Instantaneous transport of a passive scalar in a turbulent separated flow

Abstract

The results of large-eddy simulations of flow and transient solute transport over a backward facing step and through a 180° bend are presented. The simulations are validated successfully in terms of hydrodynamics and tracer transport with experimental velocity data and measured residence time distribution curves confirming the accuracy of the method. The hydrodynamics are characterised by flow separation and subsequent recirculation in vertical and horizontal directions and the solute dispersion process is a direct response to the significant unsteadiness and turbulence in the flow. The turbulence in the system is analysed and quantified in terms of power density spectra and covariance of velocity fluctuations. The injection of an instantaneous passive tracer and its dispersion through the system is simulated. Large-eddy simulations enable the resolution of the instantaneous flow field and it is demonstrated that the instabilities of intermittent large-scale structures play a distinguished role in the solute transport. The advection and diffusion of the scalar is governed by the severe unsteadiness of the flow and this is visualised and quantified. The analysis of the scalar mass transport budget quantifies the mechanisms controlling the turbulent mixing and reveals that the mass flux is dominated by advection.

Keywords: Backward facing step; Large eddy simulation; Separation flows; Solute dispersion; Turbulence.

Fig. 1

Numerical model geometry and the main sampling points, P1–P6, at which tracer dye data were collected

Fig. 2

Three dimensional representation of the numerical domain, description of boundary conditions used and specification of the nine reference points at which data time series are obtained for tracer and turbulence analysis

Fig. 3

Wall-adjacent grid spacing in wall units along the bottom wall at $x/L=0.8$ along $y/B_c\le 2.0$ for the two meshes used in the simulations

Fig. 4

Three-dimensional streamlines coloured with the mean velocity magnitude, $U_{\mathit{mag}}=\sqrt{{\overline{U}}^2+{\overline{V}}^2+{\overline{W}}^2}$, normalised by $U_b$ of compartment 1 (a) and 2 (b). Note main flow direction is from left to right in (a) and from right to left in (b)

Fig. 5

Contours of normalised time-averaged x-velocities $(\overline{U}/U_b)$ with two-dimensional streamlines from the first compartment. a y-planes at $y/B_c$ = 0.5, b x-plane at x/L = 0.5 and c z-planes at z/H = 0.35

Fig. 6

Contours of normalised time-averaged x-velocities $(\overline{U}/U_b)$ with two-dimensional streamlines from the second compartment. a y-planes at $y/B_c$ = 0.5, b x-plane at x/L = 0.5 and c z-planes at z/H = 0.35

Fig. 7

Quadrant plots in the axis $u^{\prime }/u_{\mathit{rms}}-v^{\prime }/v_{\mathit{rms}}$ (top) and $u^{\prime }/u_{\mathit{rms}}-w^{\prime }/w_{\mathit{rms}}$ (bottom) at three points in the middle of the first compartment: P1 ($z/H=0.772$; left), P3 ($z/H=0.550$; middle) and P5 ($z/H=0.024$; right)

Fig. 8

Quadrant plots in the axis $u^{\prime }/u_{\mathit{rms}}-v^{\prime }/v_{\mathit{rms}}$ (top) and $u^{\prime }/u_{\mathit{rms}}-w^{\prime }/w_{\mathit{rms}}$ (bottom) at three points in the center of the bend between the first and second chambers: P7 ($z/H=0.772$; left), P8 ($z/H=0.550$; middle) and P9 ($z/H=0.024$; right)

Fig. 9

Quadrant plots in the axis $u^{\prime }/u_{\mathit{rms}}-v^{\prime }/v_{\mathit{rms}}$ (top) and $u^{\prime }/u_{\mathit{rms}}-w^{\prime }/w_{\mathit{rms}}$ (bottom) at three points in the middle of the second chamber: P2 ($z/H=0.772$; left), P4 ($z/H=0.550$; middle) and P6 ($z/H=0.024$; right)

Fig. 10

Power Density Spectra of the u (left), v (center) and w (right) velocity components at points 1, 2 and 7 (top) and 5, 6 and 9 (bottom)

Fig. 11

Vertical profiles of normalised a horizontal, b transverse and c vertical velocities and d turbulent kinetic energy in compartment 1 at x/L = 0.25, 0.50 and 0.75, and in compartment 2 at x/L = 0.50 and 0.25

Fig. 12

Normalised tracer concentration contours ($C/C_0$) and super-imposed flow streamlines colour-coded by the instantaneous normalised x-velocity ($U/U_b$) in the middle of the first chamber $(y/B_c=0.5)$ at four different instants: a $t=27$ s $(\mathit{\theta }=0.021)$, b $t=36s(\mathit{\theta }=0.028)$, c $t=102s(\mathit{\theta }=0.08)$, and d $t=124.5s(\mathit{\theta }=0.099)$. Black squares represent the sampling points

Fig. 13

Normalised tracer concentration contours ($C/C_0$) and super-imposed flow streamlines coloured by the non-dimensional streamwise velocity ($U/U_b$) on a horizontal plane ($z/H=0.65$) extracted at the middle of the first $(y/B_c<1)$ and second $(y/B_c>1)$ chambers. a $t=27s(\mathit{\theta }=0.021)$, b $t=36$ s $(\mathit{\theta }=0.028)$, c $t=102$ s $(\mathit{\theta }=0.08)$, and d $t=124.5$ s $(\mathit{\theta }=0.099)$. Black squares represent the sampling points location

Fig. 14

Instantaneous flow field and tracer transport in the second compartment. Top: three-dimensional iso-surfaces of turbulent structures (Q = 1) and tracer concentration ($C/C_0=0.1$); bottom: solute contours and velocity streamlines centreline plane at $y/B_c$ = 1.50; left (a and c) $t=63$ s $(\mathit{\theta }=0.05)$; right (b and d) $t=102s(\mathit{\theta }=0.08)$

Fig. 15

Cumulative curves of convective (black, blue, red) and diffusive (circles) tracer mass fluxes and normalised scalar concentration (green) at P1

Fig. 16

Integral passive scalar advective and diffusive mass fluxes at six reference points as a percentage of the total transport at each location

Fig. 17

Comparison of the RTD curves obtained at the monitor point P1 between three different releases and the computed average curve

Fig. 18

RTD curves obtained from the experiments [4] and the LES of the first injection and the average of three injections at various locations a P1, b P2, c P3, d P4, e P5 and f P6 provided in Fig. 2