scholarly journals Direct numerical simulations of laminar and transitional flows in diverging pipes

2019 ◽  
Vol 30 (1) ◽  
pp. 75-92 ◽  
Author(s):  
Dhanush Vittal Shenoy ◽  
Mostafa Safdari Shadloo ◽  
Jorge Peixinho ◽  
Abdellah Hadjadj
Keyword(s):  
Velocity Profile ◽  
Numerical Simulations ◽  
Stokes Equations ◽  
Spectral Element ◽  
Skin Friction Coefficient ◽  
Finite Amplitude ◽  
Direct Numerical Simulations ◽  
Recirculation Region ◽  
Cross Sectional ◽  
Content Type

Purpose Fluid flows in pipes whose cross-sectional area are increasing in the stream-wise direction are prone to separation of the recirculation region. This paper aims to investigate such fluid flow in expansion pipe systems using direct numerical simulations. The flow in circular diverging pipes with different diverging half angles, namely, 45, 26, 14, 7.2 and 4.7 degrees, are considered. The flow is fed by a fully developed laminar parabolic velocity profile at its inlet and is connected to a long straight circular pipe at its downstream to characterise recirculation zone and skin friction coefficient in the laminar regime. The flow is considered linearly stable for Reynolds numbers sufficiently below natural transition. A perturbation is added to the inlet fully developed laminar velocity profile to test the flow response to finite amplitude disturbances and to characterise sub-critical transition. Design/methodology/approach Direct numerical simulations of the Navier–Stokes equations have been solved using a spectral element method. Findings It is found that the onset of disordered motion and the dynamics of the localised turbulence patch are controlled by the Reynolds number, the perturbation amplitude and the half angle of the pipe. Originality/value The authors clarify different stages of flow behaviour under the finite amplitude perturbations and shed more light to flow physics such as existence of Kelvin–Helmholtz instabilities as well as mechanism of turbulent puff shedding in diverging pipe flows.

The analysis and modelling of dilatational terms in compressible turbulence

1991 ◽  
Vol 227 ◽  
pp. 473-493 ◽  
Author(s):  
S. Sarkar ◽  
G. Erlebacher ◽  
M. Y. Hussaini ◽  
H. O. Kreiss
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Simulations ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Mixing Layer ◽  
Direct Numerical Simulations ◽  
Homogeneous Turbulence ◽  
Compressible Turbulence ◽  
Quasi Equilibrium ◽  
Compressible Mixing Layer

It is shown that the dilatational terms that need to be modelled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of the compressible velocity field, which generates these dilatational terms, is explored by asymptotic analysis of the compressible Navier-Stokes equations in the case of homogeneous turbulence. The lowest-order equations for the compressible field are solved and explicit expressions for some of the associated one-point moments are obtained. For low Mach numbers, the compressible mode has a fast timescale relative to the incompressible mode. Therefore, it is proposed that, in moderate Mach number homogeneous turbulence, the compressible component of the turbulence is in quasi-equilibrium with respect to the incompressible turbulence. A non-dimensional parameter which characterizes this equilibrium structure of the compressible mode is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

Simulation of water/FMWCNT nanofluid forced convection in a microchannel filled with porous material under slip velocity and temperature jump boundary conditions

2019 ◽  
Vol 30 (5) ◽  
pp. 2329-2349 ◽  
Author(s):  
Ehsan Gholamalizadeh ◽  
Farzad Pahlevanzadeh ◽  
Kamal Ghani ◽  
Arash Karimipour ◽  
Truong Khang Nguyen ◽  
...  
Keyword(s):  
Velocity Profile ◽  
Porous Material ◽  
Forced Convection ◽  
Slip Velocity ◽  
Stokes Equations ◽  
Computer Code ◽  
Darcy Number ◽  
Navier Stokes ◽  
Working Fluid ◽  
Content Type

Purpose This study aims to numerically study the forced convection effects on a two-dimensional microchannel filled with a porous material containing the water/FMWCNT nanofluid. The upper and lower microchannel walls were fully insulated thermally along 15 per cent of their lengths at each end of the microchannel, with the in-between length being exposed to a constant temperature. The slip velocity boundary condition was applied along the microchannel walls. Design/methodology/approach The Navier–Stokes equations were discretized before being solved numerically via a FORTRAN computer code. The following ranges were considered for the studied parameters: slip factor (B) equal to 0.001, 0.01 and 0.1; Reynolds number (Re) between 10 and 100; solid nanoparticle mass fraction (ϕ) between 0.0012 and 0.0025; Darcy number (Da) between 0.001 and 0.1; and porosity factor (ε) between 0.4 and 0.9. Findings Increasing the Da caused a greater increase in the velocity profile than increasing Re, whereas increasing porosity did not affect the velocity profile growth at all. Originality/value This paper is the continuation of the authors’ previous studies. Using the water/FMWCNT nanofluid as the working fluid in microchannels is among the achievements of this study.

scholarly journals Sustained gravity currents in a channel

2016 ◽  
Vol 798 ◽  
pp. 853-888 ◽  
Author(s):  
Andrew J. Hogg ◽  
Mohamad M. Nasr-Azadani ◽  
Marius Ungarish ◽  
Eckart Meiburg
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Analytical Techniques ◽  
Direct Numerical Simulations ◽  
Density Difference ◽  
Water Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Shallow Layer ◽  
Dense Fluid

Gravitationally driven motion arising from a sustained constant source of dense fluid in a horizontal channel is investigated theoretically using shallow-layer models and direct numerical simulations of the Navier–Stokes equations, coupled to an advection–diffusion model of the density field. The influxed dense fluid forms a flowing layer underneath the less dense fluid, which initially filled the channel, and in this study its speed of propagation is calculated; the outflux is at the end of the channel. The motion, under the assumption of hydrostatic balance, is modelled using a two-layer shallow-water model to account for the flow of both the dense and the overlying less dense fluids. When the relative density difference between the fluids is small (the Boussinesq regime), the governing shallow-layer equations are solved using analytical techniques. It is demonstrated that a variety of flow-field patterns are feasible, including those with constant height along the length of the current and those where the height varies continuously and discontinuously. The type of solution realised in any scenario is determined by the magnitude of the dimensionless flux issuing from the source and the source Froude number. Two important phenomena may occur: the flow may be choked, whereby the excess velocity due to the density difference is bounded and the height of the current may not exceed a determined maximum value, and it is also possible for the dense fluid to completely displace all of the less dense fluid originally in the channel in an expanding region close to the source. The onset and subsequent evolution of these types of motions are also calculated using analytical techniques. The same range of phenomena occurs for non-Boussinesq flows; in this scenario, the solutions of the model are calculated numerically. The results of direct numerical simulations of the Navier–Stokes equations are also reported for unsteady two-dimensional flows in which there is an inflow of dense fluid at one end of the channel and an outflow at the other end. These simulations reveal the detailed mechanics of the motion and the bulk properties are compared with the predictions of the shallow-layer model to demonstrate good agreement between the two modelling strategies.

Evolution of enstrophy in shock/homogeneous turbulence interaction

2012 ◽  
Vol 707 ◽  
pp. 74-110 ◽  
Author(s):  
Krishnendu Sinha
Keyword(s):  
Shock Wave ◽  
Numerical Simulations ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Interaction Analysis ◽  
Direct Numerical Simulations ◽  
Homogeneous Isotropic Turbulence ◽  
Mean Flow ◽  
Linear Interaction

AbstractInteraction of turbulent fluctuations with a shock wave plays an important role in many high-speed flow applications. This paper studies the amplification of enstrophy, defined as mean-square fluctuating vorticity, in homogeneous isotropic turbulence passing through a normal shock. Linearized Navier–Stokes equations written in a frame of reference attached to the unsteady shock wave are used to derive transport equations for the vorticity components. These are combined to obtain an equation that describes the evolution of enstrophy across a time-averaged shock wave. A budget of the enstrophy equation computed using results from linear interaction analysis and data from direct numerical simulations identifies the dominant physical mechanisms in the flow. Production due to mean flow compression and baroclinic torques are found to be the major contributors to the enstrophy amplification. Closure approximations are proposed for the unclosed correlations in the production and baroclinic source terms. The resulting model equation is integrated to obtain the enstrophy jump across a shock for a range of upstream Mach numbers. The model predictions are compared with linear theory results for varying levels of vortical and entropic fluctuations in the upstream flow. The enstrophy model is then cast in the form of$k$–$\epsilon $equations and used to compute the interaction of homogeneous isotropic turbulence with normal shocks. The results are compared with available data from direct numerical simulations. The equations are further used to propose a model for the amplification of turbulent viscosity across a shock, which is then applied to a canonical shock–boundary layer interaction. It is shown that the current model is a significant improvement over existing models, both for homogeneous isotropic turbulence and in the case of complex high-speed flows with shock waves.

Direct numerical simulations of bubbly flows. Part 1. Low Reynolds number arrays

1998 ◽  
Vol 377 ◽  
pp. 313-345 ◽  
Author(s):  
ASGHAR ESMAEELI ◽  
GRÉTAR TRYGGVASON
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Stokes Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Direct Numerical Simulations ◽  
Two Dimensional ◽  
Rise Velocity ◽  
Regular Array ◽  
Average Rise

Direct numerical simulations of the motion of two- and three-dimensional buoyant bubbles in periodic domains are presented. The full Navier–Stokes equations are solved by a finite difference/front tracking method that allows a fully deformable interface between the bubbles and the ambient fluid and the inclusion of surface tension. The governing parameters are selected such that the average rise Reynolds number is O(1) and deformations of the bubbles are small. The rise velocity of a regular array of three-dimensional bubbles at different volume fractions agrees relatively well with the prediction of Sangani (1988) for Stokes flow. A regular array of two- and three-dimensional bubbles, however, is an unstable configuration and the breakup, and the subsequent bubble–bubble interactions take place by ‘drafting, kissing, and tumbling’. A comparison between a finite Reynolds number two-dimensional simulation with sixteen bubbles and a Stokes flow simulation shows that the finite Reynolds number array breaks up much faster. It is found that a freely evolving array of two-dimensional bubbles rises faster than a regular array and simulations with different numbers of two-dimensional bubbles (1–49) show that the rise velocity increases slowly with the size of the system. Computations of four and eight three-dimensional bubbles per period also show a slight increase in the average rise velocity compared to a regular array. The difference between two- and three-dimensional bubbles is discussed.

An investigation of transition to turbulence in bounded oscillatory Stokes flows Part 2. Numerical simulations

1991 ◽  
Vol 225 ◽  
pp. 423-444 ◽  
Author(s):  
R. Akhavan ◽  
R. D. Kamm ◽  
A. H. Shapiro
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Transition To Turbulence ◽  
Quasi Equilibrium ◽  
Two Dimensional ◽  
Spectral Techniques ◽  
Periodic Steady State

The stability of oscillatory channel flow to different classes of infinitesimal and finite-amplitude two- and three-dimensional disturbances has been investigated by direct numerical simulations of the Navier–Stokes equations using spectral techniques. All infinitesimal disturbances were found to decay monotonically to a periodic steady state, in agreement with earlier Floquet theory calculations. However, before reaching this periodic steady state an infinitesimal disturbance introduced in the boundary layer was seen to experience transient growth in accordance with the predictions of quasi-steady theories for the least stable eigenmodes of the Orr–Sommerfeld equation for instantaneous ‘frozen’ profiles. The reason why this growth is not sustained in the periodic steady state is explained. Two-dimensional infinitesimal disturbances reaching finite amplitudes were found to saturate in an ordered state of two-dimensional quasi-equilibrium waves that decayed on viscous timescales. No finite-amplitude equilibrium waves were found in our cursory study. The secondary instability of these two-dimensional finite-amplitude quasi-equilibrium states to infinitesimal three-dimensional perturbations predicts transitional Reynolds numbers and turbulent flow structures in agreement with experiments.

Partially Averaged Navier-Stokes Turbulence Modeling of Flow in 5x5 PWR Fuel Assembly With Spacer Grid

2018 ◽  
Author(s):  
Giacomo Busco ◽  
Yassin A. Hassan
Keyword(s):  
Large Eddy Simulation ◽  
Numerical Simulations ◽  
Stokes Equations ◽  
Direct Numerical Simulations ◽  
Navier Stokes ◽  
Spacer Grid ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Reynolds Averaged Navier Stokes

The highly turbulent flow inside a pressurized water reactor makes unpractical the use of scale resolving simulations, due to the large number of space and time turbulent structures. The high computational cost associated with typical large eddies simulations or direct numerical simulations techniques is unsuitable due to the large spatiotemporal resolution required. Partially averaged Navier-Stokes turbulence model is presented as bridging model between Reynolds averaged Navier-Stokes equations and direct numerical simulations. As filtered representation of the Navier-Stokes equations, the model is able to continuously shift its energy-based filter, inside the turbulence spectrum, being able to resolve the turbulent scales of interest. The choice of energy based cut-off filters gives the chance to directly impose the degree of needed resolution, where the most important large scales unsteadiness are resolved at minimal computational expenses. The partially averaged Navier-Stokes modelling approach has been tested for a Reynolds number of 14,000, inside a 5 × 5 fuel bundle, with a single spacer grid and split-type mixing vanes. Four different filters have been tested, whose resolution ranged from Reynolds averaged Navier-Stokes and large eddy simulation. A comparison with large eddy simulation will be presented. The results show that the partially averaged Navier-Stokes modeling produces results comparable to those of large eddy simulation when the appropriate cut-off energy filter is chosen. The turbulence models results will be compared with the available particle image velocimetry experimental data.

Instability of strained vortex layers and vortex tube formation in homogeneous turbulence

1995 ◽  
Vol 282 ◽  
pp. 313-338 ◽  
Author(s):  
T. Passot ◽  
H. Politano ◽  
P.L. Sulem ◽  
J.R. Angilella ◽  
M. Meneguzzi
Keyword(s):  
Numerical Simulations ◽  
Vortex Tube ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Finite Amplitude ◽  
Tube Formation ◽  
Direct Numerical Simulations ◽  
Homogeneous Turbulence ◽  
Tubular Structures ◽  
Vortex Tubes

A modulational perturbation analysis is presented which shows that when a strained vortex layer becomes unstable, vorticity concentrates into steady tubular structures with finite amplitude, in quantitative agreement with the numerical simulations of Lin & Corcos (1984). Elaborated three-dimensional visualizations suggest that this process, due to a combination of compression and self-induced rotation of the layer, is at the origin of intense and long-lived vortex tubes observed in direct numerical simulations of homogeneous turbulence.

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