# Description

## Introduction

A diffuser is a component of a fluid flow system designed to reduce the flow velocity and hence increase the fluid pressure without causing significant pressure loss. Most turbomachines and many other flow systems incorporate diffusers. These include:

• The duct between the compressor and burner of a gas turbine engine
• The duct at exit from a gas turbine connected to the jet pipe
• The duct following the impellor of a centrifugal compressor
• Closed circuit wind tunnels
• Draft tubes of water turbines
• And many more.

Clearly, therefore, the design of the diffuser can have a significant impact on the performance of many of these applications and this is recognised in application challenge AC6-01 Planar Diffuser Flow and application challenge AC6-07 Draft Tube. Many other application challenges include the same underlying flow regimes.

In relative terms the geometric design of a diffuser is simple, however, the duration over which research into diffuser design has been and continues to be carried out would suggest that the fluid flow phenomena in diffusers are complex. A simple 2D section through a conical diffuser is shown in Figure 1.

Figure 1. A 2D section through a simple diffuser.

The pressure loss that occurs as flow passes through a diffuser depends on the angle of divergence and on the ratio of the upstream to the downstream flow area (the area ratio) and can be considered to be caused by two different effects. Firstly there is a contribution to the pressure loss from wall friction. For a given area ratio, this loss decreases as the angle of divergence is increased as the larger angle results in a shorter length of diffuser. Secondly, with the exception of small angles of divergence, energy is dissipated by eddies caused by the separation of the flow from the walls. For a given area ratio, this loss increases as the angle of divergence is increased. For each area ratio there is therefore an optimum angle of divergence where the sum of the two loss components is minimised.

The loss of head in a diffuser may be expressed as [2]:

${\displaystyle {\text{Head Loss}}=k{\left(1-{\frac {A_{1}}{A_{2}}}\right)}^{2}{\frac {{u_{1}}^{2}}{2g}}}$

where u1 is the mean velocity in the upstream section and k can be considered a loss coefficient. The relationship between k and the angle of divergence (θ) for three different area ratio diffusers is shown in Figure 2. Similar curves can be derived that show pressure efficiency as a function of diffuser angle.

Angle θ between diverging sides of a diffuser
Figure 2. Loss of Head in a Conical Diffuser [2]

Research has shown that the inclusion of a swirling flow component in the flow entering the diffuser can prevent the occurence of separation in a diffuser in which separation would occur without the swirling component. This implies therefore that near optimum pressure recovery may be obtained from smaller, lighter diffusers. However, an excessive amount of swirl may cause the centre line axial velocity to drop so much that reversal at the centreline occurs thus leading to reduced pressure recovery.

Some common devices where swirling flows in diffusers are encountered are combusters and draft tubes. In a combuster the swirl helps to carry out mixing and the stabilisation of the flame. The main function of the swirl in a draft tube is to reduce flow separation and thus increase pressure recovery.

In most practical engineering applications the swirling flow through a diffuser is turbulent.

Computational Fluid Dynamics (CFD) has been used by several researchers to simulate swirling diffuser flow. The underlying flow physics that need to be captured by CFD modelling include:

• Turbulence (and the effect of swirl on turbulence)
• Boundary layer flow and separation

This document presents a brief review of CFD studies of swirling diffuser flow which have included comparisons of the CFD results with experimental data and then focuses on one study in more detail. The document concludes with best practice advice for CFD modelling of swirling diffuser flow.

## Review of UFR studies and choice of test case

Numerical simulations of diffuser flow have been performed and reported by several researchers and some of these were identified by Armfield et al [4] and are summarised as follows. Okhio et al. [5] used a Prandtl mixing length model to predict mean velocities in a 16.5° diffuser with a tail pipe. Armfield and Fletcher [6] predicted the mean velocity field in a 7° diffuser using a reduced form of the Navier Stokes equations with a mixing length turbulence model. Habib and Whitelaw [7] applied the k-ε turbulence model to the simulation of swirling recirculating flows in 40-90° wide angle diffusers with tail pipes longer than the diffuser section. The mean velocities and turbulence quantities were compared with experimental data. Hah [8] used an algebraic Reynolds stress model to solve 8 and 16° diffuser flows.

More recently Page et al [9] compared the predictions made using the commerical CFD code FIDAP with the experimental results of Clausen et al. [10].

For the purpose of this document the CFD study described by Armfield et al [4] is considered in more detail in conjuction with the work reported by EDF [11]. In these studies the prediction of turbulence quantities and velocity profiles for swirling flow in conical diffusers were considered. The results of the studies have been compared with the experimental results of Clausen et al. [10]. These experimental data can be found on the ERCOFTAC database and were carried out as a complementary study to the work of Armfield et al [4].

The work reported by EDF [11] provides a summary of the updated and corrected results submitted to an ERCOFTAC (European Research Community on Flow, Turbulence and Combustion) workshop entitled Data Bases and Testing of Calculation Methods for Turbulent Flows held in Karlsruhe from April 3 to 7, 1995. As a summary document little specific detail on each simulation result is presented, however, further details can be found in the workshop proceedings, Rodi et al [12].