Backward-facing step

Figure 19.1 Annular flow arrangement and devices to oscillate fuel flow AR — annular ring BS — backward-facing step FI — fuel injector ID — inner duct MD — main duct PT — pressure transducer SR — swirl register (all dimensions are in mm), (a) annular flow arrangement (6) needle valve arrangement to oscillate fuel flow 1 — vibrator, 2 — receiver, 3 — needle, 4 — spider (c) arrangement to deliver oscillated fuel to inner duct and (d) arrangement to oscillate fuel flow with three circumferentially equispaced injectors...

Hong, B., Armaly, B.F., and Chen, T.S., "Laminar Mixed Convection in a Duct with a Backward-facing Step the Effects of Inclination Angle and Prandtl Number , Int. J. of Heal and Mass Transfer, Vol. 36. Aug. 93, pp. 3059-3067, 1993. 

K. Akselvoll and P. Moin. Large eddy simulation of a backward facing step flow. In W. Rodi and F. Martelli, editors, Proc. of the 2nd International Symposium on Eng. Turb. Modelling and Exp., volume 2, pages 303-313. Elsevier, 1993. 

Iwai and Suzuki [15] numerically investigated the effects of rarefaction and compressibility on heat transfer for a flow over a backward-facing step in a microchannel duct. They applied the velocity shp boundary condition to all the walls and considered tem-peratme jump at the heated wall. Skin friction was seen to reduce when the velocity shp was taken into account. It was further reduced if the accommodation coefficient takes smaller values, which results in larger slip velocities. They found that the compressibil-... 

Iwai, H. and Suzuki, K., Effects of Velocity Slip and Temperature Jump Conditions on Backward-Facing Step Flow in a MicroChannel, Proceedings of the 5 ASME/JSME Joint Thermal Engineering Conference, 1999, 1-8. 

Finite-length porous inserts into a duct are of a special practical importance, Fig. 3.15. The vortical motion can or cannot appear behind the inserts depending on its height h, its length Lh, and the density A. Engineers get thus a means to control the flow. The special case A = oo can be treated as the well-known problem backward facing step . The flow under consideration is so a generalization of the well-known problem. 

If the inserts become impermeable, A —> oo, another known limit case appears. There is a number of data for the backward facing step that correlates with the backward facing penetrable step. ... 

Barton, E. 1995 Computation of particle tracks over a backward-facing step. Journal of Aerosol Science 26, 887-901. 

The deterministic approach of direct numerical simulation (DNS) and the probabilistic approach of probability density function (PDF) modeling are implemented for prediction of droplet dispersion and polydis-persity in liquid-fuel combustors. For DNS, a multidomain spectral element method was used for the carrier phase while tracking the droplets individually in a Lagrangian frame. The geometry considered here is a backward-facing step flow with and without a countercurrent shear. In PDF modeling, the extension of previous work to the case of evaporating droplets is discussed. 

The MPI implementation was performed according to a method that Fischer [3] used in his incompressible Legendre hp-spectral method. The method is based on the use of three arrays that keep track of the global/local element and mortar numbering, the processor on which the local element and mortars are allocated, and the face side of the slave element of a mortar. The mortars are allocated at the same processor in which the master domain is allocated. The MPI code was tested for a laminar backward-facing step flow on the local 8-node (16-processor) Beowulf cluster and showed an efficiency of 90% for large grids (Fig. 3.1). 

More recently, the application of the code for simulation of the flow over a backward-facing step with a countercurrent flow has been considered. The step is bounded by two parallel plates at the top and the bottom and resembles the dump combustor configuration considered by Strykowski s group at the Univer-... 

Figure 3.3 Two-phase flow over a backward-facing step with (top) and without (bottom) countercurrent shear. The carrier phase is visualized by vorticity contours.

The numerical method used in this research was developed by Akselvoll and Moin [8] for backward facing step and was modified by Bewley et al. [9] for plane... 

AkselvoU, K., and P. Moin. 1995. Large eddy simulation of turbulence confined coannular jets and turbulent flow over a backward facing step. Report TF-63. Thermosciences Division, Dept, of Mech. Eng., Stanford University. 

Kasagi, N., and Matsunaga, A., Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow, Int. J. Heat and Fluid Flow, Ji>, 477-485 (1995). 

U. Kursun, J.S. Kapat, Modelling of microscale gas flows in transition regime. Part 1. Flow over backward facing steps, Nanoscale Microscale Thermophys. Eng., 2007, 33, 15-30. 

Haidekker, M.A., White, C.R., and Frangos, J.A., Analysis of temporal shear stress gradients during the onset phase of Uow over a backward-facing step, /. Biomech. Eng, 123,455, 2001. 

The influence of the Reynolds number on the velocity field of a backward-facing step is illustrated in Figure 2.1. The backward-facing step flow can be considered equivalent to two infinite parallel-plate channels with heights and /I2, and hydraulic resistances / j and R2 are... 

Figure 2.1 Flow patterns as a function of Reynolds number Re) of a backward facing step (a) Re = 0.01 and (b) Re = 100. The flow is analogous to two hydraulic resistors, R, and R, connected in series for flow inside channel 1 and channel 2 of varying cross-sections...

Verification is performed by comparison of the numerical results with highly accurate (benchmark) solutions such as 1) exact analytical solutions 2) benchmark solutions of ordinary differential equations (ODE) or 3) benchmark solutions of partial differential equations. The usual use of ODE solution is based on exploiting the symmetry properties one can solve an essentially one-dimensional problem (for example, having spherical symmetry) using a general three-dimensional grid. There are a few well-known multidimensional benchmark solutions such as laminar convection in a square cavity [50, 51] and the flow over a backward-facing step with heat transfer [52]. 

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