Nozzle geometry-induced vortices in supersonic wind tunnels

Streamwise-coherent structures were observed in schlieren images of a Mach 2.5 flow in an empty supersonic wind tunnel with rectangular cross-section. These features are studied using RANS computations in combination with wind tunnel experiments. The structures are identified as regions of streamwise vorticity embedded in the sidewall boundary layers. These vortices locally perturb the sidewall boundary layers, and can increase their thickness by as much as 37%. The vortices are caused by a region of separation upstream of the nozzle where there is a sharp geometry change, typical in supersonic wind tunnels with interchangeable nozzle blocks. Despite originating in the corners, the vortices are transported by secondary flows in the sidewall boundary layers so they end up near the tunnel centre-height, well away from any corners. The successful elimination of these sidewall vortices from the flow is achieved by replacing the sharp corner with a more rounded geometry, so that the flow here remains attached.Air Force Office of Scientific Research: Award No. FA9550-16-1-043

Simulations of incident shock boundary layer interactions

We examine the effects of varying the tunnel width to height ratio, the boundary layer thickness, and the incident shock angle on the shock boundary layer interaction of an incident oblique shock with a turbulent boundary layer. The computational domain is a simplified representation of typical wind tunnel experiments where the top wall of the tunnel is not modeled; only the flow conditions imposed by the shock are modeled on the top of the computational domain. We also examine the differences that arise from addition of Quadratic Constitutive terms to the flow equations. These terms are needed to give rise to corner flow vortices in tunnel flows without shocks and have a significant effect on the side wall corner flow that increases as the strength of shockwave boundary layer interaction increases

The influence of nozzle geometry on corner flows in supersonic wind tunnels

In supersonic flows, the separation in streamwise corners is a significant and widely encountered problem which can not be reliably predicted with the numerical methods commonly used in industry. The few previous studies on this topic have suggested conflicting corner flow topologies. Experiments of supersonic flow are typically conducted in wind tunnels with rectangular cross-sections, which use either a symmetric (full) or asymmetric (half-liner) nozzle configuration. However, the effect of the nozzle arrangement on the corner flow itself is not known. This paper examines the influence of nozzle geometry on the corner regions of a Mach 2.5 flow using a joint experimental-computational approach. The full setup and half-liner configuration are shown to produce different corner flow structures. The corner regions of the full setup and top corners of the half-liner exhibit thin sidewall boundary layers and a single primary vortex on the floor or ceiling. Meanwhile, the bottom corners of the half-liner configuration contain thick sidewall boundary layers and a counter-rotating vortex pair. Considerable vertical velocities are measured within the sidewall boundary layers. These are directed towards the tunnel centre-height for the full setup and downwards with the half-liner. The differences in sidewall cross flows between the two nozzle arrangements are likely due to distinct pressure distributions in the nozzle, where the secondary flows are set up. Measurements suggest that these nozzle-dependent transverse flows are responsible for the differences in corner flowfield between the two configurations. The proposed mechanism also explains observed differences in corner flow topology between previous studies in the literature; nozzle geometry therefore appears to be the dominant influence on corner flows in supersonic wind tunnels

Flow Characterisation for a Validation Study in High-speed Aerodynamics

Validation studies are becoming increasingly relevant when investigating complex flow problems in high-speed aerodynamics. These investigations require calibration of numerical models with accurate data from the physical wind tunnel being studied. This paper presents the characterisation process for a joint experimental-computational study to investigate the streamwise corners of a Mach 2.5 channel flow. As well as checks of flow quality typically performed for phenomenological investigations, additional quantitative tests are conducted. The extra care to obtain high quality data and eliminate any systematic errors reveal useful information about the wind tunnel flow. Further important physical insights are gained from designing and conducting wind tunnel tests in conjunction with numerical simulations. Crucially, the close experimental-computational collaboration enabled the identification of secondary flows in the sidewall boundary-layers; these strongly influence the flow in the corner regions, the target of the validation study

Nozzle geometry effects on supersonic wind tunnel studies of shock–boundary-layer interactions

AbstractMany supersonic wind tunnel experiments investigate shock–boundary-layer interactions by measuring the response of tunnel wall boundary layers to an incident shock wave. To generate the supersonic flow, these facilities typically use two-dimensional contoured converging–diverging nozzles which can be arranged in two different ways. One configuration is symmetric about the centre height, whereas this symmetry plane defines the tunnel floor in the other asymmetric arrangement. In order to determine whether these nozzle configurations, which are widely thought to be equivalent, can influence experiments on shock–boundary-layer interactions, two different nozzle geometries are compared with one another in a single facility with rectangular cross section. For each setup, a full-span 8-degree wedge introduces an oblique shock to a Mach 2.5 flow. The two setups exhibit quite dissimilar behaviour, both in the corner regions and on the tunnel’s centre span, with a difference in central separation length of as much as 35% suggesting that nozzle geometry can have a profound impact on these interactions. The observed behaviour is caused by known secondary flows in the sidewall boundary layers which are driven by vertical pressure gradients in the nozzle region. The subsequent impact on the response of the floor boundary layer is consistent with expectations based on local flow momentum affecting corner separation size and on the displacement effect of this corner separation influencing the wider flow. Graphical abstract</jats:p

Nozzle geometry effects on supersonic wind tunnel studies of shock–boundary-layer interactions

Many supersonic wind tunnel experiments investigate shock–boundary-layer interactions by measuring the response of tunnel wall boundary layers to an incident shock wave. To generate the supersonic flow, these facilities typically use two-dimensional contoured converging–diverging nozzles which can be arranged in two different ways. One configuration is symmetric about the centre height, whereas this symmetry plane defines the tunnel floor in the other asymmetric arrangement. In order to determine whether these nozzle configurations, which are widely thought to be equivalent, can influence experiments on shock–boundary-layer interactions, two different nozzle geometries are compared with one another in a single facility with rectangular cross section. For each setup, a full-span 8-degree wedge introduces an oblique shock to a Mach 2.5 flow. The two setups exhibit quite dissimilar behaviour, both in the corner regions and on the tunnel’s centre span, with a difference in central separation length of as much as 35% suggesting that nozzle geometry can have a profound impact on these interactions. The observed behaviour is caused by known secondary flows in the sidewall boundary layers which are driven by vertical pressure gradients in the nozzle region. The subsequent impact on the response of the floor boundary layer is consistent with expectations based on local flow momentum affecting corner separation size and on the displacement effect of this corner separation influencing the wider flow

Analysis and extension of the quadratic constitutive relation for RANS methods

AbstractThe quadratic constitutive relation was proposed as an extension of minimal complexity to linear eddy-viscosity models in order to improve mean flow predictions by better estimating turbulent stress distributions. However, the successes of this modification have been relatively modest and are limited to improved calculations of flow along streamwise corners, which are influenced by weak secondary vortices. This paper revisits the quadratic constitutive relation in an attempt to explain its capabilities and deficiencies. The success in streamwise corner flows cannot be entirely explained by significant improvements in turbulent stress estimates in general, but is instead due to better prediction of the particular turbulent stress combinations which appear in the mean streamwise vorticity equation. As a consequence of this investigation, a new formulation of turbulent stress modification is proposed, which appears to better predict the turbulent stress distributions for a variety of flows: channel flow, equilibrium boundary layers, pipe flow, separated boundary layers and square duct flow.This material is based upon work supported by the US Air Force O ce of Scientific Research under award FA9550–16–1–0430

Capabilities and Limitations of the Quadratic Constitutive Relation in Corner Flow Prediction

The capabilities and limitations of the quadratic constitutive relation in computing streamwise corner flows are investigated using publicly-available data from direct numerical simulations of a square duct flow. The increased accuracy of RANS computations which use the quadratic constitutive relation in corner flows is not due to significantly improved turbulent stress estimates in general. Instead, the reported success of the relation in this flow field, whose structure is governed by the presence of streamwise vortices, is a result of the particular turbulent stress combinations which appear in the mean streamwise vorticity equation being better predicted. Despite this improved prediction, the precise topology of the vorticity production terms deviates from the true distribution, particularly close to the walls, which explains why the strength and position of the corner vortices may not quite correspond to those in the physical flow. In addition, the imperfect estimate of the shear stress term is observed to be the source of additional, non-physical vortices when the QCR coefficient exceeds its recommended value.This material is based upon work supported by the US Air Force Office of Scientific Research under award number FA9550–16–1–0430