Ensemble-averaged Navier-Stokes Equations Research Articles

Effects of uniform injection and suction through perforated pentagonal cylinders on the flow and heat transfer

PurposeThe purpose of this paper is to study the effects of uniform injection and suction through a perforated pentagonal cylinder on the flow field and heat transfer.Design/methodology/approachThe finite-volume method has been used to solve the ensemble-averaged Navier-Stokes equations for incompressible flow at moderate Reynolds number (Re = 22,000) with the k-ɛ turbulence model equations.FindingsA computational fluid dynamics analysis of turbulent flow past a non-regular pentagonal cylinder with three different aspect ratios aspect ratios has been carried out to investigate the effects of uniform injection/suction through the front and all surfaces of the cylinder. It is found that flow field parameters such as drag coefficient, pressure coefficient and Nusselt number are affected considerably in some cases depend on injection/suction rate (Γ) and perforated wall position.Research limitations/implicationsTo optimize the efficiency of the injection and suction through a perforated surface, both wide-ranging and intensive further studies are required. Using various perforation ratios and injection/suction intensities are some possibilities.Practical implicationsControl of the vortex shedding and wake region behind bluff bodies is of vital interest in fluid dynamics. Therefore, applying uniform injection and suction from a perforated bluff body into the main flow can be used as a drag reduction mechanism, thermal protection and heat transfer enhancement.Originality/valueThis study provides unique insights into the active flow control method around pentagonal cylinders that can be useful for researchers in the field of fluid dynamics and aeronautics.

Modeling of Atmospheric Processes Based on the Averaged Navier-Stokes Equations

This work is devoted to the mathematical and numerical modeling of atmospheric processes based on the ensemble-averaged Navier-Stokes equations with the implementation of large eddy simulation. Within the real scientific research work are shown features of modeling atmospheric processes, the mathematical model of dynamic processes was developed in the average atmosphere, the numerical scheme and algorithm of the problem solution were developed, and realization of the problem characterized by instability of Rayleigh-Taylor about convective mass substances transfer with various densities was made.

Turbulence Models Performance Assessment for Pressure Prediction during Cylinder Water Entry

Numerical simulations of two-dimensional cylinder free droping into water are presented based on volume of fluid (VOF) method and dynamic mesh technique. Solutions with a time-accurate finite-volume method (FVM) were generated based on the unsteady compressible ensemble averaged Navier-Stokes equations for the air and the unsteady incompressible ensemble averaged Navier-Stokes equations for the water. Computed pressure histories of the cylinder were compared with experimentally measured values. The performance of various turbulence models for pressure prediction was assessed. The results indicate that Realizable k-epsilon model with Enhanced Wall Treatment is the best choice for engineering practice.

Numerical Simulation of Turbulent Flow Around a Square Cylinder with Uniform Injection or Suction and Heat Transfer

In the present study, the turbulent flow around a square cylinder with uniform injection or suction through various surfaces has been numerically studied. The wall functions of the viscous sublayer and log-law layer for velocity and temperature on the cylinder have been modified to allow for the effect of the injection or suction through the cylinder. The finite-volume method has been used for solving the ensemble averaged Navier-Stokes equations for incompressible flow in conjunction with the k − ϵ turbulence model equations that include the Kato-Launder's modification. A nonuniform staggered grid arrangement has been used. The results show that the parameters taken into account such as drag coefficient, and Strouhal and Nusselt numbers have been influenced by the uniform injection and suction through certain surfaces of the square cylinder, as well as the flow field parameters.

Using a One-and-a-Half Order Closure Model of the Atmospheric Boundary Layer for Surface Flux Footprint Estimation

A knowledge of the distribution of the contribution of upwind sources to measurements of vertical scalar flux densities is important for the correct interpretation of eddy covariance data. Several approaches have been developed to estimate this so-called footprint function. Here a new approach based on the ensemble-averaged Navier—Stokes equations is presented. Comparisons of numerical results using this approach with results from other studies under a range of environmental conditions show that the model predictions are robust. Moreover, the approach outlined here has the advantage of a potential wide applicability, due to an ability to take into account the heterogeneous nature of underlying surfaces. For example, the model showed that any variations in surface drag, such as must occur in real life heterogeneous canopies, can exert a marked influence of the shape and extent of flux footprints. Indeed, it seems likely that under such circumstances, estimates of surface fluxes will be weighted towards areas of highest foliage density (and therefore quite likely higher photosynthetic rates) close to the measurement sensor.

Numerical Prediction of Turbulent Wakes Behind a Square Cylinder

ABSTRACTThis paper presents a numerical study on turbulent vortex shedding flows past a square cylinder. The 2D unsteady periodic shedding motion was resolved in the calculation and the superimposed turbulent fluctuations were simulated with a second-order Reynolds-stress closure model. The calculations were carried out by solving numerically the fully elliptic ensemble-averaged Navier-Stokes equations coupled with the turbulence model equations together with the two-layer approach in the treatment of the near-wall region. The performance of the computations was evaluated by comparing the numerical results with data from available experiments. Results indicate that the present study gives good agreement in the shedding frequency and mean drag as well as in some phase profiles of the mean velocity.

Calculation of particle trajectories in solid-rocket motors with arbitrary acceleration

The particle trajectories in a solid-rocket motor under several acceleration conditions have been simulated using a combined Eulerian-Lagrangian analysis. This analysis uses the numerical solution of ensemble-averaged Navier-Stokes equations for the continuous phase, coupled with a Lagrangiah analysis for the discrete (particulate) phase to simulate the two-phase internal flow. A Linearized Block Implicit scheme is used to solve the governing equations for the continuous phase, which allows the use of a highly stretched grid with sublayer resolution. The motion of the particles is tracked in computational coordinate space resulting in computational efficiency. The governing equations are written in generalized noninertial reference frame so that effect of motor acceleration can be easily included. While the analysis allows complete-coupled calculations, the present study has neglected the effect of the participate phase on the gas-phase flowfield. Particle trajectories under specified acceleration conditions, that include axial acceleration, axial and lateral acceleration, as well as a centrifuge test for a tandem pulse rocket motor have been calculated. The calculated results indicate that the acceleration effects strongly influence the particle impingement patterns on the motor case and the nozzle.

Calculation of the two-phase aft-dome flowfield in solid rocket motors

The two-phase flowfield in the aft-dome region of a solid rocket motor (SRM) with submerged nozzle has been simulated using a combined Eulerian-Lagrangian analysis. This analysis uses the numerical solution of ensemble averaged Navier-Stokes equations for the continuous (gas) phase coupled with a Lagrangian analysis for the discrete (particulate) phase to simulate the two-phase internal flow. A linearized block-implicit (LBI) scheme is used to solve the governing equations for the continuous phase, which allows the use of a highly stretched grid with sublayer resolution. The motion of the particles is tracked in computational coordinate space resulting in computational efficiency, and the interphase coupling terms for the Eulerian analysis are computed from the instantaneous distribution of the particles. A low Reynolds number form of the k-e turbulence model is used with modifications for injection driven flows. Calculations have been performed for a particular grain configuration of the Space Shuttle SRM. The flowfield in the vicinity of the submerged nozzle, the particle trajectories, and the sensitivity of two-phase effects (such as slag accumulation) to the particle injection parameters are presented in this paper.

Implicit multiple-grid solution of the compressible Navier-Stokes equations using k-epsilon turbulence closure

In the present work, an algorithm for the numerical solution of the two-dimensional mass-weighted, ensemble- averaged, compressible Navier-Stokes equations is presented. Turbulence closure for the Reynolds stresses is obtained using a low-Reynolds-n umber two-equation k-s model, which includes near-wall effects. The same algorithm is used for the integration of both the Navier-Stokes and the turbulence-transport equations. The algorithm consists of a basic explicit finite-volume scheme, whose convergence is accelerated using local time-step- ping and multiple-grid techniques. Convergence is further enhanced by the use of an implicit-residual-smoothing technique, applied both in the fine and the coarser grids. The application of the numerical scheme to the solution of the k-s equations is examined in detail. Comparisons of computations with experimental data are presented for three shock-wave/turbulent boundary-layer interaction flows. Algorithm convergence rate and CPU-time require- ments are discussed. HE numerical solution of the Navier-Stokes equations for the simulation of turbulent flowfields is a subject of intense research and code development work.1 Interest is focused both on code applicability to variegated config- urations and on computational rapidity. Although direct simulation of turbulent flows2 or large-eddy numerical sim- ulations using subgrid-turbulence modeling 3'4 have appeared in the literature, current status of algorithm development and computer power indicate that for practical applications the ensemble-averaged Navier-Stokes equations should be used in conjunction with transport equations for turbulence closure.5'7 Algebraic or mixing-length models may provide satisfactory results for relatively simple flow geometries8 but require the determination of the shear-layer thickness and of the distance of each grid point from the solid boundary. Thus, they lack both geometric invariance and locality, which are highly desirable properties, from a computational viewpoint, when addressing complex flowfields with many interacting solid boundaries. Although research on Reynolds-stre ss-transport closure appears quite promising,9'10 its extension to three dimensions involves considerable increase of the number of transport equations to be solved. Also, further research con- cerning wall effects is required, the more so since the use of wall functions is considered inadequate.11 On the other hand, the use of two-equation closures, such as A>£, 12~14 is quite widespread. Notwithstanding the fact that the use of the Boussinesq hypothesis15 introduces a question- able simplification of the flow physics,16 the major drawback of the k-s model is probably the near-wall formulation which fails to reproduce correctly the effects of the solid boundary on turbulence. Several variants of the original Jones-Launder model12 have been developed in an attempt to improve upon near-wall modeling. Some ten such models have been thor- oughly examined in a critical review article by Patel et al., 17 who concluded that the models of Launder and Sharma,14

Navier-Stokes analysis of solid propellant rocket motor internal flows

A multidimensional implicit Navier-Stokes analysis that uses numerical solution of the ensemble-averaged Navier-Stokes equations in a nonorthogonal, body-fitted, cylindrical coordinate system has been applied to the simulation of the steady mean flow in solid propellant rocket motor chambers. The calculation procedure incorporates a two-equation (k-epsilon) turbulence model and utilizes a consistently split, linearized block-implicit algorithm for numerical solution of the governing equations. The code was validated by comparing computed results with the experimental data obtained in cylindrical-port cold-flow tests. The agreement between the computed and experimentally measured mean axial velocities is excellent. The axial location of transition to turbulent flow predicted by the two-equation (k-epsilon) turbulence model used in the computations also agrees well with the experimental data. Computations performed to simulate the axisymmetric flowfield in the vicinity of the aft field joint in the Space Shuttle solid rocket motor using 14,725 grid points show the presence of a region of reversed axial flow near the downstream edge of the slot.