Numerical prediction of nozzle flow separation: Issue of turbulence modeling

Numerical simulation of separated flows in rocket nozzles is challenging because existing turbulence models are unable to predict it correctly. This paper addresses this issue with the Spalart-Allmaras and Shear Stress Transport (SST) eddy-viscosity models, which predict flow separation with moderate success. Their performances have been compared against experimental data for a conical and two contoured subscale nozzles. It is found that they fail to predict the separation location correctly, exhibiting sensitivity to the nozzle pressure ratio (NPR) and nozzle type. A careful assessment indicated how the model had to be tuned for better, consistent prediction. It is learnt that SST model's failure is caused by limiting of the shear stress inside boundary layer according to Bradshaw's assumption, and by over prediction of jet spreading rate. Accordingly, SST's coefficients were empirically modified to match the experimental wall pressure data. Results confirm that accurate RANS prediction of separation depends on the correct capture of the jet spreading rate, and that it is feasible over a wide range of NPRs by modified values of the diffusion coefficients in the turbulence model. (C) 2015 Elsevier Masson SAS. All rights reserved.

The effect of wake passing on a flow separation in a low pressure turbine cascade

This paper describes an investigation into the effect that passing wakes have on a separation bubble that exists on the pressure surface and near the leading edge of a low pressure turbine blade. Previous experimental studies have shown that the behaviour of this separation is strongly incidence dependent and that it responds to its disturbance environment. The results presented in this paper examine the effect of wake passing in greater detail. Two dimensional, Reynolds averaged, numerical predictions are first used to examine qualitatively the unsteady interaction between the wakes and the separation bubble. The separation is predicted to consist of spanwise vortices whose development is in phase with the wake passing. However, comparison with experiments shows that the numerical predictions exaggerate the coherence of these vortices and also overpredict the time-averaged length of the separation. Nonetheless, experiments strongly suggest that the predicted phase locking of the vortices in the separation onto the wake passing is physical.

The Effects of Stratification on Flow Separation

Separation of stratified flow over a two-dimensional hill is inhibited or facilitated by acceleration or deceleration of the flow just outside the attached boundary layer. In this note, an expression is derived for this acceleration or deceleration in terms of streamline curvature and stratification. The expression is valid for linear as well as nonlinear deformation of the flow. For hills of vanishing aspect ratio a linear theory can be derived and a full regime diagram for separation can be constructed. For hills of finite aspect ratio scaling relationships can be derived that indicate the presence of a critical aspect ratio, proportional to the stratification, above which separation will occur as well as a second critical aspect ratio above which separation will always occur irrespective of stratification.

Flow separation and roughness lengths over large bedforms in a tidal environment

This study characterises the shape of the flow separation zone (FSZ) and wake region over large asymmetric bedforms under tidal flow conditions. High resolution bathymetry, flow velocity and turbulence data were measured along two parallel transects in a tidal channel covered with bedforms. The field data are used to verify the applicability of a numerical model for a systematic study using the Delft3D modelling system and test the model sensitivity to roughness length. Three experiments are then conducted to investigate how the FSZ size and wake extent vary depending on tidally-varying flow conditions, water levels and bathymetry. During the ebb, a large FSZ occurs over the steep lee side of each bedform. During the flood, no flow separation develops over the bedforms having a flat crest; however, a small FSZ is observed over the steepest part of the crest of some bedforms, where the slope is locally up to 15°. Over a given bedform morphology and constant water levels, no FSZ occurs for velocity magnitudes smaller than 0.1 m s**-1; as the flow accelerates, the FSZ reaches a stable size for velocity magnitudes greater than 0.4 m s**-1. The shape of the FSZ is not influenced by changes in water levels. On the other hand, variations in bed morphology, as recorded from the high-resolution bathymetry collected during the tidal cycle, influence the size and position of the FSZ: a FSZ develops only when the maximum lee side slope over a horizontal distance of 5 m is greater than 10°. The height and length of the wake region are related to the length of the FSZ. The total roughness along the transect lines is an order of magnitude larger during the ebb than during the flood due to flow direction in relation to bedform asymmetry: during the ebb, roughness is created by the large bedforms because a FSZ and wake develops over the steep lee side. The results add to the understanding of hydrodynamics of natural bedforms in a tidal environment and may be used to better parameterise small-scale processes in large-scale studies.

On the use of impact theory for slender configurations exhibiting flow separation /

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Flow of micropolar fluid through a tube with stenosis

mathematical model for the steady flow of non-Newtonian fluid through a stenotic region is presented. The results indicate that the general shape and size of the stenosis together with rheological properties of blood are important in understanding the flow characteristics and the presence of flow separation.

Surface pressure and heat transfer measurements in the unsteady separated hypersonic flow field over double cones

Reliable bench mark experimental database in the separated hypersonic flow regime is necessary to validate high resolution CFD codes. In this paper we report the surface pressure and heat transfer measurements carried out on double cones (first cone semi-apex angle = 15, 25 deg.; second cone semi-apex angle= 35, 68 deg.) at hypersonic speeds that will be useful for CFD code validation studies. The surface pressure measurements are carried out at nominal Mach number of 8.35 in the IISc hypersonic wind tunnel. On the other hand the surface heat transfer measurements are carried out at a nominal Mach number of 5.75 in the IISc hypersonic shock tunnel. The flow separation point on the first cone, flow reattachment on the second cone and the wild fluctuation of the transmitted shock on the second cone surface (25/68 deg. double cone) in the presence of severe adverse pressure gradient are some of the flow features captured in the measurements. The results from the CFD studies indicate good agreement with experiments in the attached flow regime while considerable differences are noticeable in the separated flow regime.

Simulation of Free-Surface Flow in a Tank Using the Navier-Stokes Model and Unstructured Finite Volume Method

Modelling free-surface flow has very important applications in many engineering areas such as oil transportation and offshore structures. Current research focuses on the modelling of free surface flow in a tank by solving the Navier-Stokes equation. An unstructured finite volume method is used to discretize the governing equations. The free surface is tracked by dynamically adapting the mesh and making it always surface conforming. A mesh-smoothing scheme based on the spring analogy is also implemented to ensure mesh quality throughout the computaiton. Studies are performed on the sloshing response of a liquid in an elastic container subjected to various excitation frequencies. Further investigations are also carried out on the critical frequency that leads to large deformation of the tank walls. Another numerical simulation involves the free-surface flow past as submerged obstacle placed in the tank to show the flow separation and vortices. All these cases demonstrate the capability of this numerical method in modelling complicated practical problems.

Starting Nozzle Flow Simulation Using K-G Two-Equation Turbulence Model

The starting process of two-dimensional nozzle flows has been simulated with Euler, laminar and k - g two-equation turbulence Navier-Stokes equations. The flow solver is based on a combination of LUSGS subiteration implicit method and five spatial discretized schemes, which are Roe, HLLE, MHLLE upwind schemes and AUSM+, AUSMPW schemes. In the paper, special attention is for the flow differences of the nozzle starting process obtained from different governing equations and different schemes. Two nozzle flows, previously investigated experimentally and numerically by other researchers, are chosen as our examples. The calculated results indicate the carbuncle phenomenon and unphysical oscillations appear more or less near a wall or behind strong shock wave except using HLLE scheme, and these unphysical phenomena become more seriously with the increase of Mach number. Comparing the turbulence calculation, inviscid solution cannot simulate the wall flow separation and the laminar solution shows some different flow characteristics in the regions of flow separation and near wall.

Micro-vortex generator flow control for supersonic engine inlets

To investigate the flow control potential of micro-vortex generators for supersonic mixed-compression inlets, a basic model experiment has been designed which combines a normal shock wave with a subsonic diffuser. The diffuser is formed by a simple expansion corner, with a divergence angle of 6 degrees. The diffuser entry Mach numbers were M=1.3 and M=1.5 and a number of shock locations relative to the corner position were tested. Flow control was applied in the form of counter-rotating micro-vanes with heights of approximately 20% of boundary layer thickness. Furthermore, corner fences where employed to reduce sidewall effects. It was found that micro-vortex generators were able to significantly reduce the extent of flow separation under all conditions, but could not eliminate it altogether. Corner fences also demonstrated potential for improving the flow in rectangular cross section channels and the combination of corner fences with micro-vortex generators was found to give the greatest benefits. At M=1.3 the combination of corner fences and micro-vanes placed close to the diffuser entry could prevent separation for a wide range of conditions. At the higher diffuser entry Mach number the benefits of flow control were less significant although a reduction of separation size and an improved pressure recovery was observed. It is thought that micro-vortex generators can have significant flow control potential if they are placed close to the expected separation onset and when the adverse pressure gradient is not too far above the incipient separation level. The significant beneficial effects of corner fences warrant a more comprehensive further investigation. It is thought that the control methods suggested here are capable of reducing the bleed requirement on an inlet, which could provide significant performance advantages.

Transport phenomena in radial flow MOCVD reactor with three concentric vertical inlets

Transport phenomena in radial flow metalorganic chemical vapor deposition (MOCVD) reactor with three concentric vertical inlets are studied by two-dimensional numerical modeling. By varying the parameters such as gas pressure, flow rates combination of multi-inlets, geometric shapes and sizes of reactor and flow distributor, temperatures of susceptor and ceiling, and susceptor rotation, the corresponding velocity, temperature, and concentration fields inside the reactor are obtained; the onset and change of flow recirculation cells under influences of those parameters are determined. It is found that recirculation cells, originated from flow separation near the bend of reactor inlets, are affected mainly by the reactor height and shape, the operating pressure, the flow rates combination of multi-inlets, and the mean temperature between susceptor and ceiling. By increasing the flow rate of mid-inlet and the mean temperature, decreasing the pressure, maintaining the reactor height below certain criteria, and trimming the bends of reactor wall and flow distributor to streamlined shape, the recirculation cells can be minimized so that smooth and rectilinear flow prevails in the susceptor region, which corresponds to smooth and rectilinear isotherms and larger reactant concentration near the susceptor. For the optimized reactor shape, the reactor size can be enlarged to diameter D = 40 cm and height H = 2 cm without flow recirculation. The susceptor rotation over a few hundred rpm around the reactor central axis will induce the recirculation cell near the exit and deflect the streamlines near the susceptor, which is not the case for vertical reactors. (c) 2006 Elsevier B.V. All rights reserved.