Plane Asymmetric Diffuser Research Articles

Unsteady flow control of a plane diffuser based on a Karman-vortex generator

Implicit large-eddy simulation is employed to simulate the flow in an asymmetric plane diffuser at Re=9000. Flow separation exists near the throat and evolves to large-scale, unsteady separation in the expansion section and the downstream region. An unconventional flow control method, namely, a cylindrical Karman-vortex generator (KVG) with different sizes and locations that induces periodic spanwise vortex shedding, is set upstream of the throat to suppress the flow separation. An appropriately designed KVG can enhance the mixing of the outer flow and the low energy fluid near the wall region by the periodic shedding Karman-vortices, and effectively reduce the separation bubble size. For the present optimal case, the length and height of the separation bubble are decreased 50.4% and 90.9%, respectively. The static pressure recovery coefficient is also increased by about 50%. Moreover, the velocity and total pressure distributions at the end of the expansion section are more uniform with lower fluctuation in the case with KVG installed. An optimal KVG diameter DK is suggested to be 3–4% of the expansion section length LE. The gap ratio to the lower wall G/DK and the length ratio to the throat Lt/DK are suggested to be 2.0–3.0 and 5.0–10.0, respectively.

Development of k-R turbulence model for wall-bounded flows

A new low-Reynolds-number turbulence model is formulated based on the turbulent kinetic energy k and eddy-viscosity parameter R=k2/ϵ. In the derivation, most of the diffusion terms emerging from the transformation have been preserved in the proposed model, maintaining the closest relationship with its parent k-ϵ model; the near-wall viscous balance is guaranteed by including a far-wall damping function. The turbulent structure parameter (i.e., Bradshaw-relation) that may enhance the predicted accuracy for non-equilibrium flows, is incorporated into the current model. The coefficients and functions are constructed such as to preserve the anisotropic characteristics of turbulence, encountered in rotational and irrotational flows. Fully-developed turbulent channel and flat-plate flows are computed to validate the model ability in replicating the near-wall turbulence. Two-dimensional asymmetric plane diffuser and airfoil flows are simulated to verify the model accuracy in capturing non-equilibrium flows with separation and reattachment. Computation of a three-dimensional wing with shock-wave is presented, rectifying the model competency in predicting large adverse-pressure-gradient flows. Furthermore, model predictions are compared with other two frequently-used turbulence models; a good correlation is obtained between the current model and experimental data.

Large-Eddy Simulation of an Asymmetric Plane Diffuser: Comparison of Different Subgrid Scale Models

Large-eddy simulation (LES) of separated turbulent flow through an asymmetric plane diffuser is investigated. The outcome of an actual LES depends on the quality of the subgrid-scale (SGS) model, as well as the accuracy of the numerical method used to solve the equations for the resolved scales. In this paper, we focus on the influence of SGS models for LES of the diffuser flow through using a high-order finite difference method to solve the equations for the resolved scales. Six resolutions are computed to investigate the influence of mesh resolution. Four existing SGS models, a new one-equation dynamic SGS model and a direct numerical simulation (DNS) are conducted in the diffuser flow. A series of computational analyses is performed to assess the performance of different SGS models on the coarse grids. By comparison with the experiment and DNS, the results produced by the new one-equation dynamic model give better agreement with experiment and DNS than the four other existing SGS models.

Developing code-friendly variant of V2F turbulence model

Relevant modifications to the code-friendly variant of v¯2−f turbulence model is proposed that accounts for the distinct effects of low-Reynolds number and near-wall turbulence. It incorporates compatible formulations for inter-dependent coefficients Cϵ(1,2) and σ(k,ϵ) to amplify the level of dissipation in non-equilibrium flow regions, thus reducing the turbulent kinetic energy and time/length scale magnitudes to improve prediction of adverse pressure gradient flows, involving flow separation and reattachment. A non-linear eddy-viscosity coefficient with a realizable eddy-viscosity bound that may enhance the predicted accuracy for complex flows, is introduced with the present model. Coefficients of the elliptic-relaxation equation are constructed such as to preserve the anisotropic characteristics of turbulence, encountered in rotational and irrotational flows. Fully-developed turbulent channel and flat-plate flows are computed to validate the model ability in replicating the near-wall turbulence. An asymmetric plane diffuser flow is simulated to verify the model accuracy in capturing non-equilibrium flows with separation and reattachment. The Computation of flow over a three-dimensional (3D) axisymmetric hill is presented, rectifying the model competency in predicting an adverse-pressure-gradient flow with 3D turbulent separation. Model predictions are compared with the widely used SST (shear stress transport) k−ω model; a good correlation is obtained between the current model and DNS/experimental data.

Automated shape optimisation of a plane asymmetric diffuser using combined Computational Fluid Dynamic simulations and multi-objective Bayesian methodology

An approach for shape optimisation of the flow through a diffuser is presented in this work. This multi-objective problem focuses on maximising the diffuser performance by simultaneously increasing the static pressure recovery across the geometry and the flow uniformity at the outflow. The hydrodynamic analysis of the geometry was conducted using the Computational Fluid Dynamics (CFD) software OpenFOAM, while a recently proposed multi-objective Bayesian approach was used for optimisation. The CFD and Bayesian methodology have been combined for fully automated operation using a Python-based framework. The proposed design parameterisation focuses on reshaping the diffuser in the expansion region. Catmull–Clark subdivision curves were employed to represent the shape of the diffuser wall; the influence of the number of control points (design points) for the curves on the optimum design was investigated. The optimal designs exhibit a reasonable performance improvement compared with the base design.

Development of a k–ω–ϕ–α turbulence model based on elliptic blending and applications for near-wall and separated flows

ABSTRACTA new turbulence model based on elliptic blending, termed as k − ω − ϕ − α model, is developed. This model uses the latest version of Wilcox's k − ω model in near-wall region and changes gradually to the model elsewhere. The capabilities of the present model are evaluated on near-wall and separation flows, i.e. the 2D fully developed channel flow, the asymmetric plane diffuser flow and the 2D backward-facing step flow, in comparison with available direct numerical simulation (DNS) and experimental data. The computational results are compared also to those from the popular model and the original model, and the present model is more stable than the model in complex flows. The present model provides indistinguishable velocity profiles and improved turbulent kinetic energy profiles compared to the model in the channel flow, while in the separation flows tested herein, the present model can obtain comparable results with the model, and both of them show improvements to some extent compared with the model.

Numerical Investigation of Flow in an Asymmetric Plane Diffuser Using a Multi-Scale Turbulence Model

The flow in an asymmetric plane diffuser was simulated using both the multiscale turbulence model based on the variable interval time average method and the standardk-εmodel based on the Reynolds average method. The numerical method used in this simulation is an unstructured staggered mesh scheme. The capability of the multi-scale model to simulate flow in an asymmetric plane diffuser has been validated. Pressure coefficient, frictional resistance coefficient and mean velocity profiles downstream are in agreement with experiments. Moreover, the results predicted by the multi-scale model are better than that predicted by the standardk-εmodel. The computational results show that the multiscale turbulence model can successfully simulate this type of separated flow.

Control of the turbulent flow in a plane diffuser through optimized contoured cavities

A passive control strategy, which consists in introducing contoured cavities in solid walls, is applied to a plane asymmetric diffuser at a Reynolds number that implies fully-turbulent flow upstream of the diffuser divergent part. The analysed reference configuration, for which experimental and numerical data were available, is characterized by an area ratio of 4.7 and a divergence angle of 10°. A large zone of steady flow separation is present in the diffuser without the introduction of the control. One and two subsequent contoured cavities are introduced in the divergent wall of the diffuser and a numerical optimization procedure is carried out to obtain the cavity geometry that maximizes the pressure recovery in the diffuser and minimizes the flow separation extent. The introduction of one optimized cavity leads to an increase in pressure recovery of the order of 6.9% and to a significant reduction of the separation extent, and further improvement (9.6%) is obtained by introducing two subsequent cavities in the divergent wall. The most important geometrical parameters are also identified, and the robustness of the solution to small changes in their values and in the Reynolds number is assessed. The present results show that the proposed control strategy, previously tested in the laminar regime, is effective also for turbulent flows at higher Reynolds numbers. As already found for laminar flow, the success of the control is due both to a virtual geometry modification of the diffuser and to a favourable effect of the cavities in reducing the momentum losses near the wall.

On choice of turbulence models and grid parameters for computation of flows in diffuser ducts

The results of analyzing the reliability of six turbulence models are presented as applied to calculations of flows in the asymmetric plane diffuser. The influence of grid parameters upon the calculation results is studied and the accuracy of flow separation and reattachment points prediction is determined. Also carried out is the comparison of processor time spent for calculations with the aid of each model.

A robust implicit multigrid method for RANS equations with two-equation turbulence models

The design of a new, truly robust multigrid framework for the solution of steady-state Reynolds-Averaged Navier-Stokes (RANS) equations with two-equation turbulence models is presented. While the mean-flow equations and the turbulence model equations are advanced in time in a loosely-coupled manner, their multigrid cycling is strongly coupled (FC-MG). Thanks to the loosely-coupled approach, the unconditionally positive-convergent implicit time-integration scheme for two-equation turbulence models (UPC) is used. An improvement to the basic UPC scheme convergence characteristics is developed and its extension within the multigrid method is proposed. The resulting novel FC-MG-UPC algorithm is nearly free of artificial stabilizing techniques, leading to increased multigrid efficiency. To demonstrate the robustness of the proposed algorithm, it is applied to linear and non-linear two-equation turbulence models. Numerical experiments are conducted, simulating separated flow about the NACA4412 airfoil, transonic flow about the RAE2822 airfoil and internal flow through a plane asymmetric diffuser. Results obtained from numerical simulations demonstrate the strong consistency and case-independence of the method.

Analysis of Non-steady Separated Turbulent Flow in an Asymmetric Plane Diffuser by Direct Numerical Simulations

Direct numerical simulations (DNS) of turbulent flow through an asymmetric plane diffuser, consisting of a flat wall and an inclined wall, were performed using a high-order finite difference method, to reveal the relationship between turbulence and flow separations under negative pressure gradients. A typical feature of this flow field is the non-steady three-dimensional separation region formed near the inclined wall. At the opening of the diffuser, low speed streaks in wall turbulence cause the initial non-steady separation layer, which includes small-scale reverse flow regions. Because turbulent eddies growing from this initial separation suppress the separated flow, a small reattachment section is formed downstream. When turbulent eddies start to decay and the negative pressure gradient begins to dominate, the flow separates again, and then a large-scale separation region is formed. In summary, the intensity of turbulent eddies affects the formation of the separation and reattachment regions near the inclined wall.

The separating flow in a plane asymmetric diffuser with 8.5° opening angle: mean flow and turbulence statistics, temporal behaviour and flow structures

The flow in a plane asymmetric diffuser with an opening angle of 8.5° has been studied experimentally using time-resolving stereoscopic particle image velocimetry. The inlet condition is fully developed turbulent channel flow at a Reynolds number based on the inlet channel height and bulk velocity of Re = 38000. All mean velocity and Reynolds stress components have been measured. A separated region is found on the inclined wall with a mean separation point at 7.4 and a mean reattachment point at 30.5 inlet channel heights downstream the diffuser inlet (the inclined wall ends 24.8 channel heights downstream the inlet). Instantaneous flow reversal never occurs upstream of five inlet channel heights but may occur far downstream the point of reattachment. A strong shear layer in which high rates of turbulence production are found is located in a region outside the separation. The static wall pressure through the diffuser is presented and used in an analysis of the balance between pressure forces and momentum change. It is demonstrated that production of turbulence causes a major part of the losses of mean flow kinetic energy. The character of the large turbulence structures is investigated by means of time-resolved sequences of velocity fields and spatial auto-correlation functions. Pronounced inclined structures are observed in the spanwise velocity and it is suggested that these are due to the legs of hairpin-like vortices.

Turbulent Forced Convection in a Plane Asymmetric Diffuser: Effect of Diffuser Angle

A simulation of two-dimensional turbulent forced convection in a plane asymmetric diffuser with an expansion ratio of 4.7 is performed, and the effect of the diffuser angle on the flow and heat transfer is reported. This geometry is common in many heat exchanging devices, and the turbulent convective heat transfer in it has not been examined. The momentum transport in this geometry, however, has received significant attention already, and the studies show that the results from the υ2¯‐f type turbulence models provide better agreement with measured velocity distributions than that from the k‐ε or k‐ω turbulence models. In addition, the υ2¯‐f type turbulence models have been shown to provide good heat transfer results for separated and reattached flows. The k‐ε‐ζ (υ2¯‐f type) turbulence model is used in this study due to its improved numerical robustness, and the FLUENT-CFD code is used as the simulation platform. User defined functions for the k‐ε‐ζ turbulence model were developed and incorporated into the FLUENT-CFD code, and that process is validated by simulating the flow and the heat transfer in typical benchmark problems and comparing these results with available measurements. This new capability is used to study the effect of the diffuser angle on forced convection in an asymmetric diffuser, and the results show that the angle influences significantly both the flow and the thermal field. The increase in that angle increases the size of the recirculation flow region and enhances the rate of the heat transfer.

Application of a local SGS model based on coherent structures to complex geometries

A coherent structure model (CSM) as a subgrid-scale (SGS) model [Kobayashi, H., 2005. The subgrid-scale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow. Phys. Fluids 17, 045104] is applied to complex geometries and is assessed its performance in large-eddy simulation. The CSM is one of the local SGS models, which mean herein “no averaging in homogeneous directions”. Two types of simulation code are tested for the assessment: a structured-mesh code is used for a flow over a backward-facing step, and an unstructured-mesh one is used for a flow in an asymmetric plane diffuser and for staggered jets in crossflow. For all configurations, the CSM gives good predictions and is almost the same performance as the dynamic models. This local model is simple and stable, and suitable for complex geometries.

Analysis of Unsteady Separated Turbulent Flow in Asymmetric Plane Diffuser by Direct Numerical Simulation

Direct numerical simulation (DNS) of turbulent flow through an asymmetric plane diffuser, which consists of flat and inclined walls, was carried out using a high-order finite difference method, in order to establish a database for non-equilibrium turbulence in the adverse pressure gradient. Typical feature of this flow field is the unsteady three-dimensional reverse flow region in the inclined wall side. At the beginning of the diffuser, low speed streaks in the wall turbulence cause the first unsteady separation which includes small-scale reverse flow regions. Following this region, because the turbulent eddy growing from the first unsteady separation suppresses the separated flow, a small reattachment section is formed in the downstream of the first unsteady separation. When the turbulent eddy declines and the adverse pressure gradient becomes dominant, the flow tends to separate again. And then, a large scale separation region is formed. In summary, the intensity of the turbulent eddy affects the formation of the separation and reattachment region on the inclined wall.

A Reynolds stress closure description of separation control with vortex generators in a plane asymmetric diffuser

A way to model the effects of streamwise vortices in a turbulent flow with one homogeneous direction is presented. The Reynolds averaged Navier-Stokes equations are solved with a differential Reynolds stress turbulence model. Assuming that the vortices can be approximated with the Lamb-Oseen model, wall-normal Reynolds stress distributions are calculated, corresponding to the spanwise variances of the estimated velocity distribution downstream of the vortex generators. The Reynolds stress contributions that are due to the vortex generators are added to the Reynolds stresses from the turbulence model so as to mimic the increased mixing due to the vortex generators. Volume forces are applied also in the mean momentum equations to account for the drag of the vortex generators. The model is tested and compared with experimental data from a plane asymmetric diffuser flow which is separating without vortex generators. The results indicate that the model is able to mimic the major features of vortex generator flow control and that the flow case in question is susceptible to separation control. The model results show that the pressure recovery of the diffuser could be increased by almost 10% by applying vortex generators and that, if keeping the shape of the vortex generators fixed, their optimal position is close to the diffuser inlet. Computations also indicated that the time to re-establish the separation zone when the control suddenly is turned off is substantially longer than the time it takes to remove the separation after the control is turned on again. Some work on adapting a differential Reynolds stress turbulence model was necessary in order to make it capable of realistic predictions of the asymmetric diffuser flow in which the vortex generator model is tested. However, the main focus of the article is on the modelling of vortex generator effects.

Hybrid LES-RANS: An approach to make LES applicable at high Reynolds number

The main bottle neck for using large eddy simulations (LES) at high Reynolds number is the requirement of very fine meshes near walls. Hybrid LES-Reynolds-averaged Navier-Stokes (RANS) was invented to get rid of this limitation. In this method, unsteady RANS (URANS) is used near walls and away from walls LES is used. The matching between URANS and LES takes place in the inner log-region. In the present paper, a method to improve standard LES-RANS is evaluated. The improvement consists of adding instantaneous turbulent fluctuations (forcing conditions) at the matching plane in order to provide the equations in the LES region with relevant turbulent structures. The fluctuations are taken from a DNS of a generic boundary layer. Simulations of fully developed channel flow and plane asymmetric diffuser flow are presented. Hybrid LES-RANS is used both with and without forcing conditions.

Numerical and experimental study of separated flow in a plane asymmetric diffuser

Computations of the turbulent flow through plane asymmetric diffusers for opening angles from 8° to 10° have been carried out with the explicit algebraic Reynolds stress model (EARSM) of Wallin and Johansson [J. Fluid Mech. 403 (2000) 89]. It is based on a two-equation platform in the form of a low- Re K− ω formulation, see e.g. Wilcox [Turbulence Modeling for CFD, DCW Industries Inc., 1993]. The flow has also been studied experimentally for the 8.5° opening angle using PIV and LDV. The models under-predict the size and magnitude of the recirculation zone. This is, at least partially, attributed to an over-estimation of the wall normal turbulence component in a region close to the diffuser inlet and to the use of damping functions in the near-wall region. By analyzing the balance between the production and dissipation of the turbulence kinetic energy we find that the predicted dissipation is too large. Hence, we can identify a need for improvement of the modeling the transport equation for the turbulence length-scale related quantity.

242 非対称ディフューザ内の空間発展乱流の DNS

242 非対称ディフューザ内の空間発展乱流の DNS