Showing papers in "Flow Turbulence and Combustion in 1999"

Subgrid-scale stress modelling based on the square of the velocity gradient tensor

Abstract: A new subgrid scale model is proposed for Large Eddy Simulations in complex geometries. This model which is based on the square of the velocity gradient tensor accounts for the effects of both the strain and the rotation rate of the smallest resolved turbulent fluctuations. Moreover it recovers the proper y 3 near-wall scaling for the eddy viscosity without requiring dynamic procedure. It is also shown from a periodic turbulent pipe flow computation that the model can handle transition.

Progress in the use of non-linear two-equation models in the computation of convective heat-transfer in impinging and separated flows

Abstract: The paper considers the application of the Craft et al. [6]non-linear eddy-viscosity model to separating and impinging flows. The original formulation was found to lead to numerical instabilities when applied to flow separating from a sharp corner. An alternative formulation for the variation of the turbulent viscosity parameterc μ with strain rate is proposed which, together with a proposed improvement in the implementation of the non-linear model, removes this weakness. It does, however, lead to worse predictions in an impinging jet, and a further modification in the expression for c μ is proposed, which both retains the stability enhancements and improves the prediction of the stagnating flow. The Yap [24] algebraic length-scale correction term, included in the original model, is replaced with a differential form, developed from that proposed by Iacovides and Raisee [10]. This removes the need to prescribe the wall-distance, and is shown to lead to superior heat-transfer predictions in both an abrupt pipe flow and the axisymmetric impinging jet. One predictive weakness still, however, remains. The proposed model, in common with other near-wall models tested for the abrupt pipe expansion, returns a stronger dependence of Nusselt number on the Reynolds number than that indicated by the experimental data.

Effects of the similarity model in finite-difference LES of isotropic turbulence using a Lagrangian dynamic mixed model

Abstract: A Lagrangian dynamic formulation of the mixed similarity subgrid (SGS) model for large-eddy simulation (LES) of turbulence is proposed. In this model, averaging is performed over fluid trajectories, which makes the model applicable to complex flows without directions of statistical homogeneity. An alternative version based on a Taylor series expansion (nonlinear mixed model) is also examined. The Lagrangian models are implemented in a finite difference code and tested in forced and decaying isotropic turbulence. As comparison, the dynamic Smagorinsky model and volume-averaged formulations of the mixed models are also tested. Good results are obtained, except in the case of low-resolution LES (323) of decaying turbulence, where the similarity coefficient becomes negative due to the fact that the test-filter scale exceeds the integral scale of turbulence. At a higher resolution (643), the dynamic similarity coefficient is positive and good agreement is found between predicted and measured kinetic energy evolution. Compared to the eddy viscosity term, the similarity or the nonlinear terms contribute significantly to both SGS dissipation of kinetic energy and SGS force. In order to dynamically test the accuracy of the modeling, the error incurred in satisfying the Germano identity is evaluated. It is found that the dynamic Smagorinksy model generates a very large error, only 3% lower than the worst-case scenario without model. Addition of the similarity or nonlinear term decreases the error by up to about 50%, confirming that it represents a more realistic parameterization than the Smagorinsky model alone.

Studies on Lifted Jet Flames in Coflow: The Stabilization Mechanism in the Near- and Far-Fields

Abstract: This paper presents the results of a parametric study concerning the phenomenon of liftoff of a nonpremixed jet flame. The dependence of liftoff height on jet exit velocity and coflow velocity is described. It is shown that lifted flames become less sensitive to jet exit velocity as the stabilization point recedes from the burner exit. The results reveal that in cases of extreme liftoff height, increases in jet exit velocity with a constant coflow cause some ethylene flames to stabilize closer to the burner. The success of current theories on lifted flame stabilization in comparison to the experimental results of this study are assessed. The existence of multiple regimes for flame stabilization, incorporating aspects of both premixed and nonpremixed combustion, is proposed.

Symmetries, Invariance and Scaling-Laws in Inhomogeneous Turbulent Shear Flows

Abstract: An approach to derive turbulent scaling laws based on symmetry analysis is presented It unifies a large set of scaling laws for the mean velocity of stationary parallel turbulent shear flows The approach is derived from the Reynolds averaged Navier–Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations For the plane case the results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a Couette flow and in the centre of a rotating channel flow, and a new exponential mean velocity profile that is found in the mid-wake region of high Reynolds number flat-plate boundary layers The algebraic scaling law is confirmed in both the centre and the near wall regions in both experimental and DNS data of turbulent channel flows For a non-rotating and a moderately rotating pipe about its axis an algebraic law was found for the axial and the azimuthal velocity near the pipe-axis with both laws having equal scaling exponents In case of a rapidly rotating pipe, a new logarithmic scaling law for the axial velocity is developed The key elements of the entire analysis are two scaling symmetries and Galilean invariance Combining the scaling symmetries leads to the variety of different scaling laws Galilean invariance is crucial for all of them It has been demonstrated that two-equation models such as the k–∈ model are not consistent with most of the new turbulent scaling laws

Application of PDF modeling to swirling and nonswirling turbulent jets

Abstract: The turbulence modeling in probability density function (PDF) methods is studied through applications to turbulent swirling and nonswirling co-axial jets and to the temporal shear layer. The PDF models are formulated at the level of either the joint PDF of velocity and turbulent frequency or the joint PDF of velocity, wave vector, and turbulent frequency. The methodology of wave vector models (WVMs) is based on an exact representation of rapidly distorted homogeneous turbulence, and several models are constructed in a previous paper [1]. A revision to a previously presented conditional-mean turbulent frequency model [2] is constructed to improve the numerical implementation of the model for inhomogeneous turbulent flows. A pressure transport model is also implemented in conjunction with several velocity models. The complete model yields good comparisons with available experimental data for a low swirl case. The individual models are also assessed in terms of their significance to an accurate solution of the co-axial jets, and a comparison is made to a similar assessment for the temporal shear layer. The crucial factor in determining the quality of the co-axial jet simulations is demonstrated to be the proper specification of a parameter ratio in the modeled source of turbulent frequency. The parameter specification is also shown to be significant in the temporal shear layer.

Predicting Buoyant Shear Flows Using Anisotropic Dissipation Rate Models

Abstract: This paper examines the modeling of two-dimensional homogeneous stratified turbulent shear flows using the Reynolds-stress and Reynolds-heat-flux equations. Several closure models have been investigated-, the emphasis is placed on assessing the effect of modeling the dissipation rate tensor in the Reynolds-stress equation. Three different approaches are considered: one is an isotropic approach while the other two are anisotropic approaches. The isotropic approach is based on Kolmogorov's hypothesis and a dissipation rate equation modified to account for vortex stretching. One of the anisotropic approaches is based on an algebraic representation of the dissipation rate tensor, while another relies on solving a modeled transport equation for this tensor. In addition, within the former anisotropic approach, two different algebraic representations are examined one is a function of the Reynolds-stress anisotropy tensor, and the other is a function of' the mean velocity gradients. The performance of these closure models is evaluated against experimental and direct numerical simulation data of pure shear flows. pure buoyant flows and buoyant shear flows. Calculations have been carried out over a range of Richardson numbers (Ri) and two different Prandtl numbers (Pr); thus the effect of Pr on the development of counter-gradient heat flux in a stratified shear flow can be assessed. At low Ri, the isotropic model performs well in the predictions of stratified shear flows; however, its performance deteriorates as Ri increases. At high Ri, the transport equation model for the dissipation rate tensor gives the best result. Furthermore, the results also lend credence to the algebraic dissipation rate model based on the Reynolds stress anisotropy tensor. Finally, it is found that Pr has an effect on the development of counter-gradient heat flux. The calculations show that, under the action of shear, counter-gradient heat flux does not occur even at Ri = 1 in an air flow.

Physical Eddy Recovery through Bi-Orthogonal Decomposition in an Acoustically Forced Plane Jet

Abstract: Phase-locked X-probe hot-wire measurements were made in the near field of an acous-tically forced plane jet at a Reynolds number of 5600. They revealed leapfrog pairings during which the trailing eddy's convection velocity grew up to 1.2 times the exit velocity. Two-dimensional bi-orthogonal decomposition of the velocity field yielded spatial (topos) and temporal (chronos) eigenmodes which were compared with the afore-mentioned eddies. It appeared that at least five two-dimensional eigenmodes were required for a satisfactory reconstruction. Besides, it was shown that as expected, in such spatially evolving flows, eigenmodes depended on the domain of the measurements. Further, one-dimensional decomposition showed the possibility of eddy detection in a coherent structure education scheme as well as the relevance of bi-orthogonal entropy in the description of flow organization.

Effects of small- and large-scale structures in a piloted jet diffusion flame

Abstract: Laser Doppler Anemometry (LDA) and Planar Laser-Induced Fluorescence (PLIF) measurements have been performed in a turbulent nonpremixed jet flame. One of the features of this configuration is a central co-axial fuel jet surrounded by a turbulent annular air flow. The whole is placed within a low-speed coflowing air stream. This three-flow system with turbulent primary air differs from flow systems used for nonpremixed jet flames reported in the literature and is very useful for obtaining information on the mixing process between fuel and primary air. Next to the characterization of the velocity field, special attention has been paid to the conditional seeding of the central fuel jet and of the annular air flow. Together with visualizations of the OH radical, an important combustion intermediate which is formed during combustion, and the NO radical, which is seeded to the central jet flow, the resulting statistics reveal the properties of small- and large-scale structures in the flame.

Localisation of Large Scale Structures in a Supersonic Mixing Layer: A New Method and First Analysis

Abstract: The space-time description of the organised structures in a supersonic mixing layer with a convective Mach number of 0.6 is given. Fourier analysis gives some evidence of the existence of large scales nearly periodic in time, but gives only global information on length and velocity scales. A new method based on the wavelet transform is then proposed to perform a space-time analysis localised in time. It is used to detect and to analyse such structures, in particular to determine their convection velocity. Characteristic time and length scales are given and compared with the scales deduced from the spectral analysis. The results are used to extract the contribution of the large scales to the turbulence signal. The flow under examination has a convective Mach number of 0.6. Therefore, in contrast with subsonic mixing layers, there are probably significant three-dimensional effects. Results on spacing between large eddies are discussed in terms of merging processes and of three-dimensional effects. A conclusion is that diffusion and/or entrainment are modified rather than the type and frequency of merging.

Comparison of Experimental and Numerical Investigation on Local and Global Heat Transfer in Turbulent Square Channel Flow with Roughness Elements in the Form of V-Shaped Broken Ribs

Abstract: Local and global heat transfer in turbulent square channel flow with roughness elements in the form of V-shaped broken ribs attached at two opposite walls has been investigated experimentally and numerically for the first time. The results of a high resolution (0.063 by 0.063 mm2) ammonia absorption measurement technique allows a detailed description of the local heat (mass) transfer distribution. These results can be used as a reference to evaluate turbulence heat transfer models. The local heat transfer distributions are compared with numerical results of the well established Low Reynolds Number (LRN) k–e model of Launder and Sharma and a new version of this model category for near wall flow by Lien and Leschziner. Both models predict qualitative correct local Nusselt number distributions for the rough and smooth walls. The Lien and Leschziner model gives better quantitative agreement with experiment than the Launder and Sharma model although still some weaknesses remain. For increased local accuracy the adoption of higher order turbulence models with special regard to near wall effects will be necessary.

Calculation of the Flow around a High-Pressure Turbine Blade with Cooling-Jet Injection from Slots at the Leading Edge

Abstract: A fully vectorised, basically three-dimensional finite-volume multi-block method for flows with complex boundaries is applied in a stripped-down two-dimensional version for the investigation of the flow field in the leading-edge region of a high-pressure turbine blade with slot cooling-jet injection. The calculation results are compared with experiments and the numerical results of other investigators. The present method yields excellent agreement with the experiments for the isentropic Mach number distributions on the blade surface. All numerical results for the velocity field were found to be in very good agreement with each other and with experiments on the suction side, while the agreement is not as good on the pressure side.

On the stability of a laminar wall jet with heat transfer

Abstract: The hydrodynamic stability of a low speed, plane, non-isothermal laminar wall jet at a constant temperature boundary condition was investigated theoretically and experimentally. The mean velocity and temperature profiles used in the stability analysis were obtained by implementing the Illingworth–Stewartson transformation that allows one to extend the classical Glauert solution to a thermally non-uniform flow. The stability calculations showed that the two unstable eigenmodes coexisting at moderate Reynolds numbers are significantly affected by the heat transfer. Heating is destabilizing the flow while cooling is stabilizing it. However, the large-scale instabilities associated with the inflection point of the velocity profile still amplify in spite of the high level of the stabilizing temperature difference. The calculated stability characteristics of the wall jet with heat transfer were compared with experimental data. The comparison showed excellent agreement for small amplitudes of the imposed perturbations. The agreement is less good for the phase velocities of the sub-harmonic wave and this is attributed to experimental difficulties and to nonlinear effects.

On the Electric Potential Induced by a Homogeneous Magnetic Field in a Turbulent Pipe Flow

Abstract: In this paper we study a turbulent pipe flow of a weakly electrical conducting fluid subjected to a homogeneous magnetic field which is applied perpendicular to the flow. This configuration forms the basis of a so-called electromagnetic induction flow meter. When the Hartmann number is small so that modification of flow by the Lorenz force can be neglected, the influence of the magnetic field results only in a spatially and temporally varying electric potential. The magnitude of the potential difference across the pipe is then proportional to the flow rate and this constitutes the principle of the flow meter. In this study the flow and electric potential are computed with help of a numerical flow simulation called Large-Eddy Simulation (LES) to which we have added an equation for the electrical potential. The results of the LES have been compared with experiments in which the electric potential is measured as a function of time at several positions on the circumference of the pipe. Both the experimental and numerical results for the mean potential at the pipe wall agree very well with an exact solution that can be obtained in this particular case of a homogeneous magnetic field. Furthermore, it is found that fluctuations in the electric potential due to the turbulence, are small compared to the velocity fluctuations. Based on the results we conclude that electrical-magnetic effects in pipe flow can be accurately computed with LES.

Loss reduction by means of two-dimensional roughness elements on the suction surface of a linear turbine rotor cascade

Abstract: This paper reports the results of experimental investigations carried out to reduce pressure losses by means of two-dimensional roughness elements (in the form of stainless steel tubes of different diameters). The roughness elements are fixed at various axial stations on the suction surface of 120° turning, 175 mm chord, impulse turbine rotor blades. Flow measurements are carried out at the exit of the cascade at five axial stations, using a five-hole probe operating in non-nulling mode. In addition, the blade surface static pressure distribution is measured. The data from the five-hole probe measurements are used to calculate pressure, velocity and flow angle distributions at the cascade exit and these results are used to calculate mass averaged values and integral parameters such as wake half-width, loss coefficient, etc. The static pressure distribution is altered very little except near the roughness element. The lift coefficient remains almost constant for all configurations and the drag coefficient is reduced for some configurations. The non-dimensional total pressure defects in the wake for all configurations followed Gaussian distribution. A two-dimensional roughness element of 0.6 mm diameter placed at 0.65 chord on the suction surface showed an appreciable reduction in pressure losses.

Solidification or melting initiation over a limited portion of an edge in a plate

Abstract: This paper proposes a method for obtaining short-time analytical solutions to problems in pure heat conduction, and heat conduction with phase change. The method employs the notion of ‘fictitious initial temperatures’ in some fictitious extensions of the original phase region. Analytical results obtained in the case of a heat conduction problem in a rectangular plate are presented first and compared with numerical solutions. This analytical solution is also required later in the determination of liquid temperature in the phase change problem. The method is then extended to a two-phase solidification problem in which solidification starts over a limited portion of one of the vertical edges of the rectangular plate. The freezing front in this case consists of spread along the vertical edge and growth towards the interior. The spread along the edge can have asymptotic behaviour not commonly found. The method is applicable to other geometries, e.g. inside and outside of a long cylinder, a three-dimensional slab, etc.

The Influence of a Fracture in a Rectangular Dam on the Pressure Gradient and the Phreatic Surface

Abstract: The shape of the phreatic surface inside a non-homogeneous dam is a unique function of hydraulic conductivity. Consequently, monitoring the phreatic surface can reveal possible deterioration of the inner part of the dam. Two-dimensional flow through an idealized dam with an artificial fracture is studied both theoretically and experimentally in a Hele–Shaw cell. The theoretical solution is a generalization of Baiocchi's solution. The results show that the method for identifying a possible imperfection in a dam works better for a wide homogeneous dam than for a rock fill dam with a narrow core.