5 results
The formulation of the RANS equations for supersonic and hypersonic turbulent flows
- H. Zhang, T.J. Craft, H. Iacovides
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- Journal:
- The Aeronautical Journal / Volume 125 / Issue 1285 / March 2021
- Published online by Cambridge University Press:
- 12 October 2020, pp. 525-555
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Accurate prediction of supersonic and hypersonic turbulent flows is essential to the design of high-speed aerospace vehicles. Such flows are mainly predicted using the Reynolds-Averaged Navier–Stokes (RANS) approach in general, and in particular turbulence models using the effective viscosity approximation. Several terms involving the turbulent kinetic energy (k) appear explicitly in the RANS equations through the modelling of the Reynolds stresses in such approach, and similar terms appear in the mean total energy equation. Some of these terms are often ignored in low, or even supersonic, speed simulations with zero-equation models, as well as some one- or two-equation models. The omission of these terms may not be appropriate under hypersonic conditions. Nevertheless, this is a widespread practice, even for very high-speed turbulent flow simulations, because many software packages still make such approximations. To quantify the impact of ignoring these terms in the RANS equations, two linear two-equation models and one non-linear two-equation model are applied to the computation of five supersonic and hypersonic benchmark cases, one 2D zero-pressure gradient hypersonic flat plate case and four shock wave boundary layer interaction (SWBLI) cases. The surface friction coefficients and velocity profiles predicted with different combinations of the turbulent kinetic energy terms present in the transport equations show little sensitivity to the presence of these terms in the zero-pressure gradient case. In the SWBLI cases, however, comparisons show that inclusion of k in the mean flow equations can have a strong effect on the prediction of flow separation. Therefore, it is highly recommended to include all the turbulent kinetic energy terms in the mean flow equations when dealing with simulations of supersonic and hypersonic turbulent flows, especially for flows with SWBLIs. As a further consequence, since k may not be obtained explicitly in zero-equation, or certain one-equation, models, it is debatable whether these models are suitable for simulations of supersonic and hypersonic turbulent flows with SWBLIs.
Computational modelling of the flow and heat transfer in dimpled channels
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- K. Abo Amsha, T.J. Craft, H. Iacovides
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- Journal:
- The Aeronautical Journal / Volume 121 / Issue 1242 / August 2017
- Published online by Cambridge University Press:
- 17 July 2017, pp. 1066-1086
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The flow and heat transfer characteristics over a single dimple and an array of staggered dimples have been investigated using the Reynolds Averaged Navier-Stokes (RANS) approach. The objective is to determine how reliably RANS models can predict this type of complex cooling flows. Three classes of low-Reynolds number RANS models have been employed to represent the turbulence. These included a linear Eddy Viscosity Model (EVM), a Non-Linear Model (NLEVM) and a Reynolds Stress transport Model (RSM). Variants of the k-ε model have been used to represent the first two categories. Steady and time-dependent simulations have been carried out at a bulk Reynolds number of around 5,000 with dimple print diameter to channel height ratios of D/H = 1.0, 2.0 and ratios of dimple depth to channel height of δ/H = 0.2, 0.4. The linear EVM and the RSM tested both produce symmetric circulations in the dimples, while the NLEVM produces an asymmetric pattern. The mean velocity profiles predicted numerically are generally in good agreement with the data. The main flow characteristics are reproduced by the RANS models, but some predictive deviations from available data point to the need for further investigations. All models report an overall enhancement in heat transfer levels when using dimples in comparison to those of a plane channel.
3 - Closure Modelling Near the Two-Component Limit
- Edited by B. E. Launder, University of Manchester Institute of Science and Technology, N. D. Sandham, University of Southampton
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- Book:
- Closure Strategies for Turbulent and Transitional Flows
- Published online:
- 06 July 2010
- Print publication:
- 21 February 2002, pp 102-126
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Summary
Introduction
Most widely-used turbulence models have been developed and tested with reference to flows near local equilibrium, where there are only moderate levels of Reynolds stress anisotropy. The present contribution considers the development of models which are designed to give the correct behaviour in much more extreme situations, where the turbulence approaches a 2-component state.
To illustrate the type of flow situation to be considered, Figure 1 illustrates the flow in the vicinity of a wall. While all turbulent velocity components must vanish at the wall, the normal fluctuations, v, must vanish more rapidly since by continuity ∂v/∂y must always be zero there (as ∂u/∂x and ∂w/∂z both vanish), Figure 2. A similar two-component structure arises close to the free surface of a liquid flow where again fluctuating velocities normal to the free surface become negligible compared with fluctuations lying in the plane of the free surface. Clearly, the turbulence structure in such a flow will be very different from that found in free flows, where the stress anisotropy is much smaller. Consequently, it might be expected that simple models developed and tuned for the latter flows are unlikely to give good predictions in near-wall or free-surface regions, or other flows which are close to the 2-component limit.
The importance of explicitly respecting this two-component limit in turbulence modelling originated from two papers from the 1970s. First, a short note by Schumann (1977) advocated that modelling proposals should make it impossible for unrealizable values of the turbulence variables to be generated (such as negative values for the mean square velocity fluctuations in any direction). Shortly thereafter, Lumley (1978) remarked that if such realizability was to be ensured one needed to focus on the behaviour of the model at the moment when one of the velocity components had just fallen to zero. When this two-component state has been reached one must ensure that, for the normal stress that has fallen to zero, its rate of change also vanishes. That is essential to prevent the stress field achieving unrealizable values at the next instant of time.
Shih and Lumley (1985) were the first to apply realizability constraints to the modelling of the pressure correlation terms in both the Reynolds stress and scalar flux transport equations.
11 - Modelling of Separating and Impinging Flows
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- By T.J. Craft
- Edited by B. E. Launder, University of Manchester Institute of Science and Technology, N. D. Sandham, University of Southampton
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- Book:
- Closure Strategies for Turbulent and Transitional Flows
- Published online:
- 06 July 2010
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- 21 February 2002, pp 341-360
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Summary
Introduction
Flows involving separation, reattachment and impingement occur widely in many diverse engineering applications. A number of cooling and drying processes rely on the high heat transfer rates that can be obtained by impinging fluid onto a solid surface. Separation and reattachment are, of course, found in numerous situations, including external aerodynamics, flow over obstacles and internal flow through ducts and pipes with rapidly varying cross-section or flow direction. Many of these internal flows are also associated with heat transfer, such as internal cooling passages for gas-turbine blades.
Since heat transfer rates are predominantly determined by the flow behaviour in the immediate vicinity of the wall, it is often necessary to employ low-Reynolds-number turbulence models, which can adequately resolve the near-wall region, when computing applications involving wall heating or cooling. However, the turbulence mechanisms near reattachment or impingement zones are significantly different from those found in simple shear flows where most turbulence models have been developed. In particular, as will be seen, the popular ϵ based models are often found to predict extremely large lengthscales in such flows, leading to the prediction of excessive heat transfer rates and the necessity of including additional modelling terms to correct for the defect. Furthermore, the irrotational straining found in impinging flows exposes a number of weaknesses in both eddy-viscosity based models and in widely-used stress transport closures.
As an example of the problems encountered in computing impinging flows, Figure 1 shows the predicted and measured Nusselt number, plotted against radial distance from the stagnation point, in an axisymmetric impinging jet flow studied experimentally by Baughn and Shimizu (1989) and Cooper et al. (1992). The jet issues from a long length of pipe, at a Reynolds number of 23000, and impinges perpendicularly onto a flat plate at a distance of 2 jet diameters from the pipe exit. The flow has been computed using a zonal modelling approach, with a high-Reynolds-number stress transport scheme in the fully turbulent region, and the Launder–Sharma k-ϵ model in the near-wall viscosity-affected region. Without additional modifications, it can be seen that, whilst the predictions are in agreement with the data at large radial distances (where the flow becomes a radial wall jet), the model fails, fairly spectacularly, in the stagnation zone, overpredicting the Nusselt number by a factor of four or more.
The following sections consider the problems encountered in the modelling of impinging and reattaching flows, including a discussion of some of the different solutions proposed, and example applications.
14 - Application of TCL Modelling to Stratified Flows
- Edited by B. E. Launder, University of Manchester Institute of Science and Technology, N. D. Sandham, University of Southampton
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- Book:
- Closure Strategies for Turbulent and Transitional Flows
- Published online:
- 06 July 2010
- Print publication:
- 21 February 2002, pp 407-423
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Summary
Introduction
Chapter [3] has provided the rationale and the associated analysis for replacing the Basic Model of the pressure-strain process in second-moment closure by a more widely applicable approach – namely one satisfying the two-component limit (TCL). The present chapter will show that extending that model to include flow problems where gravitational effects are important also brings clear benefits in terms of accuracy and, sometimes, reductions in computing times, too.
However, not all closure problems in stably-stratified flows can be resolved merely by ensuring that the non-dispersive pressure-containing correlations satisfy the two-component limit. If generation by mean shear is effectively obliterated by the sink associated with the stable stratification, the computed behaviour of the second moments becomes particularly sensitive to secondmoment transport processes. While convective transport is, of course, handled exactly at this closure level, the same is not true of diffusive transport. Usually a very simple gradient-diffusion model is adopted for these processes. Such a practice, however, is motivated by the desire to adopt a cheap and stable approximation for a process that is frequently of little importance. However, transport can be of great importance in strongly inhomogeneous, stably-stratified flow – so something better must be provided.
Section 2 focuses on modelling the extra pressure-containing correlations arising from buoyancy and provides a comparison of computational results from implementing this model both with experimental data and, where available, with the Basic Model. Then Section 3 goes on to consider a case of a stably-stratified mixing layer where a partial third-moment treatment is required. The analysis is first developed before comparisons with experiments are discussed.
Closure Modelling for Stratified Flow
The Second-Moment Equations
The equation set (2.1)–(2.4) is, of course, unclosed, for the processes denoted ϕ, d and ϵ (representing the non-diffusive action of fluctuating pressure, diffusion and dissipation) all require approximation. In this section, we focus especially on the modelling of ϕij and ϕiθ for, in the flows to be considered, these are the vital processes to be approximated. As a preliminary, however, the following paragraphs indicate briefly the practices adopted for the dissipation and diffusion processes.