuracy is excellent for a narrow correlation function (or small integral length scale), while significant errors are incurred in case of a wide correlation function. A procedure to improve the reconstruction accuracy of the CBC algorithm is proposed in this study.

Axisymmetric Swirling Flow Simulation of the Draft Tube Vortex in Francis Turbines at Partial Discharge

The flow in the draft tube cone of Francis turbines operated at partial discharge is a complex hydrodynamic phenomenon where an incoming steady axisymmetric swirling flow evolves into a three-dimensional unsteady flow field with precessing helical vortex (also called vortex rope) and associated pressure fluctuations. The paper addresses the following fundamental question: is it possible to compute the circumferentially averaged flow field induced by the precessing vortex rope by using an axisymmetric turbulent swirling flow model? In other words, instead of averaging the measured or computed 3D velocity and pressure fields we would like to solve directly the circumferentially averaged governing equations. As a result, one could use a 2D axi-symmetric model instead of the full 3D flow simulation, with huge savings in both computing time and resources. In order to answer this question we first compute the axisymmetric turbulent swirling flow using available solvers by introducing a stagnant region model (SRM), essentially enforcing a unidirectional circumferentially averaged meridian flow as suggested by the experimental data. Numerical results obtained with both models are compared against measured axial and circumferential velocity profiles, as well as for the vortex rope location. Although the circumferentially averaged flow field cannot capture the unsteadiness of the 3D flow, it can be reliably used for further stability analysis, as well as for assessing and optimizing various techniques to stabilize the swirling flow. In particular, the methodology presented and validated in this paper is particularly useful in optimizing the blade design in order to reduce the stagnant region extent, thus mitigating the vortex rope and expending the operating range for Francis turbines.

A novel spectral analysis algorithm to obtain local scalar field statistics from line-of-sight measurements in turbulent flows

Statistical tomography to obtain local field variables from non-intrusive line-of-sight measurements in turbulent flows has been an intriguing subject for some time. In this study, a novel algorithm is presented to obtain statistical information on the local scalar field in axisymmetric turbulent flows. The algorithm uses line-of-sight transverse deflection angle measurements in only one view direction to greatly simplify the optical configuration. The validity of the algorithm is examined using noise-free synthetically generated scalar data that simulate the concentration field of a turbulent helium jet. Results show that the proposed algorithm provides excellent reconstruction of integral length scale and variance of refractive index difference, which can be related to scalar physical properties such as density, temperature and/or species concentrations. Good reconstruction accuracy and the need for a simple optical configuration make the proposed algorithm a promising method to characterize the scalar field in turbulent flows using path-integrated measurements.

Computation of Axisymmetric Turbulent Viscous Flow Around Sphere

Axisymmetric turbulent viscous flow around sphere is computed using finite volume method based on Reynolds-averaged Navier-Stokes (RANS) equations. Two-dimensional axisymmetric flow solver has been used to analyze flow at Reynolds number of 5×106. Spalart-Allmaras (S-A) and shear stress transport (SST) k-ω turbulence models are used to capture turbulent viscous flow. The numerical results in terms of the skin friction coefficient, pressure coefficient and drag coefficient for different Reynolds numbers have been shown either graphically or in the tabular form. Velocity vectors have been displayed graphically. The computed results show good agreement with published experimental measurements. Keywords: Axisymmetric body of revolution; Sphere; Viscous drag; CFD; Turbulence model; Reynolds-averaged Navier-Stokes (RANS) equations. © 2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i2.1286

Dynamics of the viscous interaction of a ring vortex with a flat screen

A separation turbulent flow has been mathematically simulated on the basis of numerical solution of nonstationary Navier-Stokes equations for determining the dynamics of viscous interaction of a ring vortex with a flat screen. The problem was solved for an axisymmetric turbulent flow at Reynolds numbers falling within the range 105–107. On the basis of the calculation data obtained, the interaction of a ring vortex with a turbulent flow induced on the screen and with the secondary ring vortices was investigated. The data obtained are in qualitative agreement with the analogous data obtained by other authors with the use of the discrete-vortex method and the boundary-layer theory as well as with the available experimental and calculation data obtained for a laminar flow.

Effect of Prandtl number on heat transfer characteristics in an axisymmetric sudden expansion: A numerical study

Using the standard k-e turbulence model, an incompressible, axisymmetric turbulent flow with a sudden expansion was simulated. Effect of Prandtl number on heat transfer characteristics downstream of the expansion was investigated. The simulation revealed circulation downstream of the expansion. A secondary circulation (corner eddy) was also predicted. Reattachment was predicted at approximately 10 step heights. Corresponding to Prandtl number of 7.0, a peak Nusselt number 13 times the fully-developed value was predicted. The ratio of peak to fully-developed Nusselt number was shown to decrease with decreasing Prandtl number. Location of maximum Nusselt number was insensitive to Prandtl number.

Inleakage of a vortex-ring bunch onto a plane screen

A method is suggested for simulating axisymmetric laminar or turbulent flows formed during the motion of a vortex-ring bunch of given geometry and circulation toward a plane screen. Earlier, similar problems were simulated with the numerical solution of the Navier-Stokes equations for laminar flows. Turbulent flows have remained unconsidered until now. When a vortex ring approaches the screen, the secondary nonstationary flow is induced near the screen’s surface and this secondary flow causes the formation of the radial boundary layer (provided that air viscosity is taken into account). First, the medium spreads out from the critical point at the screen’s center with the negative pressure gradient along the radial coordinate and then detaches in the region of the positive pressure gradient. This radial wall flow and the corresponding boundary layer are considered in the quasi-stationary approximation. When the boundary layer detaches at successive instances, the flow is replenished with the radially moving secondary vortex rings whose circulations have the sign opposite to that of the circulation of the primary vortex ring. It is the interaction of the primary and secondary vortices that governs process dynamics, which differs substantially from that in the case when the formation of secondary vortices is disregarded. The suggested method is based on the method of discrete vortices (a perfect liquid) and the boundary-layer (laminar or turbulent) theory. During the development of the flow under investigation, the nonstationary ascending flow in the direction perpendicular to the screen’s plane is formed and then this flow decays and dissipates. Simulations for large Reynolds numbers corresponding to the formation of the turbulent boundary layer show that the velocity of ascending vortices in the plane of the initial vortex bunch is less than one-tenth of the initial velocity of the descending vortex ring. The boundary layer is introduced into calculations with the sole goal of determining the parameters of the secondary vortex rings formed during boundary-layer detachments. The interaction of the primary and secondary vortices is then considered within the framework of a perfect medium. Simulations for large Reynolds numbers corresponding to the formation of the turbulent boundary layer on the screen were correlated with the available data obtained in laboratory experiments for small Reynolds numbers. Qualitative agreement between the simulations and experiments is fairly satisfactory. The simulation for one combination of the circulation and vortex-ring geometry takes at most 10–15 min with the use of an average PC.

Stability and Mixing of a Vertical Axisymmetric Buoyant Jet in Shallow Water

The stability, mixing and effect of downstream control on axisymmetric turbulent buoyant jets discharging vertically into shallow stagnant water is studied using 3D Reynolds-averaged Navier–Stokes equations (RANS) combined with a buoyancy-extended k –e model. The steady axisymmetric turbulent flow, temperature (or tracer concentration) and turbulence fields are computed using the finite volume method on a high resolution grid. The numerical predictions demonstrate two generic flow patterns for different turbulent heated jet discharges and environmental parameters (i) a stable buoyant discharge with the mixed fluid leaving the vertical jet region in a surface warm water layer; and (ii) an unstable buoyant discharge with flow recirculation and re-entrainment of heated water. A stratified counterflow region always appears in the far-field for both stable and unstable buoyant discharges. Provided that the domain radius L exceeds about 6H, the near field interaction and hence discharge stability is governed chiefly by the jet momentum length scale to depth ratio lM/H, regardless of downstream control. The near field jet stability criterion is determined to be lM/H = 3.5. A radial internal hydraulic jump always exists beyond the surface impingement region, with a 3- to 6-fold increase in dilution across the jump compared with vertical buoyant jet mixing. The predicted stability category, velocity and temperature/concentration fields are well-supported by experiments of all previous investigators.

Properties of Steady States in Turbulent Axisymmetric Flows

We experimentally study the properties of mean and most probable velocity fields in a turbulent von Kármán flow. These fields are found to be described by two families of functions, as predicted by a recent statistical mechanics study of 3D axisymmetric flows. We show that these functions depend on the viscosity and on the forcing. Furthermore, when the Reynolds number is increased, we exhibit a tendency for Beltramization of the flow, i.e., a velocity-vorticity alignment. This result provides a first experimental evidence of nonlinearity depletion in nonhomogeneous nonisotropic turbulent flow.

A model relating Eulerian spatial and temporal velocity correlations

In this paper we propose a model to relate Eulerian spatial and temporal velocity autocorrelations in homogeneous, isotropic and stationary turbulence. We model the decorrelation as the eddies of various scales becoming decorrelated. This enables us to connect the spatial and temporal separations required for a certain decorrelation through the ‘eddy scale’. Given either the spatial or the temporal velocity correlation, we obtain the ‘eddy scale’ and the rate at which the decorrelation proceeds. This leads to a spatial separation from the temporal correlation and a temporal separation from the spatial correlation, at any given value of the correlation relating the two correlations. We test the model using experimental data from a stationary axisymmetric turbulent flow with homogeneity along the axis.

Numerical calculations of erosion in an abrupt pipe contraction of different contraction ratios

AbstractErosion predictions in a pipe with abrupt contraction of different contraction ratios for the special case of two‐phase (liquid and solid) turbulent flow with low particle concentration are presented. A mathematical model based on the time‐averaged governing equations of 2‐D axi‐symmetric turbulent flow is used for the calculations of the fluid velocity field (continuous phase). The particle‐tracking model of the solid particles is based on the solution of the governing equation of each particle motion taking into consideration the effect of particle rebound behaviour. Models of erosion were used to predict the erosion rate in mg/g. The effect of Reynolds number and flow direction with respect to the gravity was investigated for three contraction geometries considering water flow in a carbon steel pipe. The results show that the influence of the contraction ratio on local erosion is very significant. However, this influence becomes insignificant when the average erosion rates over the sudden contraction area are considered. The results also indicate the significant influence of inlet velocity variations. The influence of buoyancy is significant for the cases of low velocity of the continuous flow. A threshold velocity below which erosion may be neglected was indicated. Copyright © 2004 John Wiley & Sons, Ltd.

Verification of Finite Volume Computations on Steady-State Fluid Flow and Heat Transfer

This work presents a post-processing tool for the verification of steady-state fluid flow and heat transfer finite volume computations. It is based both on the generalized Richardson extrapolation and the Grid Convergence Index GCI. The observed order of accuracy and a error band where the grid independent solution is expected to be contained are estimated. The results corresponding to the following two and three-dimensional steady-state simulations are post-processed: a flow inside a cavity with moving top wall, an axisymmetric turbulent flow through a compressor valve, a premixed methane/air laminar flat flame on a perforated burner, and the heat transfer from an isothermal cylinder enclosed by a square duct. Discussion is carried out about the certainty of the estimators obtained with the post-processing procedure. They have been shown to be useful parameters in order to assess credibility and quality to the reported numerical solutions.

Experimental Study of the Constitutive Equation for an Axisymmetric Complex Turbulent Flow

Nonlinear constitutive equations have been proposed to overcome the limitations of linear eddy-viscosity models to describe complex turbulent flows. These new equations have been mainly indirectly compared to experimental data, through the outputs of numerical models. It is proposed in this paper to directly check the constitutive equation, using a projection of the stress tensor onto a tensor basis. The test case chosen is a complex axisymmetric flow generated by a double annular burner. Measurements have been taken on a fine grid, enabling the local estimate of the stress and strain tensors. A map of the Prandtl mixing-length is then given, together with the experimental evaluation of several invariants of the flow. The nonlinear constitutive equation is then tested using a 4 terms development. The angles of the stress tensor with the terms of the tensor basis are plotted, indicating which direction is predominant for each region of the flow. The different invariants are finally used to experimentally estimate the dissipation rate.

Approximate method for calculating turbulent two-phase flow in a channel with permeable walls

Based on a model of a double-velocity and two-temperature medium the authors constructed a system of equations that describes plane or axisymmetric turbulent flow of a gas suspension in a channel with permeable walls. The system of equations of motion and heat transfer reduces to a system of ordinary differential equations, whose integration is much less difficult than solution of the initial system. The authors obtained the distribution of the velocity and local characteristics of turbulence in the channel with injection with allowance for the inverse effect of a condensed phase.

Dispersion and deposition of particles in a turbulent pipe flow with sudden expansion

Numerical simulations of dispersion and deposition of particles in an axisymmetric turbulent pipe flow with sudden expansion are performed. The cases that particles of different sizes are released from point sources and/or are uniformly distributed are studied. The effects of turbulence diffusion, Brownian dispersion, lift force, and gravity are included in the computational model. A thermodynamically consistent, rate-dependent algebraic stress model is used to simulate the mean velocity and turbulent intensity fields. The instantaneous fluctuating velocity is simulated as a continuous Gaussian random vector field. The Brownian force is modeled as a Gaussian white noise random process. Ensembles of several thousand particle trajectories are evaluated and are statistically analyzed. The effects of particle source location, particle size, and gravity on dispersion and deposition are studied. The particle capture efficiency for an initially uniform distribution is also evaluated. The predicted particle and fluid velocities are compared with the available experimental data and reasonable agreement is observed.

Dispersion and deposition of particles in a turbulent pipe flow with sudden expansion

Numerical simulations of dispersion and deposition of particles in an axisymmetric turbulent pipe flow with sudden expansion are performed. The cases that particles of different sizes are released from point sources and/or are uniformly distributed are studied. The effects of turbulence diffusion, Brownian dispersion, lift force, and gravity are included in the computational model. A thermodynamically consistent, rate-dependent algebraic stress model is used to simulate the mean velocity and turbulent intensity fields. The instantaneous fluctuating velocity is simulated as a continuous Gaussian random vector field. The Brownian force is modeled as a Gaussian white noise random process. Ensembles of several thousand particle trajectories are evaluated and are statistically analyzed. The effects of particle source location, particle size, and gravity on dispersion and deposition are studied. The particle capture efficiency for an initially uniform distribution is also evaluated. The predicted particle and fluid velocities are compared with the available experimental data and reasonable agreement is observed.