Turbulent atmospheric flow over a backward-facing step

The phenomenon of atmospheric shear layer separation over a man-made structure such as a building (modeled as a backward-facing step) has been analyzed theoretically by (1) solving the two-dimensional equations of motion in the two variables, stream function and vorticity, and by (2) employing an approximate integral technique. Boundary conditions for the undisturbed flow are that of the turbulent atmospheric shear flow over a rough terrain. In the first approach a two-equation model of turbulence was used. In the second approach an approximate technique was utilized in an attempt to describe the details of the flow in the recirculation zone behind the step. The results predict velocity profiles in sufficient detail that the presence of the corner eddy in the region of negative surface pressure gradient is evident. The magnitude of the reversed flow velocity in the recirculation eddy has been found to agree with that found from experiments. Also, a surface eddy viscosity distribution has been an outgrowth of the method which realistically follows the magnitude of the surface pressure gradient distribution as found experimentally

Computation of turbulent flows over backward-facing step

A numerical method for computing incompressible turbulent flows is presented. The method is tested by calculating laminar recirculating flows and is applied in conjunction with a modified Kappa-epsilon model to compute the flow over a backward-facing step. In the laminar regime, the computational results are in good agreement with the experimental data. The turbulent flow study shows that the reattachment length is underpredicted by the standard Kappa-epsilon model. The addition of a term to the standard model that accounts for the effects of rotation on turbulent flow improves the results in the recirculation region and increases the computed reattachment length

Heat transfer in a recirculation zone at steady-state and oscillating conditions - the back facing step test case

Steady state and transient heat transfer is a very important aspect of any combustion process. To properly simulate gas to wall heat transfer in a turbulent flow, an accurate prediction of the flow and the thermal boundary layer is required. A typical gas turbine combustion chamber flow presents similarities with the academic backward facing step case, especially in the near wall regions where the heat transfer phenomena take place. For this reason, due to its simple geometry and the availability of well documented experiments, the backward facing step with wall heat transfer represents an interesting validation case. Results of steady-state and transient calculations with the use of various turbulence models are compared here with available experimental data

Convective instability and transient growth in flow over a backward-facing step

Transient energy growths of two- and three-dimensional optimal linear perturbations to two-dimensional flow in a rectangular backward-facing-step geometry with expansion ratio two are presented. Reynolds numbers based on the step height and peak inflow speed are considered in the range 0–500, which is below the value for the onset of three-dimensional asymptotic instability. As is well known, the flow has a strong local convective instability, and the maximum linear transient energy growth values computed here are of order 80×103 at Re = 500. The critical Reynolds number below which there is no growth over any time interval is determined to be Re = 57.7 in the two-dimensional case. The centroidal location of the energy distribution for maximum transient growth is typically downstream of all the stagnation/reattachment points of the steady base flow. Sub-optimal transient modes are also computed and discussed. A direct study of weakly nonlinear effects demonstrates that nonlinearity is stablizing at Re = 500. The optimal three-dimensional disturbances have spanwise wavelength of order ten step heights. Though they have slightly larger growths than two-dimensional cases, they are broadly similar in character. When the inflow of the full nonlinear system is perturbed with white noise, narrowband random velocity perturbations are observed in the downstream channel at locations corresponding to maximum linear transient growth. The centre frequency of this response matches that computed from the streamwise wavelength and mean advection speed of the predicted optimal disturbance. Linkage between the response of the driven flow and the optimal disturbance is further demonstrated by a partition of response energy into velocity components

Upstream open loop control of the recirculation area downstream of a backward-facing step

The flow downstream a backward-facing step is controlled using a pulsed jet placed upstream of the step edge. Experimental velocity fields are computed and used to the recirculation area quantify. The effects of jet amplitude, frequency and duty cycle on this recirculation area are investigated for two Reynolds numbers (Re=2070 and Re=2900). The results of this experimental study demonstrate that upstream actuation can be as efficient as actuation at the step edge when exciting the shear layer at its natural frequency. Moreover it is shown that it is possible to minimize both jet amplitude and duty cycle and still achieve optimal efficiency. With minimal amplitude and a duty-cycle as low as 10\% the recirculation area is nearly canceled