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NASA NTRS1979

Investigation of a reattaching turbulent shear layer Flow over a backward-facing step

The paper studies incompressible flow over a backward-facing step in order to investigate the flow characteristics in the separated shear layer, the reattachment zone, and the redeveloping boundary layer after reattachment. It is shown that turbulent intensities and shear stress reach maxima in the reattachment zone, followed by rapid decay near the surface after reattachment. In addition, it is found that downstream of reattachment, the flow returns very slowly to the structure of an ordinary turbulent boundary layer.

Kim, J.↗

NASA NTRS1984

Effect of initial conditions on turbulent reattachment downstream of a backward-facing step

The reattachment of a fully turbulent, two-dimentional shear layer downstream of a backward-facing step has been studied experimentally. The work examines the effect of variations in inlet conditions on the process of reattachment. A series of experiments was conducted in a low-speed wind tunnel using specialized instrumentation suited to the highly turbulent reversing flow near reattachment. Accurate characterization of the time-mean features of the reattaching flows was possible. Assuming linear scaling normalized on distance from reattachment, distributions of normalized pressure coefficient and forward flow fraction, and time-averaged skin friction coefficient appear universal for two-dimensional reattachment, independent of initial conditions and step height, for given duct geometry (area ratio) and for high step-height Reyolds numbers with thin separating boundary layers. The results suggest universal flow structure in the reattachment zone.

Westphal, R. V.↗

NASA NTRS1976

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.

Kaul, U. K.↗

NASA NTRS1983

Effects of expansion ratio on the calculation of parallel-walled backward-facing step flows - Comparison of four models of turbulence

This paper presents a numerical study of the effects of expansion ratio on two-dimensional separating and reattaching flows in plane backward-facing step geometries with parallel walls. Closure of the Reynolds equations was achieved by four different turbulence models: k-epsilon, 'modified' k-epsilon, algebraic stress, and 'modified' algebraic stress models. The k-epsilon model relates the Reynolds stresses to the mean rate of strain through the definition of an isotropic turbulent viscosity. The more advanced algebraic stress model calculates the stresses from implicit algebraic relationships containing the stresses themselves, the mean rate of strain, and the turbulent kinetic energy and its dissipation rate. 'Modified' versions of the models employ a new dissipation rate equation whose production term was made more sensitive to streamwise curvature effects. A new nonequilibrium wall function treatment proposed by Chieng and Launder (1980) was also incorporated into each model.

Sindir, M. M.↗

NASA NTRS1983

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.

Mansour, N. N.↗

NASA NTRS1983

Calculation of deflected-walled backward-facing step flows Effects of angle of deflection on the performance of four models of turbulence

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Sindir, M. M.↗

DOE OSTI2025

Mesh-based super-resolution of fluid flows with multiscale graph neural networks

A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on localized meshes of elements (or cells) directly. To facilitate mesh-based GNN representations in a manner similar to spectral (or finite) element discretizations, a baseline GNN layer (termed a message passing layer, which updates local node properties) is modified to account for synchronization of coincident graph nodes, rendering compatibility with commonly used element-based mesh connectivities. Furthermore, the architecture is multiscale in nature, and is comprised of a combination of coarse-scale and fine-scale message passing layer sequences (termed processors) separated by a graph unpooling layer. The coarse-scale processor embeds a query element (alongside a set number of neighboring coarse elements) into a single latent graph representation using coarse-scale synchronized message passing over the element neighborhood, and the fine-scale processor leverages additional message passing operations on this latent graph to correct for interpolation errors. Demonstration studies are performed using hexahedral mesh-based data from Taylor–Green Vortex and backward-facing step flow simulations at Reynolds numbers of 1600 and 3200. Through analysis of both global and local errors, the results ultimately show how the GNN is able to produce accurate super-resolved fields compared to targets in both coarse-scale and multiscale model configurations. Reconstruction errors for fixed architectures were found to increase in proportion to the Reynolds number. Geometry extrapolation studies on a separate cavity flow configuration show promising cross-mesh capabilities of the super-resolution strategy.

Backward-facing step↗

NASA NTRS1984

Application of a fractional-step method to incompressible Navier-Stokes equation

A numerical method for computing three dimensional, time dependent incompressible flows is presented. The method is based on a fractional step, or time-splitting, scheme in conjunction with the approximate-factorization technique. The use of velocity boundary conditions for the intermediate velocity field leads to inconsistent numerical solutions. Appropriate boundary conditions for the intermediate velocity field are derived and tested. Numerical solutions for flow inside a driven cavity and over a backward-facing step are presented and compared with experimenal data and other numerical results.

Kim, J.↗

NASA NTRS1985

Application of a fractional-step method to incompressible Navier-Stokes equations

Kim, J.↗

DOE OSTI2025

Vortical interactions in turbulent thermoacoustic systems

This study examines the dynamics of vortical interactions and their implications for mitigating thermoacoustic instability in a turbulent combustor. The regions of intense vortical interactions are identified as vortical communities in the network space of weighted directed vortical networks constructed from two-dimensional experimental velocity data. One can expect vortical interactions in the combustor to be strongest near the moment of vortex shedding, as the shed vortices gradually weaken due to dissipation while convecting downstream. However, we show that, during the state of thermoacoustic instability, there is a non-trivial consistent phase lag of approximately 52° between the shedding of the coherent structures from the backward-facing step and the time instant when the vortical interactions attain their local maximum value. We explain this phase lag by investigating the correlation between acoustic pressure fluctuations, spatio-temporal dynamics of coherent structures and vortical interactions in the reaction field of the combustor. We also show the aperiodic variation of vortical interactions during the states of combustion noise and aperiodic epochs of intermittency. Furthermore, the spatio-temporal evolution of pairs of vortical communities with the maximum inter-community interactions provides insight into explaining the critical regions detected in the reaction field during the states of intermittency and thermoacoustic instability, also identified in previous studies. As a result, we further show that the most efficient suppression of thermoacoustic instability via air microjet injection is achieved when steady air jets are introduced to disrupt the maximum inter-community interactions present during the state of thermoacoustic instability.

Sahay, Ankit [Indian Institute of Technology Madra↗

NASA NTRS1973

Base pressure in laminar supersonic flow.

An asymptotic description is proposed for supersonic laminar flow over a wedge or a backward-facing step, for large Reynolds number and for a base or step height which is small compared with the boundary-layer length. The analysis is carried out for adiabatic wall conditions and a viscosity coefficient proportional to temperature. In a particular limit corresponding to a very thick boundary layer, a similarity law is obtained for the base pressure. For a thinner boundary layer an asymptotic form for the base pressure is obtained which shows the dependence on the parameters explicitly and which permits good agreement with experiment. This latter result is based on an inviscid-flow approximation for the corner expansion and for reattachment with viscous forces important primarily in a thin sublayer about the dividing streamline. A prediction of the pressure distribution at reattachment is given and the result is compared with experimental pressure distributions.

Messiter, A. F.↗

NASA NTRS1983

Reattaching turbulent shear layers with perturbed structure

The reattachment of a fully turbulent, two-dimensional shear layer downstream of a backward-facing step has been studied experimentally. The work examines the effect of modifications in shear layer structure upstream of reattachment. A series of experiments were conducted in a low-speed wind tunnel using specialized instrumentation suited to the highly turbulent, reversing flow near reattachment. Accurate characterization of the time-mean features of the reattaching flows was possible. Assuming linear scaling normalized on distance from reattachment, distributions of the normalized pressure coefficients, the time-averaged skin friction coefficient, and the forward flow fraction appear universal for two-dimensional reattachment, independent of initial conditions and steep height, for given duct geometry (area ratio) and for high step height Reynolds numbers. The results suggest universal flow structure in the reattachment zone.

Westphal, R. V.↗

NASA NTRS1983

Numerical modeling of turbulent flow in a channel

Two-dimensional incompressible turbulent flow in a channel with a backward-facing step was studied numerically by Chorin's Random Vortex Method (RVM), an algorithm capable of tracing the action of elementary turbulent eddies and their cumulative effects without imposing any restrictions upon their motions. The step occurs in one side of a channel with otherwise flat, parallel walls; its height equals 1/3, 1/4 or 1/5 the width of the channel downstream. The main objective was to investigate the behavior of the large-scale turbulent eddies in a flow and the flow characteristics in the separated shear layer, the reattached zone, and the rebuilding boundary layer after reattachment. The unsteady vorticity field and the distribution of time-averaged turbulent statistics were obtained. The effects of expansion step height and initial boundary layer state were also studied. Comparisons were made with the available experimental results. The agreement is satisfactory in the velocity profiles and in the reattachment length, and fairly good in the turbulence profiles. Also a mechanism of the development of the reattaching turbulent flow was suggested by the numerical results.

Dai, Y. W.↗

NASA NTRS1984

Turbulent transport models for scramjet flowfields

Turbulence modeling approaches were examined from the standpoint of their capability to predict the complex flowfield features observed in scramjet combustions. Thus, for example, the accuracy of each turbulence model, with respect to the prediction of recirculating flows, was examined. It was observed that for large diameter ratio axisymmetric sudden expansion flows, a choice of turbulence model was not critical because of the domination of their flowfields by pressure forces. For low diameter ratio axisymmetric sudden expansions and planar backward-facing steps flows, where turbulent shear stresses are of greater significance, the algebraic Reynolds stress approach, modified to increase its sensitivity to streamline curvature, was found to provide the best results. Results of the study also showed that strongly swirling flows provide a stringent test of turbulence model assumptions. Thus, although flows with very high swirl are not of great practical interest, they are useful for turbulence model development. Finally, it was also noted that numerical flowfields solution techniques have a strong interrelation with turbulence models, particularly with the turbulent transport models which involve source-dominated transport equations.

Sindir, M. M.↗

NASA NTRS1983

A hot-wire method for high-intensity turbulent flows

A measuring technique for determing instantaneous, three-dimensional velocity vectors in highly turbulent flows by means of a 4-sensor hot-wire probe is described. As is well known, the hot-wire signal received in reversing flows cannot uniquely be interpreted. This difficulty is circumvented by tracking the thermal wake of a heated wire. Whenever the approximate flow direction is indicated by a temperature-sensitive wake detector, all components of the instantaneous velocity vector are evaluated by means of a digital data reduction method. Uniqueness of the solution derived from the triple-hot-wire response equations is examined. A first application of the proposed measuring technique in the recirculating flow downstream of a backward-facing step is described.

Mueller, U. R.↗

NASA NTRS1984

Accelerated convergence for incompressible flow calculations

Two improved algorithms which solve the steady-state Navier-Stokes equations, PISO and SIMPLER, are studied. Computations were carried out on progressively finer grids for the driven cavity and flow over a backward-facing step. The effects of relaxation factor, number of grid nodes and number of sweeps through the pressure equations are studied to evaluate the performance of the PISO and SIMPLER schemes. Results show that these improved schemes accelerate the convergence rate of the solution generally by a factor of two as compared to the SIMPLE method.

Neely, G. M.↗

NASA NTRS1985

An implicit finite-difference code for a two-equation turbulence model for three-dimensional flows

An implicit finite difference code was developed which solves the transport equations for the turbulence kinetic energy and its dissipation rate in generalized coordinates in three dimensions. The finite difference equations are solved using the Beam-Warming algorithm. The kinetic energy-dissipation code, KEM, provides the closure; i.e., the turbulent viscosity for calculation of either compressible or incompressible flows. Turbulent internal flow over a backward-facing step has been calculated using the present code in conjunction with the Incompressible Navier-Stokes Code, INS3D. The results are in good agreement with experiments and two dimensional computations of other researchers.

Kaul, U. K.↗

NASA NTRS1985

Accelerated convergence for incompressible flow calculations

Neely, G. M.↗