Some new developments of explicit algebraic Reynolds stress turbulence models (EARSM) are presented. The new developments include a new near-wall treatment ensuring realizability for the individual stress components, a formulation for compressible flows, and a suggestion for a possible approximation of diffusion terms in the anisotropy transport equation. Recent developments in this area are assessed and collected into a model for both incompressible and compressible three-dimensional wall-bounded turbulent flows. This model represents a solution of the implicit ARSM equations, where the production to dissipation ratio is obtained as a solution to a nonlinear algebraic relation. Three-dimensionality is fully accounted for in the mean flow description of the stress anisotropy. The resulting EARSM has been found to be well suited to integration to the wall and all individual Reynolds stresses can be well predicted by introducing wall damping functions derived from the van Driest damping function. The platform for the model consists of the transport equations for the kinetic energy and an auxiliary quantity. The proposed model can be used with any such platform, and examples are shown for two different choices of the auxiliary quantity.

An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows

Modern developments in shear-stress measurement ☆

Review and assessment of turbulence models for hypersonic flows

Nomenclature a = constant; Fig. 1 C , C 0 = constants k = roughness element height, ft N k = average roughness element height, ft L = vehicle length, ft M = Mach number n = exponent; Fig. 1 N R = Poll’s transition parameter; Eq. (1) Reke = roughnessReynolds number based on height k and edge conditions Rekk = roughnessReynolds number based on height k and conditions at k Reμ = Reynolds number based on height μ and edge conditions U = velocity component parallel to test surface or velocity component perpendicularto attachment line, ft /s V = velocity component parallel to attachment line, ft/s X = generalized disturbanceparameter or axial coordinate along windward centerline x = coordinate perpendicular to attachment line, ft Y = generalized transition parameter ® = angle of attack, deg ± = smooth-wall laminar boundary-layer thickness, ft = Poll’s length scale [Eq. (2)], ft μ = smooth-wall laminar boundary-layermomentum thickness, ft 1 = viscosity, lbm/ft ¢ s o = kinematic viscosity, ft2/s 1⁄2 = density, lbm/ft

Review and synthesis of roughness-dominated transition correlations for reentry applications

Modern nonintrusive techniques are used to make skin-friction and heat transfer measurements in two shockwave/turbulent boundary-layer interactions (SWTBLIs). The two-dimensional SWTBLI is generated by impingement of an incident oblique shock wave on a flat-plate boundary layer. The three-dimensional SWTBLI results from the interaction of the swept shock generated by a fin with a flat-plate boundary layer. The measurements are made using the global interferometry skin-friction technique for the skin friction and the quantitative infrared thermography technique for the heat transfer rate. The results show that, for the two- and three-dimensional interactions, there is a clear difference in the behavior of skin friction and heat transfer as the strength of the shock is changed. This observation suggests that the analogy between momentum and heat transfer, which is the basis of many simplified physical models, is not valid in SWTBLIs. These new data supplement the previous measurements that include boundary-layer properties, surface pressure distributions, and patterns of the limiting streamlines. Taken together, these data complete a data set that is suited for computational fluid dynamics validation.

Skin Friction and Heat Flux Measurements in Shock Boundary Layer Interaction Flows

Documentation of two-dimensional impinging shock/turbulent boundary layer interaction flow

We present boundary-layer transition data on swept cylinders in hypersonic flow that were obtained in the hypersonic Ludwieg-tube wind tunnel of DLR. Experiments were conducted at M∞ = 5.0 and 6.9 for three swept cylinders with and without end plates and sweep angles of 30, 45, and 60 deg, respectively. To determine the state of the boundary layers, the liquid-crystal technique was applied. In addition, the response of attachment-line transition to surface roughness heights due to trip wires for sweep angles of 45 and 60 deg at M∞ = 5.0 was investigated. Freestream Reynolds numbers based on cylinder diameter for attachment-line transition were about 0.2-0.3 x 10 6 for the end plate disturbances and 0.9-1.2 x 10 6 for no contaminations. Trends of attachment-line transition Reynolds numbers with surface roughness heights are roughly similar to subsonic ones with respect to critical roughness heights. The behavior of the attachment-line transition around the critical roughness heights, however, depended strongly on spanwise Mach numbers. With flow visualizations, off-attachment-line transition could be observed, as well as fine streak pattern in laminar flow region upstream of the transition front, confirming streamwise vortices induced by crossflow instability at hypersonic speeds.

Boundary-layer transition on swept cylinders at hypersonic speeds

We present boundary-layer transition data on swept cylinders in hypersonic flow that were obtained in the hypersonic Ludwieg-tube wind tunnel of DLR Experiments were conducted at M∞ = 50 and 69 for three swept cylinders with and without end plates and sweep angles of 30, 45, and 60 deg, respectively To determine the state of the boundary layers, the liquid-crystal technique was applied In addition, the response of attachment-line transition to surface roughness heights due to trip wires for sweep angles of 45 and 60 deg at M∞ = 50 was investigated Freestream Reynolds numbers based on cylinder diameter for attachment-line transition were about 02-03 x 10 6 for the end plate disturbances and 09-12 x 10 6 for no contaminations Trends of attachment-line transition Reynolds numbers with surface roughness heights are roughly similar to subsonic ones with respect to critical roughness heights The behavior of the attachment-line transition around the critical roughness heights, however, depended strongly on spanwise Mach numbers With flow visualizations, off-attachment-line transition could be observed, as well as fine streak pattern in laminar flow region upstream of the transition front, confirming streamwise vortices induced by crossflow instability at hypersonic speeds

Boundary layer transition on swept cylinders at hypersonic speeds

The paper describes the application offlow visualisation procedures in the DLRGoettingen Ludwieg Tube Facility RWG. Abrief introduction of the experimentalfacility and its main features will bepresented. The techniques which aredescribed in use in the facility are Schlierenor shadowgraph visualisation of the flowfields, oil film interferometry to obtain skinfriction data in complex flow field regionson a model and liquid crystal coatingswhich are used for visualisation of theglobal thermal load distribution on a model.1. IntroductionThe resolution of experimental data on floweffects in aerodynamic investigations oftenis limited by the number of data acquisitionchannels and the space needed for thesensors to be placed on sometimes fairlysmall wind tunnel models. Especially forhigh supersonic or even hypersonic flowconditions the experimental facilities, foreconomic reasons, are designed and built asshort duration run time facilities. In additionto measured flow properties visualisation ofthe flow field about the model or floweffects at the model wall can contributevaluable information to the understandingand interpretation of the experimentalresults.In the following a special type of super/hypersonic wind tunnel facility and anumber of flow visualisation methods,routinely used in it, will be described. Additionally, some more sophisticatedmethods which have been exploratorilyapplied will be mentioned.2. The DLR Ludwieg Tube Facil ityThe basic idea of a low cost tube windtunnel for high speed and high Reynoldsnumber flow originally was developed byProfessor Ludwieg some forty years ago.He proposed to use a long tube as pressurereservoir which is closed at one end and tothe other end a quick-opening device, a gatevalve or a diaphragm, is attached, followedby a super-sonic nozzle, test section and adump tank [1]. The flow is started by anunsteady expansion wave which propagatesthrough the pressurized test gas along thetube after opening the gate valve orrupturing the diaphragm. Behind theexpansion wave test gas flows out of thetube at constant stagnation conditionsthrough nozzle and test section into thedump tank, as long as the expansion waveneeds to travel to the closed tube end whereit is reflected and finally approaches again atthe nozzle throat. Then a new expansionwave generates undergoing the sameprocedure, as long as the pressure ratiosuffices the desired flow establishment.To Ludwieg`s honor, this principle inanglican literature, later, commonly wascalled " Ludwieg T u be".

Paul Krogmann

Papers

Documentation of two-dimensional impinging shock/turbulent boundary layer interaction flow

Boundary-layer transition on swept cylinders at hypersonic speeds

Boundary layer transition on swept cylinders at hypersonic speeds

Flow Visualizations in a Short-Duration Super-Hypersonic Wind Tunnel