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Modeling of Flow Transition Using an Intermittency Transport Equation
Abstract
A new transport equation for intermittency factor is proposed to model transitional flows. The intermittent behavior of the transitional flows is incorporated into the computations by modifying the eddy viscosity, mu(sub t), obtainable from a turbulence model, with the intermittency factor, gamma: mu(sub t, sup *) = gamma.mu(sub t). In this paper, Menter's SST model (Menter, 1994) is employed to compute mu(sub t) and other turbulent quantities. The proposed intermittency transport equation can be considered as a blending of two models - Steelant and Dick (1996) and Cho and Chung (1992). The former was proposed for near-wall flows and was designed to reproduce the streamwise variation of the intermittency factor in the transition zone following Dhawan and Narasimha correlation (Dhawan and Narasimha, 1958) and the latter was proposed for free shear flows and was used to provide a realistic cross-stream variation of the intermittency profile. The new model was used to predict the T3 series experiments assembled by Savill (1993a, 1993b) including flows with different freestream turbulence intensities and two pressure-gradient cases. For all test cases good agreements between the computed results and the experimental data are observed.
... The intermittency (γ) transition model [64] solves one transport equation for intermittency (see Equation (11)), where the production term controls the length of transition and the dissipation term allows the boundary layer to re-laminarize by dissipating the intermittency fluctuations. The momentum thickness Reynolds number is algebraically computed using local variables [64]. ...
... The intermittency (γ) transition model [64] solves one transport equation for intermittency (see Equation (11)), where the production term controls the length of transition and the dissipation term allows the boundary layer to re-laminarize by dissipating the intermittency fluctuations. The momentum thickness Reynolds number is algebraically computed using local variables [64]. ...
The operational regime of Unmanned Aerial Vehicles (UAVs) is distinguished by the dominance of laminar flow and the flow field is characterized by the appearance of Laminar Separation Bubbles (LSBs). Ice accretion on the leading side of the airfoil leads to the formation of an Ice-induced Separation Bubble (ISB). These separation bubbles have a considerable influence on the pressure, heat flux, and shear stress distribution on the surface of airfoils and can affect the prediction of aerodynamic coefficients. Therefore, it is necessary to capture these separation bubbles in the numerical simulations. Previous studies have shown that these bubbles can be modeled successfully using the Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) but are computationally costly. Also, for numerical modeling of ice accretion, the flow field needs to be recomputed at specific intervals, thus making LES and DNS unsuitable for ice accretion simulations. Thus, it is necessary to come up with a Reynolds-Averaged Navier–Stokes (RANS) equation-based model that can predict the LSBs and ISBs as accurately as possible. Numerical studies were performed to assess the fidelity of various RANS turbulence models in predicting LSBs and ISBs. The findings are compared with the experimental and LES data available in the literature. The structure of these bubbles is only studied from a pressure coefficient perspective, so an attempt is made in these studies to explain it using the skin friction coefficient distribution. The results indicate the importance of the use of transition-based models when dealing with low-Reynolds-number applications that involve LSB. ISB can be predicted by conventional RANS models but are subjected to high levels of uncertainty. Possible recommendations were made with respect to turbulence models when dealing with flows involving LSBs and ISBs, especially for ice accretion simulations.
... Another popular approach is to use universal intermittency profile 'γ' due to Dhawan and Narasimha [3] defined as the fraction of time the flow becomes turbulent. Some more approaches such as Abu-Ghannam and Shaw [4], Mayle [5] and Suzen et al. [6,7] uses empirical correlations to determine the transition critical Reynolds number where the momentum thickness Reynolds number (Re θ ) at the boundary layer edge is determined and the turbulence model is activated when it exceeds the quantity obtained from the empirical correlation. Though simple to use in a 2D framework involving non-local operations such as search along body-normal grid direction or integration along external streamlines, these methods when coupled with RANS are powerful enough to provide significant improvements to engineering transition prediction. ...
... [10] model uses a transport equation for intermittency along with turbulent quantities evaluated using k-ε turbulence model. Suzen and Huang [6,7] proposed the transport equation for intermittency to blend the laminar and turbulent regions based on correlations, and coupled it with the SST k-ω turbulence model. Papp and Dash [11] used the compressibility corrected SSGZ k-ε turbulence model with algebraic transition model as well as a transport equation for intermittency. ...
Scope of present work covers implementation to validation of the Langtry-Menter two equation γ-Reθt Local Correlation based Transition Model (LCTM) in CERANS code for modeling subsonic to hypersonic flow transition. The LCTM is coupled with SST k-ω turbulence model. The governing equations of γ-Reθt model is discretized in finite volume framework similar to the RANS model and implicitized using the point Jacobi method. Transition correlations based on freestream as well as local turbulence intensity and critical momentum thickness Reynolds number were integrated with the model, and the code is validated for several standard transition test cases involving low subsonic to hypersonic high enthalpy flows covering a wide range of turbulent intensities.
... The terms P j , x are the rate of the turbulent kinetic energy production and the specific turbulence dissipation rate, respectively. r j , r x , and r x2 are Prandtl number-like parameters for the transport j and x: F 1 is a blending function that simplifies combining the standard j − e model and the Wilcox j − x model [42][43][44]. S represents the absolute value of the shear strain rate and b 1 , b 2 are the model constant. The term c is used in Equation (4) to reduce the rate of turbulence production inflows that are not fully turbulent, and it ranges between 0 to 1. ...
... Combining a c transport equation with the k-e turbulent model, Cho and Chung 7 developed the k-e-c model, which is suitable for simulating transition behaviors in free shear flows. To describe the intermittency behavior in both the streamwise and crosswise directions, Suzen and Huang 8 proposed a c equation that combines the advantages of Refs. 6 and 7. ...
Based on the original γ-Reθ transition model framework, in this work, an improved local correlation-based transition closure model is developed for high-speed flows. The local correlation between the vorticity Reynolds number and the momentum thickness Reynolds number obtained by compressible boundary-layer self-similar solutions, local compressibility correction including the pressure gradient parameter and momentum thickness Reynolds number, and local crossflow correlation are applied to improve the original γ-Reθ model for hypersonic transition predictions. The function Fonset1 used to control the transition onset and several relevant model parameters are also modified to make the improved model suitable for high-speed flow. The improved transition model is validated through several basic test cases under a wide range of flow conditions, including high-speed flat plates, sharp cones, double ramp, Hypersonic International Flight Research Experimentation, and complex hypersonic configuration X-33 vehicles. The numerical results show that the transition onset locations and the changes of heat transfer rate predicted by the present improved transition model are reasonably consistent with experimental results. The proposed model predicts the high-speed boundary layer transition behaviors induced by streamwise and crossflow instabilities with reasonable precision.
Computing the flow field under free convection in a cavity becomes particularly challenging for low-Prandtl-number (Pr) fluids typically encountered for liquid metals. The objective of the present study is to investigate the natural convection process in a differentially heated square cavity employing the transition shear stress transport (SST) model for the Prandtl number Pr 2 ½0:001; 0:1 and the Rayleigh number
Ra 2 ½104; 10 10. The mean flow field is visualized through streamlines, isotherms, non-dimensional velocity, and temperature profiles, turbu-
lence intensity, contours of intermittency ðcÞ times, the production of turbulent kinetic energy ðPjÞ, and distribution of skin friction coeffi-
cient and the Nusselt number (Nu). The transition SST model can capture the mean flow field and thermal transport over the entire
parametric regime successfully. An average Nusselt number ðNuÞ on the hot wall is found to scale with a certain power (n) of the Boussinesq
number (Bo), the product of Ra and Pr. The value of n is 0.18 for Ra up to 106 and 0.25 for higher Ra.
Future space transportation systems will heavily rely on predicting and understanding Boundary Layer Transition (BLT) during atmospheric entry, especially in the hypersonic phase. Several transition models compatible with RANS solvers have been proposed. However, the majority of them have been developed for low-speed flows, and attempts to extrapolate them to the hypersonic regime are documented in only a limited number of studies, specifically focusing on simplified geometries.This paper focuses on evaluating prediction capabilities for such models on complex 3D geometries int he hypersonic regime, using the International Boundary Layer Transition (BOLT) Flight Experiment as a test case.
In this paper, we present an overview of numerical simulation methods for the flow around typical underwater vehicles at high Reynolds numbers, which highlights the dominant flow structures in different regions of interest. This overview covers the forebody, midbody, stern, wake region, and appendages and summarizes flow phenomena, including laminar-to-turbulent transition, turbulent boundary layers, flow under the influence of curvatures, wake interactions, and all associated complex vortex structures. Furthermore, the current issues and challenges of capturing these flow structures are addressed. This overview provides a deep insight into the use of numerical simulation methods, including the Reynolds-averaged Navier–Stokes (RANS) method, large eddy simulation (LES) method, and the hybrid RANS/LES method, and evaluates their applicability in capturing detailed flow features.
The focus of the study was the validation of transition flow model which works with jet impingement applications. Reynolds averaged Navier Stokes (RANS) techniques, including a variation of transition options, such as γ−GEKO−k−ω, γ−SST−k−ω, transition SST and transition k−kl−ω, were employed to simulate the turbulent flow fields. ANSYS-Fluent 2022R2 was the tool used in the study and a constant surface heat flux on a flat plate was chosen for the test case. The flow characteristics and averaged Nusselt number prediction were investigated and compared with measurement data. The results show that the collapse of turbulence performed the flow became lamina-like in the transition region, 1 < r/D < 3, while the shape of velocity distribution within that region was parabolic profiles near a target wall. That means the relaminarization mechanism was captured by the transition SST model. Moreover, the thermal results demonstrated that the highest values of the Nusselt number prediction were located near the stagnation point and decreased monotonically within the wall jet regions. The predicted results from γ−SSTk−ω and transition SST models provided strong agreement with experimental data. Secondary peaks of the Nusselt number in the radial direction were also depicted by transition SST models, and these second peaks were still aligned on the ratio (1 ≤ r/D ≤ 3) which was not impacted by jet diameter variation. This range will be used in the next step of developing a prototype of a dehumidifying unit for use in archeological applications.
This paper summarises recent progress which has been made in evaluating by-pass transition models as part of a European Research Community On Flow Turbulence And Combustion (ERCOFTAC) Special Interest Group Project. In particular new results, from a variety of closure models, are presented for a wider range of Test Cases based on both experimental studies and Direct Numerical Simulations. It would appear that a Reynolds stress scheme offers the best predictive capability for 2D by-pass transition under high free-stream turbulence intensities and variable pressure gradient or Reynolds number conditions. Such a scheme also has the potential to handle both anisotropic and lower intensity free-stream turbulence effects. However present low-Re treatments need to be refined against DNS for transitional flow (so that a clearer distinction can be made between low-Re near-wall and low-Re transition region modelling) before additional curvature, heat transfer and leading edge separation effects can be considered.
A comprehensive and critical review of closure approximations for two-equation turbulence models has been made. Particular attention has focused on the scale-determining equation in an attempt to find the optimum choice of dependent variable and closure approximations. Using a combination of singular perturbation methods and numerical computations, this paper demonstrates that: (1) conventional κ-ε and κ-ω+2$/ formulations generally are inaccurate for boundary layers in adverse pressure gradient; (2) using 'wall functions' tends to mask the shortcomings of such models; and (3) a more suitable choice of dependent variables exists that is much more accurate for adverse pressure gradient. Based on the analysis, a two-equation turbulence model is postulated that is shown to be quite accurate for attached boundary layers in adverse pressure gradient, compressible boundary layers, and free shear flows.
Boundary layer measurements are presented through transition for six different free-stream turbulence levels and a complete range of adverse pressure gradients for attached laminar flow.
Measured intermittency distributions provide an excellent similarity basis for characterizing the transition process under all conditions tested when the Narasimha procedure for determining transition inception is used. This inception location procedure brings consistency to the data.
Velocity profiles and integral parameters are influenced by turbulence level and pressure gradient and do not provide a consistent basis. Under strong adverse pressure gradients transition occurs rapidly and the velocity profile has not fully responded before the completion of transition. The starting turbulent layer does not attain an equilibrium velocity profile.
A change in pressure gradient from zero to even a modest adverse level is accompanied by a severe reduction in transition length. Under diffusing conditions the physics of the transition process changes and the spot formation rate increases rapidly; instead of the “breakdown in sets” regime experienced in the absence of a pressure gradient, transition under strong adverse pressure gradients is more related to the amplification and subsequent instability of the Tollmien-Schlichting waves. Measurements reveal an exponential decrease in transition length with increasing adverse pressure gradient; a less severe exponential decrease is experienced with increasing turbulence level. Correlations of transition length are provided which facilitate its prediction in the form of suitable length parameters including spot formation rate.
Natural transition of boundary layers is investigated for a flat plate in a low-speed wind tunnel with free-stream turbulence intensities ranging from 0.3 to 5 per cent, and with pressure-gradient histories typical of turbomachinery blades without separation.
Empirical relationships are proposed for the prediction of the start and end of transition, as well as the development of the boundary layer during transition. These relations are based on the recent measurements made with a hot-wire anemometer, and augmented, mainly for the start of transition, by results of previously reported research.
Finally, these experimental relationships are used in conjunction with well established methods to predict the entire unseparated boundary layer. To utilize the prediction, all that is required is a knowledge of the free-stream turbulence level and the free-stream velocity distribution, which itself can be derived from potential flow theory.
The transition region is considered to be characterized by the intermittent appearance of turbulent spots, which grow as they move downstream until they finally merge into one another to form the turbulent boundary layer. The intermittency factor for arbitrary axisymmetric body with zero angle of attack has been derived in an expression which can be reduced to the form of universal intermittency distribution of Dhawan and Narasimha in the case of straight tube or flat plate. A key factor to control flow conditions in the transition zone appears to be the spot formation rate, which has been deduced from the available data of the extent of transition zone. It was found that the spot formation rate depends not only on the transition Reynolds number but also on the Mach number. A comparison of the deduced spot formation rate with the neutral stability curves indicated that the neutral stability curves can be used as a guide to relate the spot formation rate to the transitional Reynolds number. Calculations of the transitional heat-transfer rate on a sphere in supersonic flow agree well with the experimental results.
The present study considers the use of low-Reynolds number, single-point closures for transition prediction at high levels of free-stream turbulence. The work is focused on two differential Reynolds Stress Transport models, which are compared with the k - epsilon model of Launder and Sharma. Calculations are carried our for attached boundary layer flow on a flat plate equipped with a sharp lending edge at zero-pressure gradient and for various free-stream turbulence levels. Comparisons with results from a large eddy simulation reveal significant shortcomings in the modeling of the dissipation, with a large overprediction in the pretransitional boundary layer. The present results are in some cases in conflict with other results reported in the literature, and it is shown that the discrepancies can be ascribed to the implementation of the free-stream boundary conditions.
Measurements of boundary layer transition covering a wide range of
turbulence levels and adverse pressure gradients are reported. Under
high levels of free-stream turbulence (FST) and adverse pressure
gradient, the results show a pronounced subtransition. Using the
Narasimha procedure to determine transition inception gives a strong
degree of similarity in the observed streamwise variation of
intermittency through the transition region for all conditions. The
effects of FST on the velocity profile in the early stages of transition
are particularly strong. In the subtransition regime the entire velocity
profile appears to be affected. Under the adverse pressure gradients
typical of axial flow compressor operation, transition occurs much more
rapidly than had previously been appreciated.