Two‐Dimensional Direct Numerical Simulations of Jet Spray under High Pressure

Direct numerical simulations of single-species and binary-species temporal boundary layers at high pressure are performed with special attention to species-mass diffusion. The working fluids are nitrogen or a mixture of nitrogen and methane. Mean profiles and turbulent fluctuations of mass fraction show that their qualitative characteristics are different from those of streamwise velocity and temperature, due to the different boundary conditions. In a wall-parallel plane near the wall, the streamwise velocity and temperature have streaky patterns and the fields are similar. However, the mass fraction field at the same location is different from the streamwise velocity and temperature fields indicating that species-mass diffusion is not similar to the momentum and thermal diffusion. In contrast, at the centre and near the edge of the boundary layer, the mass fraction and temperature fields have almost the same pattern, indicating that the similarity between thermal and species-mass diffusion holds away from the wall. The lack of similarity near the wall is traced to the Soret effect that induces a temperature-gradient-dependent species-mass flux. As a result, a new phenomenon has been identified for a non-isothermal binary-species system – uphill diffusion, which in its classical isothermal definition can only occur for three or more species. A quadrant analysis for the turbulent mass flux reveals that near the wall the Soret effect enhances the negative contributions of the quadrants. Due to the enhancement of the negative contributions, small species-concentration fluid tends to be trapped near the wall.

Download Full-text

Direct numerical simulations of laminar separation bubbles: investigation of absolute instability and active flow control of transition to turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.123 ◽

2014 ◽

Vol 747 ◽

pp. 141-185 ◽

Cited By ~ 24

Author(s):

Martin Embacher ◽

H. F. Fasel

Keyword(s):

Numerical Simulations ◽

Three Dimensional ◽

Secondary Instability ◽

Direct Numerical Simulations ◽

Absolute Instability ◽

Two Dimensional ◽

Periodic Forcing ◽

Laminar Separation ◽

Flow Response ◽

Separation Bubbles

AbstractLaminar separation bubbles generated on a flat plate by an adverse pressure gradient are investigated using direct numerical simulations (DNSs). Two-dimensional periodic forcing is applied at a blowing/suction slot upstream of separation. Control of separation through forcing with various frequencies and amplitudes is examined. For the investigation of absolute instability mechanisms, baseflows provided by two-dimensional Navier–Stokes calculations are analysed by introducing pulse disturbances and computing the three-dimensional flow response using DNS. The primary instability of the time-averaged flow is investigated with a local linear stability analysis. Employing a steady flow solution as baseflow, the nonlinear and non-parallel effects on the self-sustained disturbance development are illustrated, and a feedback mechanism facilitated by the upstream flow deformation is identified. Secondary instability is investigated locally using spatially periodic baseflows. The flow response to pulsed forcing indicates the existence of an absolute secondary instability mechanism, and the results indicate that this mechanism is dependent on the periodic forcing. Results from three-dimensional DNS provide insight into the global instability mechanisms of separation bubbles and complement the local analysis. A forcing strategy was devised that suppresses the temporal growth of three-dimensional disturbances, and as a consequence, breakdown to turbulence does not occur. Even for a separation bubble that has transitioned to turbulence, the flow relaminarizes when applying two-dimensional periodic forcing with proper frequencies and amplitudes.

Download Full-text

Direct numerical simulations of two- and three-dimensional turbulent natural convection flows in a differentially heated cavity of aspect ratio 4

Journal of Fluid Mechanics ◽

10.1017/s0022112007006908 ◽

2007 ◽

Vol 586 ◽

pp. 259-293 ◽

Cited By ~ 86

Author(s):

F. X. TRIAS ◽

M. SORIA ◽

A. OLIVA ◽

C. D. PÉREZ-SEGARRA

Keyword(s):

Natural Convection ◽

Rayleigh Number ◽

Aspect Ratio ◽

Numerical Simulations ◽

Three Dimensional ◽

Direct Numerical Simulations ◽

Two Dimensional ◽

Turbulent Statistics ◽

Large Eddies ◽

Three Dimensional Simulations

A set of complete two- and three-dimensional direct numerical simulations (DNS) in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is presented in this paper. Although the physical phenomenon is three-dimensional, owing to its prohibitive computational costs the majority of the previous DNS of turbulent and transition natural convection flows in enclosed cavities assumed a two-dimensional behaviour. The configurations selected here (Rayleigh number based on the cavity height 6.4 × 108, 2 × 109 and 1010, Pr = 0.71) are an extension to three dimensions of previous two-dimensional problems.An overview of the numerical algorithm and the methodology used to verify the code and the simulations is presented. The main features of the flow, including the time-averaged flow structure, the power spectra and probability density distributions of a set of selected monitoring points, the turbulent statistics, the global kinetic energy balances and the internal waves motion phenomenon are described and discussed.As expected, significant differences are observed between two- and three-dimensional results. For two-dimensional simulations the oscillations at the downstream part of the vertical boundary layer are clearly stronger, ejecting large eddies to the cavity core. In the three-dimensional simulations these large eddies do not persist and their energy is rapidly passed down to smaller scales of motion. It yields on a reduction of the large-scale mixing effect at the hot upper and cold lower regions and consequently the cavity core still remains almost motionless even for the highest Rayleigh number. The boundary layers remain laminar in their upstream parts up to the point where these eddies are ejected. The point where this phenomenon occurs clearly moves upstream for the three-dimensional simulations. It is also shown that, even for the three-dimensional simulations, these eddies are large enough to permanently excite an internal wave motion in the stratified core region. All these differences become more marked for the highest Rayleigh number.

Download Full-text

The dynamics of a laminar flow in a symmetric channel with a sudden expansion

Journal of Fluid Mechanics ◽

10.1017/s0022112001004086 ◽

2001 ◽

Vol 436 ◽

pp. 283-320 ◽

Cited By ~ 60

Author(s):

T. HAWA ◽

Z. RUSAK

Keyword(s):

Reynolds Number ◽

Laminar Flow ◽

Numerical Simulations ◽

Direct Numerical Simulations ◽

Sudden Expansion ◽

Asymptotically Stable ◽

Two Dimensional ◽

Stable Mode ◽

Symmetric States ◽

Asymmetric Equilibrium

Bifurcation analysis, linear stability study, and direct numerical simulations of the dynamics of a two-dimensional, incompressible, and laminar flow in a symmetric long channel with a sudden expansion with right angles and with an expansion ratio D/d (d is the width of the channel inlet section and D is the width of the outlet section) are presented. The bifurcation analysis of the steady flow equations concentrates on the flow states around a critical Reynolds number Rec(D/d) where asymmetric states appear in addition to the basic symmetric states when Re [ges ] Rec(D/d). The bifurcation of asymmetric states at Rec has a pitchfork nature and the asymmetric perturbation grows like √Re − Rec(D/d). The stability analysis is based on the linearized equations of motion for the evolution of infinitesimal two-dimensional disturbances imposed on the steady symmetric as well as asymmetric states. A neutrally stable asymmetric mode of disturbance exists at Rec(D/d) for both the symmetric and the asymmetric equilibrium states. Using asymptotic methods, it is demonstrated that when Re < Rec(D/d) the symmetric states have an asymptotically stable mode of disturbance. However, when Re > Rec(D/d), the symmetric states are unstable to this mode of asymmetric disturbance. It is also shown that when Re > Rec(D/d) the asymmetric states have an asymptotically stable mode of disturbance. The direct numerical simulations are guided by the theoretical approach. In order to improve the numerical simulations, a matching with the asymptotic solution of Moffatt (1964) in the regions around the expansion corners is also included. The dynamics of both small- and large-amplitude disturbances in the flow is described and the transition from symmetric to asymmetric states is demonstrated. The simulations clarify the relationship between the linear stability results and the time-asymptotic behaviour of the flow. The current analyses provide a theoretical foundation for previous experimental and numerical results and shed more light on the transition from symmetric to asymmetric states of a viscous flow in an expanding channel. It is an evolution from a symmetric state, which loses its stability when the Reynolds number of the incoming flow is above Rec(D/d), to a stable asymmetric equilibrium state. The loss of stability is a result of the interaction between the effects of viscous dissipation, the downstream convection of perturbations by the base symmetric flow, and the upstream convection induced by two-dimensional asymmetric disturbances.

Download Full-text

Direct numerical simulations of bubbly flows Part 2. Moderate Reynolds number arrays

Journal of Fluid Mechanics ◽

10.1017/s0022112099004310 ◽

1999 ◽

Vol 385 ◽

pp. 325-358 ◽

Cited By ~ 127

Author(s):

ASGHAR ESMAEELI ◽

GRÉTAR TRYGGVASON

Keyword(s):

Reynolds Number ◽

Numerical Simulations ◽

Volume Fraction ◽

Three Dimensional ◽

Direct Numerical Simulations ◽

Dimensional System ◽

Two Dimensional ◽

Reynolds Stresses ◽

Bubble Distribution ◽

Moderate Reynolds Number

Direct numerical simulations of the motion of two- and three-dimensional finite Reynolds number buoyant bubbles in a periodic domain 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 rise Reynolds numbers are around 20–30 for the lowest volume fraction, but decrease as the volume fraction is increased. The rise of a regular array of bubbles, where the relative positions of the bubbles are fixed, is compared with the evolution of a freely evolving array. Generally, the freely evolving array rises slower than the regular one, in contrast to what has been found earlier for low Reynolds number arrays. The structure of the bubble distribution is examined and it is found that while the three-dimensional bubbles show a tendency to line up horizontally, the two-dimensional bubbles are nearly randomly distributed. The effect of the number of bubbles in each period is examined for the two-dimensional system and it is found that although the rise Reynolds number is nearly independent of the number of bubbles, the velocity fluctuations in the liquid (the Reynolds stresses) increase with the size of the system. While some aspects of the fully three-dimensional flows, such as the reduction in the rise velocity, are predicted by results for two-dimensional bubbles, the structure of the bubble distribution is not. The magnitude of the Reynolds stresses is also greatly over-predicted by the two-dimensional results.

Download Full-text

Oblique route to turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.49 ◽

2011 ◽

Vol 674 ◽

pp. 1-4

Author(s):

MUJEEB R. MALIK

Keyword(s):

Boundary Layer ◽

Numerical Simulations ◽

Flat Plate ◽

Boundary Layers ◽

Plate Boundary ◽

Direct Numerical Simulations ◽

Two Dimensional ◽

Mach 3 ◽

Transition Scenario ◽

Flat Plate Boundary Layer

Direct numerical simulations have been performed by Mayer, Von Terzi & Fasel (J. Fluid Mech., this issue, vol. 674, 2011, pp. 5–42) to demonstrate that oblique-mode breakdown leads to fully turbulent flow for a Mach 3 flat-plate boundary layer. Since very low level of initial disturbances is required for this transition scenario, oblique-mode breakdown is the most potent mechanism for transition in two-dimensional supersonic boundary layers in low-disturbance environments relevant to flight.

Download Full-text