2D Boundary layers with pressure gradients (B)

Underlying Flow Regime 3-18 © copyright ERCOFTAC 2004

Description

Preface

The underlying flow regime (UFR) chosen here is the 2D boundary layer in an adverse pressure gradient. Reliable predictions of the point of separation, reattachment if any, and boundary layer recovery downstream of reattachment are desirable, as these phenomena occur in many industrial sectors, for example transportation and power generation. External separating flows influence lift and drag which in turn affect vehicle handling and fuel consumption. Internal flow separation in expanding ducts create nonuniformities degrade the life of component parts such as catalizers and filters.

Studies of such flows are widely reported in the literature, and are used to rate the performance of turbulence models, and indeed to callibrate them. A traditional view is that the combination of turbulence model and near-wall treatment are critical to correct prediction, and should together account for effects of turbulence non-isotropy and boundary layer pressure gradients. Varying level of success therefore are demonstrated throught the use of wall-function of low-Reynolds number near-wall treatments, linear and non-linear eddy-viscosity models or Reynolds stress closures, and laterly of Large Eddy Simulation.

The case on which we focus here is the flow through a 2D plane diffuser, which was chosen as Test Case 8.2 at the 8th ERCOFTAC/IAHR/COST Workshop on Refined Turbulence Modelling [1], 1999. Experiments have been performed by Obi, Aoki and Madsuda [2] and Buice and Eaton [3]. The Workshop documents the utilisation of a wide variety of turbulence models and near-wall treatments, and reports on conciensious sensitivities into grid and boundary conditions dependency, and all of which adopt higher order discretisation practices. Later studies are also published, the most notable of which are on the V2F turbulence model [4] and Large Eddy Simulation [5].

Introduction

2D boundary layers in adverse pressure gradients, that is where the boundary layer experiences the static pressure increasing in the flow direction, undergo a rapidly increasing momentum deficit in the wall-adjacent layer often characterised by an inflection in the velocity profile. The retarded flow eventually reverses.

At low Reynolds numbers, the pre-separated boundary layer may be laminar, in which case separation may cause a transition to turbulence, possibly inducing reattachment thereby resulting in the so-called laminar separation bubble. This phenomenon is recognised to be very difficult to model. Fortunately, most industrial flows of interest occur at higher Reynolds numbers, where the pre-separated boundary layer is already turbulent, and offers a greater resistance to separation due to higher wall adjacent shear stresses. The modelling does not have to account for the added complication of transition effects.

In confined flows, the boundary layer eventually reattaches. Meanwhile, the separated flow can experience strong curvature effects, secondary, tertiary and unsteady motions. After reattachment, the boundary layer experiences a pressure recovery characterised by an increase in the wall shear stress, and reduction of the wall-normal pressure gradient.

The case chosen here, insofar as it exhibits separation, reattachment and boundary layer recovery, is of relevance to a number of the stated QNET-CFD Application Challenges, particularly in the Thematic Areas of External Aerodynamics (1-02, 1-03, 1-08, 1-09 involving aerofoils and wings) and Turbomachinery Internal Flow (6-02, 6-03, 6-04, 6-05, 6-06, 6-08, 6-09 and 6-10 involving low and high speed axial and centrigugal compressors and turbines).

Review of UFR studies and choice of test case

Reviews of adverse pressure gradient experiments and computations are widespread, also well summarised in the complimentary UFR3-03 documentation detailing the CS0 diffuser case, and will not be repeated here.

The 2D plane diffuser of Obi [2] and Eaton [3] chosen here is characterised as follows, see Figure 1;

inlet conditions are well defined,

the inlet channel is turbulent and fully developed,

smooth wall separation occurs due to an adverse pressure gradient,

downstream flow exhibits reattachment and boundary redevelopment/recovery.

Prediction of the separation and the extent of the recirculation zone poses a significant challenge for computational models. The physics of reattachment and recovery are not well understood. Computational studies may potentially provide a valuable insight.

This case has been studied extensively in a recognised international comparison exercise as recently as 1999 [1]. A rich variety of turbulence models were exercised and this case has been used subsequently (1999, 2000) to demonstrate the successes of more advanced turbulence modelling techniques [4,5]

These characterisations make it a suitable choice for this UFR.

There are some uncertainties however, associated with the mass flow control and assumed inlet conditions, which have either been adequately addressed in the reported studies, or which seem not to be of detriment to the overall value of the dataset.

Contributors: Fred Mendonca - Computational Dynamics Ltd