Determining critical Reynolds number of laminar-turbulent transition in a flat Poiseuille problem based on “discontinuous functions” method

Trudy MAI ◽  
2019 ◽  
pp. 3-3
Author(s):  
Olga Khatuntseva
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Discontinuous Functions ◽  
Turbulent Transition ◽  
Laminar Turbulent Transition

Experiments on critical Reynolds number and global instability in roughness-induced laminar–turbulent transition

2018 ◽  
Vol 844 ◽  
pp. 878-904 ◽  
Author(s):  
Dominik K. Puckert ◽  
Ulrich Rist
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Water Channel ◽  
Plate Boundary ◽  
Linear Stability Theory ◽  
Global Instability ◽  
Turbulent Transition ◽  
Roughness Elements ◽  
Hot Film ◽  
Laminar Turbulent Transition

The effects of isolated, cylindrical roughness elements on laminar–turbulent transition in a flat-plate boundary layer are investigated in a laminar water channel. Our experiments aim at providing a comparison to global linear stability theory (LST) by means of hot-film anemometry and particle image velocimetry. Although the critical Reynolds number from theory does not match the transition Reynolds number observed in experiments, there are distinct experimental observations indicating a changeover from purely convective to absolute/global instability very close to the critical Reynolds number predicted by theory. Forcing with a vibrating wire reveals the evolution of the system dynamics from an amplifier to a wavemaker when the critical Reynolds number is exceeded. The mode symmetry is varicose for thick roughness elements and a changeover from varicose to sinuous modes is observed at the critical Reynolds number for thin roughness elements. Therefore, most predictions by global LST can be confirmed, but additional observations in the physical flow demonstrate that not all features can be captured adequately by global LST.

Numerical Assessment of Turbulent Models at a Critical Regime on Unstructured Meshes

2011 ◽  
Author(s):  
Ju Yeol You ◽  
Oh Joon Kwon
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Critical Reynolds Number ◽  
Flow Simulation ◽  
Critical Regime ◽  
Computational Domain ◽  
Turbulent Transition ◽  
Flow Features ◽  
Turbulent Models ◽  
Laminar Turbulent Transition

The main objective of the present study is to investigate the performance of different turbulent models for the flow simulation around a circular cylinder at a critical Reynolds number regime (Re = 8.5×105, Tu = 0.7%). To simulate the various flow features such as laminar-turbulent transition inside the boundary layer and the unsteady vortex shedding in the wake region, a hybrid RANS/LES model (SAS model) and a correlation-based transition model (γ - Reθ model) were used and the feasibilities of them for the flow simulation at a critical Reynolds number regime were demonstrated. A vertex-centered finite-volume method was adopted to discretize the incompressible Navier-Stokes equations and an unstructured mesh technique was used to discretize the computational domain. The inviscid fluxes were evaluated by using 2nd-order Roe’s FDS and the viscous fluxes were computed based on central differencing. A dual-time stepping method and the Gauss-Seidel iteration were used for unsteady time integration. To reduce the computational costs, the parallelization strategy using METIS and MPI libraries was adopted. The unsteady characteristics and time-averaged quantities of the flow fields were compared between the turbulent models. The numerical results have been also compared with experimental data. At the critical regime, turbulent models have showed quite different results due to the different abilities of each model to predict various flow features such as laminar-turbulent transition, unsteady vortex shedding.

Common features between the Newtonian laminar–turbulent transition and the viscoelastic drag-reducing turbulence

2019 ◽  
Vol 877 ◽  
pp. 405-428 ◽  
Author(s):  
Anselmo S. Pereira ◽  
Roney L. Thompson ◽  
Gilmar Mompean
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Turbulent Flows ◽  
Temporal Dynamics ◽  
Homoclinic Orbits ◽  
Theoretical Development ◽  
Transitional Flows ◽  
Turbulent Transition ◽  
Laminar Turbulent Transition

The transition from laminar to turbulent flows has challenged the scientific community since the seminal work of Reynolds (Phil. Trans. R. Soc. Lond. A, vol. 174, 1883, pp. 935–982). Recently, experimental and numerical investigations on this matter have demonstrated that the spatio-temporal dynamics that are associated with transitional flows belong to the directed percolation class. In the present work, we explore the analysis of laminar–turbulent transition from the perspective of the recent theoretical development that concerns viscoelastic turbulence, i.e. the drag-reducing turbulent flow obtained from adding polymers to a Newtonian fluid. We found remarkable fingerprints of the variety of states that are present in both types of flows, as captured by a series of features that are known to be present in drag-reducing viscoelastic turbulence. In particular, when compared to a Newtonian fully turbulent flow, the universal nature of these flows includes: (i) the statistical dynamics of the alternation between active and hibernating turbulence; (ii) the weakening of elliptical and hyperbolic structures; (iii) the existence of high and low drag reduction regimes with the same boundary; (iv) the relative enhancement of the streamwise-normal stress; and (v) the slope of the energy spectrum decay with respect to the wavenumber. The maximum drag reduction profile was attained in a Newtonian flow with a Reynolds number near the boundary of the laminar regime and in a hibernating state. It is generally conjectured that, as the Reynolds number increases, the dynamics of the intermittency that characterises transitional flows migrate from a situation where heteroclinic connections between the upper and the lower branches of solutions are more frequent to another where homoclinic orbits around the upper solution become the general rule.

Prediction of Lapse Rate in Low Pressure Turbines With and Without Modeling of the Laminar-Turbulent Transition

2007 ◽  
Author(s):  
Mahmoud L. Mansour ◽  
S. Murthy Konan ◽  
Shraman Goswami
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Test Data ◽  
Low Pressure ◽  
Lapse Rate ◽  
Test Cases ◽  
Low Pressure Turbine ◽  
Turbulent Transition ◽  
Transition Modeling ◽  
Laminar Turbulent Transition

Although turbo-machinery main stream flows are predominantly turbulent, the low pressure turbine airfoil surface boundary layer may be either laminar or turbulent. When boundary layer flow is laminar and passes through a zone of adverse pressure gradient, bypass or separation transition can occur via the Tollmien-Schlichting or Kelvin-Helmholtz instabilities. As the gas turbine’s low pressure turbine operating condition changes from sea level take-off to the altitude cruise, Reynolds number is significantly lowered and the turbine’s performance loss increases significantly. This fall-off in performance characteristic is known as lapse rate. Ability to accurately model such phenomenon is a prerequisite for reliable loss prediction and essential for improving low pressure turbine designs. Establishing such capability requires the validation and evaluation of existing low Reynolds number turbulence models, with laminar-turbulent transition modeling capability, against test cases with measured data. This paper summarizes the results of evaluating and validating two 3D viscous “RANS” Reynolds-Averaged Navier-Stokes programs for two test cases with test data. The first test case is the ERCOFTAC’ flat plate with and without pressure gradient, and the second is a Honeywell three-and-half-stage low pressure turbine with available test data at high and low Reynolds number operations. In addition to evaluating the CFD codes against test data, the flat plate test cases were used to establish the meshing and modeling best practice for each code before performing the validation for the Honeywell multistage low pressure turbine. The RANS CFD programs are Numeca’s Fine Turbo and ANSYS/CFX. Numeca’s Fine Turbo employs a two-equation K-ε turbulence model without laminar-turbulent transition modeling capability and the one-equation Spallart-Allmaras turbulence model with laminar-turbulent transition modeling capability. The ANSYS/CFX, on the other hand, employs a two-equation K-ω turbulence model (AKA SST or shear stress transport) with ability to model laminar-turbulent transition. Predictions of the CFD codes are compared with test data and the impact of modeling the laminar-turbulent transition on the prediction accuracy is assessed and presented. Both CFD codes are commercially available and the evaluation presented here is based on users’ prospective that targets the applicability of such predictive tools in the turbine design process.

A Numerical Investigation on the Onset of the Various Flow Regimes in a Spherical Annulus

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Lalaoua Adel ◽  
Bouabdallah Ahcene
Keyword(s):  
Reynolds Number ◽  
Flow Behavior ◽  
Flow Regimes ◽  
Skin Friction Coefficient ◽  
Formation Mechanisms ◽  
Turbulent Regime ◽  
Turbulent Transition ◽  
Inner Sphere ◽  
Spherical Couette ◽  
Laminar Turbulent Transition

The spherical Couette system, consisting of the flow in the annular gap between two concentric rotating spheres, is a convenient problem for studying the laminar–turbulent transition. Many of the transitional phenomena encountered in this flow are of fundamental relevance for the understanding of global processes in the planetary atmospheres as well as in astrophysical and geophysical motions. Furthermore, the study of spherical Couette flow (SCF) is of basic importance in the field of hydrodynamic stability. This paper focuses principally on the numerical prediction of various transitions between flow regimes in a confined spherical gap between a rotating inner sphere and a fixed outer spherical shell. The finite-volume-based computational fluid dynamics, FLUENT software package, is adopted to investigate numerically the flow of a viscous incompressible fluid in the closed spherical gap. Two important dimensionless parameters completely define the flow regimes: the Reynolds number, Re = Ω1R12/ν, for the rotation of the inner sphere and the gap width, β = (R2 − R1)/R1 = 0.1, for the geometry. The numerical calculations are carried out over a range of Reynolds number from two until 60,000. The numerical results are compared with the experimental data available in the literature, and the agreement between the two approaches is very good. The laminar–turbulent transition, the onset of different instabilities, the formation mechanisms of various structures, and the flow behavior are examined and described in detail by the pressure field, meridional streamlines, circumferential velocity, and skin friction coefficient. In addition, the velocity time series and the corresponding power spectral density are considered and analyzed over a large range of Reynolds number. Three kinds of fundamental frequencies expressed by F0, F1, and F2 are obtained corresponding to the spiral mode associated with the wavy mode (SM + WM), the wavy mode (WVF), and the chaotic fluctuation (CF), respectively. However, no sharp fundamental frequency components are observed for the turbulent regime.

A Theory of Transitional and Turbulent Flow of Non-Newtonian Slurries Between Flat Parallel Plates

1971 ◽  
Vol 11 (01) ◽  
pp. 52-56 ◽  
Author(s):  
Richard W. Hanks ◽  
Maheshkumar P. Valia
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Critical Reynolds Number ◽  
Frictional Resistance ◽  
Newtonian Fluids ◽  
Transitional Flow ◽  
Parallel Plates ◽  
Bingham Plastic ◽  
Turbulent Transition ◽  
Large Width

Abstract A theoretical model is developed which Permits prediction of velocity profiles and frictional prediction of velocity profiles and frictional resistance factors for the isothermal flow of Bingham plastic non-Newtonian slurries in laminar, transitional, and turbulent flow between that parallel walls, in rectangular ducts of large width-to-height ratios, or in concentric annuli with radius ratios approaching unity. The theory is tested with available frictional resistance data for a range of Hedstrom numbers from 10(4) to 10(8) and a set of theoretical design curves of friction factor vs Reynolds number is developed. The model indices that for certain ranges of Hedstrom number (the non-Newtonian index) turbulence is suppressed relative to Newtonian flow behavior, whereas for other ranges of Hedstrom number, the converse is true. Introduction The handling of non-Newtonian fluids in turbulent motion is an important operation in many modern technological processes. Despite this fact, however, little has been done to develop models which are comparable to those available for Newtonian turbulent flow. In particular, a model of the transitional flow regime is notably lacking. Recently, a theory of laminar-turbulent transition for non-Newtonian slurries flowing in pipes and parallel plates was presented. A theory of parallel plates was presented. A theory of transitional and turbulent flow of Newtonian fluids in pipes and parallel plate ducts has also recently been developed. This theory permits the analytic calculation of the friction factor-Reynolds number curves as a continuous function of Reynolds number from the critical Reynolds number of laminar turbulent transition to any condition of turbulent flow. In this paper these two theories will be combined in order to develop a theory for the transitional and turbulent flow of non-Newtonian slurries in parallel plate ducts, rectangular ducts of large width-to-height ratio, or concentric annuli with radius ratios approaching unity. THEORETICAL ANALYSIS The rheological model which will be used to represent the non-Newtonian slurry behavior is the linear Bingham plastic model, ..............(1) ............(2) For this model the laminar flow curve is given by ..............(3) where q = 2v/b, b is one-half the distance between the plates, w = b(−dp/dz) is the wall shear stress, and D = o/ w. The end of the laminax flow, region is determined by the equations ........(4) .........(5) where N Rec = 4bp vc/ p is the critical Reynolds number, Dc is the critical transitional value of D and N He -16bp o/ p is the Hedstrom number expressed in terms of the hydraulic diameter for parallel plates. parallel plates. The calculation of the transitional flow field for this type of fluid will be based upon the model developed by Hanks for Newtonian fluids. SPEJ P. 52

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