Heat and mass transfer in a system of plane turbulent jets with diffusion combustion

We consider turbulent motion of premixed chemically active gases in an infinite system of plane turbulent jets in the presence of diffusive combustion. The proposed calculation method permits determining the distribution of all the parameters in the mixing zone, including the longitudinal pressure. Numerical examples of the calculation of hydrogen combustion in air are presented.The study of heat and mass transfer in jet flows presents major difficulties at the present time. Therefore all the existing methods for calculating jet flows with heat and mass transfer and chemical processes [1–5] are based on an extension of the known semiempirical theories of free turbulence to the more complex cases of flow with chemical reactions. The present study is no exception in this sense; it covers an investigation of the motion in an infinite system of plane turbulent jets with diffusive combustion.     

Estimate of the correlation between pressure pulsations and the divergence of the velocity in subsonic flows of variable density

In flows with variable density, the turbulence energy equation contains a large number of correlations, about which little is at present known [1]. One of the least studied is the correlation between the pressure and the divergence of the velocity. Usually, this correlation is ignored [2, 3]. The aim of the present paper is to estimate the pulsations of the divergence of the velocity and the correlation with the pressure pulsations in a subsonic turbulent flow with variable density. Three cases are considered: 1) mixing of gases having different densities, 2) diffusion combustion, 3) combustion of a homogeneous mixture. It is assumed that the Mach number is small, the Reynolds number large, and the coefficients of molecular diffusion and thermal diffusivity equal; external forces are absent.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 4–11, May–June, 1979.     

Investigation of turbulence modification in a non-reactive two-phase flow

In a two-phase flow the influence of a dispersed phase on the turbulence properties of a continuous phase, known as turbulence modification, is investigated. An experimental approach is discussed that is suitable for studying the decay of grid-generated turbulence in a vertically orientated wind tunnel with a cross-section large enough to avoid influences from walls. Phase Doppler anemometry is used to characterize both single and two-phase flow by measuring mean axial and radial velocity components, velocity fluctuations, turbulent kinetic energy, and integral time scales. By direct comparison of results from single- and two-phase flows, the feedback of the dispersed phase on the continuous phase can be isolated. The data is used to deduce a source term for particle-induced turbulence production appropriate for a numerical simulation of the flow, based on the Reynolds-averaged Navier-Stokes equations. Although of special importance for a detailed understanding of turbulent two-phase combustion, additional complexity introduced by evaporation and chemical reactions is avoided by using glass beads as dispersed phase.     

Limiting regimes of self-similar gas flows with account for finite chemical-reaction rate

One-dimensional unsteady flows of a combustible gas mixture with account for the finite chemical-reaction rate were studied in [1]. The conditions for self-similarity of such flows were indicated, mathematical formulation of the problem was given, and several numerical calculations were carried out.The authors pointed out the necessity for conducting additional studies, since they were not able to obtain numerically, by means of passages to the limit, self-sustaining detonation waves propagating with the Chapman-Jouguet (CJ) velocity.In this article we point out the reason why it was not possible to reach the CJ regime in [1], and a qualitative analysis is made, by means of the results of [2], of the system of equations describing the self-similar flows of a gas with finite chemical-reaction rate, and the passage to the limit is made to the self-sustaining CJ detonation waves in the presence of chemical reactions. It is also shown that the problem of unsteady flows of a combustible mixture of gases with finite chemical-reaction rate is analogous to the problem of the flow of a gas heated by radiation, examined in [3].In conclusion the authors wish to thank I. V. Nemchinov and A. G. Kulikovskii for discussions of this study.     

An Experimental Database for Benchmarking Simulations of Turbulent Premixed Reacting Flows: Lean Extinction Limits and Velocity Field Measurements in a Dump Combustor

This contribution is aimed at drawing the attention of the computational fluid dynamics community on the availability of an experimental database regarding turbulent lean premixed prevaporised (LPP) reacting flows stabilised behind a double symmetric, plane sudden expansion fed by two fully developed turbulent channel flows of air plus propane. This flow configuration can be thought of as a relevant benchmark for testing turbulence and/or combustion models aimed at helping for the design of reliable LPP combustion chambers. This database contains a large amount of raw and processed data regarding essentially the velocity field for one inert and three different reacting flows configurations. Additional pieces of information are available and concern the lean extinction properties and the wall static pressure evolution in the feeding channels. For the reacting flows, the presence of a large scale coherent motion is clearly visible in the velocity spectra and it is shown how a data processing based on the semi-deterministic approach that decomposes the velocity signal into the sum of its steady time average, its coherent fluctuations and its stochastic fluctuations can permit to evaluate their respective contribution to the total velocity fluctuations.     

Numerical simulation of expansion/compression effect on shock induced turbulent flow

The interaction of homogeneous and isotropic turbulence with a shock wave is observed by solving the Reynolds-averaged Navier–Stokes equations with the k–? turbulence model. All turbulent fluctuations are measured at the period of expansion in the turbulent field and during compression by the reflected shock on turbulent field, and it is observed that the longitudinal turbulent velocity fluctuation is enhanced more at the period of expansion due to incident shock wave movement far from the turbulent field. The amplification of the turbulent kinetic energy (TKE) level in the shock/turbulence interaction depends on the shock wave strength and the longitudinal velocity difference across the shock wave. On decreasing the longitudinal velocity difference across the shock, the turbulent kinetic energy (TKE) level is less amplified. The TKE level is amplified by the factor of 1.5–1.8 in the shock/turbulence interaction where the dissipation rate of TKE decreases in all cases of shock/turbulence interaction. After the shock/turbulence interaction, the turbulent dissipative-length scale is amplified slightly and the amplification of the length scales decreases when increasing the shock strength. To cite this article: M.A. Jinnah, K. Takayama, C. R. Mecanique 333 (2005).     

Experimental characterization of non-premixed turbulent jet propane flames

This paper reports an experimental study conducted on turbulent jet propane flames aiming at further understanding of turbulent structure in non-premixed slow-chemistry combustion systems. Measurements of mean and fluctuating velocity and temperature fields, mean concentration of major chemical species, correlation between velocity and temperature fluctuations, and dissipation of temperature fluctuations are reported in a turbulent round jet non-premixed propane flame, Re=20 400 and 37 600, issuing vertically in still air. The experimental conditions were designed to provide a complete definition of the upstream boundary conditions in the measurement domain for the purpose of validating computational models. The measured data depicts useful flow field information for describing turbulent non-premixed slow-chemistry flames. Velocity–temperature correlation measurements show turbulent heat fluxes tended to be restricted to the mixing layer where large temperature gradients occurred. Observations of non-gradient diffusion of heat at x/D=10 were verified. Temperature fluctuation dissipation, χ, showed the highest values in the shear layer, where the variance of temperature fluctuations was maximum and combustion occurred. The isotropy between the temperature dissipation in the radial and tangential directions was confirmed. By contrast, the observed anisotropy between axial and radial directions of dissipation suggests the influence of large structures in the entrainment shear layer on the production of temperature fluctuations in the flame region. The value of the normalized scalar dissipation at the stoichiometric mixture fraction surface, χ_st, was calculated, and ranges between 2 and 4 s⁻¹. The measured data were used to estimate the budgets in the balance equations for turbulent kinetic energy, Reynolds shear stresses, turbulent heat flux and temperature variance, quantifying the mechanisms involved in the generation of turbulence as well as in the transport of the temperature.     

Speckle optical measurement of a turbulent scalar field with high fluctuation amplitudes

A turbulent temperature field is produced in the gas flow downstream of a turbulence grid by passing the flow through a plane combustion front at the grid that serves as a flame holder. RMS values of the temperature fluctuations of up to 33 K are generated thereby. Properties of the turbulent scalar are measured with an optical speckle technique. The experimental results are compared with theoretical models described by Rotta (1972) and Driscoll and Kennedy (1985). From this comparison it is evident that, even at these high fluctuation amplitudes, the turbulent temperature field still behaves as a passive scalar.     

可压缩各向同性衰减湍流直接数值模拟研究

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性 和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等. 研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大 尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量(压缩)耗散率所占比率也显著增长. 标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高(p ≥ 5)时,纵向速度结构函数的扩展自相似性则不再成立. 对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的 间歇性要强于横向湍流脉动.     

Die Wirkung von Polymerzusätzen auf die Turbulenzstruktur in der ebenen Mischungsschicht zweier Ströme

The plane mixing layer formed between two parallel streams moving with different velocities is one of the simplest types of free turbulent boundary layers and has frequently been studied for Newtonian fluids. As a result of this and because of its good experimental accessibility this type of flow provides a good opportunity for obtaining information about the influence of drag reducing additives on the structure of free turbulence. This is all the more so because of the presence of a characteristic vortex structure which can be clearly distinguished from the overlying statistical fine turbulence. The turbulence field was investigated using an existent laser Doppler anemometer system that had been designed for space-time correlation measurements. This enabled measurements to be made of the mainstream velocity as well as of the longitudinal and transversal turbulent fluctuations and, after a simple modification, also of the Reynolds shear stresses and the cross correlation coefficients. The main result of the addition of 50 ppm of the polymer used (Separan AP30) was found to be an intensification of the Reynolds shear stresses. The resulting substantially more rapid increase (than in water) in the thickness of the shear layer can be explained theoretically; such behaviour has also been observed in free jets. On the other hand, the reduced thickness of the mixing layer in the initial region and the associated enhancement of the longitudinal fluctuations and damping of the transversal fluctuations indicate that the main shear flow induces a flow anisotropy by uncoiling and aligning the polymer molecules. The increase in the spreading angle suggests that the entrainment process at the edges of the mixing layer is intensified. This can be explained by the enhancement of the large energy carrying vortices in the turbulence spectrum. This is probably also the reason for the general increase in the correlation coefficients observed at all positions along the centreline of the flow field. However, a complete discussion of the energy transfer mechanism present here, in particular with inclusion of the fine turbulence responsible for dissipation, is only possible with the help of a detailed analysis of the vortex structure in the mixing layer. This is presented in a following paper. The relation between the degree of drag reduction and the intensity of the Reynolds shear stresses enables the direct influence of the rheological properties of the fluid on the turbulent momentum transfer to be clearly recognized.     

Effect of particles suspended in a fluid flow on the decay of isotropic turbulence

Dynamic equations have been obtained for the two-point double correlations of the fluctuation velocities of a fluid and the particles suspended in it at low volume concentrations of the solid phase. In the case of uniform isotropic turbulence these equations can be considerably simplified. The final period of decay of isotropic turbulence has been studied in detail. At this stage in the case of high-inertia particles the inhomogeneous-fluid turbulence is similar to the turbulence of a homogeneous fluid (without particles) in the sense that the presence of the particles affects only the fluctuation energy but leaves unchanged the spatial scales of turbulence and the spatial energy spectrum function. The suspended particles lead to exponential damping of the turbulent pulsations.Little theoretical information is available on the hydrodynamics of a suspension of fine particles in a turbulent liquid or gas. Research has been mainly confined to the behavior of the individual particles in a given turbulence field [1]. The problem of the turbulent motion of the mixture as a whole has been examined by Barenblatt [2], who derived the equations of motion of the mixture, using Kolmogorov's hypothesis to close them. Hinze [3] has also attempted to derive equations for turbulent pulsations of the mixture. However, as Murray showed [4], Hinze' s equations contradict Newton' s third law.The effect of suspended particles on the turbulence of a two-phase flow is governed by the noncorrespondence of the local velocities of the particles and the medium. The forces of resistance to the motion of the particles relative to the fluid lead to additional dissipation of fluctuation energy and decay of turbulence [2]. On the other hand, if the averaged velocities of particles and medium do not correspond, the suspended particles may also have a destabilizing effect [5, 6], causing energy transfer from the averaged to the pulsating motion. Below we shall consider the case where the averaged velocities of the two phases coincide, i.e., we shall deal only with the first of the two above-mentioned effects.The authors thank G.I. Barenblatt for his useful advice.     

Compressibility effects due to turbulent fluctuations

This paper deals with intrinsic effects of compressibility, i.e. with dilatation fluctuations in response to pressure fluctuations. Three different types of turbulent flows are considered in more detail: homogeneous turbulent shear flow, wall-bounded turbulent shear flow and shock/turbulence interaction. A survey of the present knowledge in this field, mainly based on DNS data, is given. Using the linear inviscid perturbation equations a direct link between fluctuations of dilatation and of velocity in the direction of mean shear is presented for homogeneous shear flow. This relation might form the basis for a more universal pressure-dilatation model. It is conjectured that the insignificance of intrinsic compressibility effects in wall-bounded supersonic shear flow is mainly due to the impermeability constraint of the wall. To this end, a linear stability analysis of supersonic channel flow along cooled, but permeable walls has been performed based on Coleman et al.'s [5] mean flow data. It shows an increase in the moduli of eigenfunctions related to compressibility, like pressure, and in moduli of quantities derived from eigenfunctions such as ‘pressure dilatation’ and squared dilatation. Although these results do not prove our hypothesis they provide hints in this direction. Shock/turbulence interaction is viewed as a source of compressibility. Former DNS data of Hannappel and Friedrich [10] for shock/isotropic turbulence interaction showing the effect of compressibility on the amplification of fluctuations are interpreted based on linear perturbation equations.     

Effect of turbulence of external flow on the turbulent boundary layer at a plate

In [1, 2] turbulence of the external flow was taken into account by specifying the turbulent energy at the external boundary of the boundary layer on integrating the energy-balance equation for the turbulence. In [3] a special correction that allowed the turbulence of the external flow to be taken into account was introduced in determining the mixture path. In [4, 5] the turbulent energy calculated from the energy-balance equation of the turbulence was added to the energy induced by turbulence of the external flow, the energy distribution of the induced turbulence being specified using an empirically selected function. In [6, 7] a method of taking into account the effect of turbulence of the external flow on a layer of mixing and a jet was proposed. In the present work, this method is applied to the boundary layer at a plate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 26–31, May–June, 1977.     

Calculation of principal characteristics of turbulent streams in a state of structural equilibrium

A review of articles on the study of turbulent streams having transverse displacement, in which a turbulent energy balance equation is used, is contained in [1]. Levin [2] proposed a certain development of Rotta's method [3] making it possible to determine the characteristics of the average flow and the radial distribution of pulsation magnitudes. However, in this article the scale of the turbulence (the quantityl) was given as an empirical function of the coordinates. At the same time it is clear that the distribution of the turbulence scale depends on the conditions of the problem. A special differential equation proposed in [4,5] describing the variation in time and space of the quantityl has the drawback that in deriving this equation it is necessary to invoke additional hypotheses which are difficult to test experimentally. In the present article, along with the velocity of the average flow, the pressure, and the pulsation magnitudes, the scale of the turbulence is considered as an important characteristic of the stream, determined by the reference system which consists of the Reynolds equations, continuity equations, and equations for the component of the Reynolds stress tensor. Rotta's approximate semiempirical relations and an experimental relation for the single-point correlation coefficient between the turbulent pulsations in velocity are used for closure of the system obtained. An approximate calculation is given for the principal average and pulsation characteristics of the flow for the region of the stream where the turbulence is in a state of structural equilibrium [6]. A comparison of the calculated and experimental data is presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 95–99, January–February, 1973.     

二次燃烧对底排装置尾部流场影响的数值模拟

为研究二次燃烧对底排尾部流场的影响,建立了底排装置尾部流场的化学非平衡流数学物理模型。其中二次燃烧模型采用10组分25步反应的H₂-CO燃烧模型,运用统一算法的思路编程求解二维轴对称方程组。数值模拟结果与实验结果较吻合。在此基础上,对尾部流场以及燃烧特性进行了数值预测, 结果表明:二次燃烧所释放的热能远大于排气本身的热能,对增压减阻的贡献可达78%。二次燃烧改变了尾部的温度分布规律,使温度峰值分布在两个回流区内。排气沿着两回流区间的狭缝流入剪切层发生燃烧。一部分混气回流入底部附近,其中氧气不充足,存在大量CO和少量H₂未直接反应。一部分混气沿着剪切层流入下游以及主回流区内,氧含量逐渐增多,H₂和CO被反应殆尽。结果可为进一步研究底排增压减阻提供参考。     

Stationary modes of combustion in a fine-scale turbulent stream

The majority of models of the turbulent combustion of gases are based mainly on intuitive concepts concerning the processes occurring in the flame. The characteristics of a turbulent flame are estimated from considerations of dimensionality and similarity. A detailed review of works on turbulent combustion is given in [1]. Problems on the calculation of the combustion rate in a turbulent stream as a proper value of the equations of heat and mass transfer and of the corresponding boundary conditions have recently been raised. Here too one must rest on assumptions of a semiempirical nature, which in large measure is connected with the inadequate level of development of turbulence theory. In the present work the equation of propagation of the zone of chemical reactions in the stream is averaged statistically by analogy with studies of turbulent flows. Correct averaging is possible at scales of hydrodynamic disturbances smaller than the flame thickness (fine-scale turbulence). The temperature pulsations are related with the size of the heat flux using the theory of mixing lengths. The main influence is specific to effects arising during averaging of the heat release function. Two stationary modes, distinguished by the normal propagation velocity ₁, are isolated within the framework of the Cauchy problem with a given initial mixture temperature and zero heat flux in the burned gas. A heat conduction mode occurs with a stream velocity > ₁ and an induction mode with < ₁. An expression is found for ₁ which reflects the principal effects in the flame and which in the limit coincides with the equation of Zel'dovich and Frank-Kamenetskii for a laminar flame. In those cases when the distorting effect of the heat release function is small, the turbulence affects the combustion rate through mechanisms of intensification of transport processes.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 118–124, September–October, 1973.     

Events of High Polymer Activity in Drag Reducing Flows

The mechanism of drag reduction in turbulent flows due to polymers has been investigated with help of a direct numerical simulation. In particular, we consider the interaction between turbulent velocity fluctuations and polymers in terms of elastic energy that can be stored in the polymer. To this end all the terms of the elastic energy budget have been computed. The most interesting term is the production of elastic energy due to turbulent fluctuations, because it describes the interaction between polymers and turbulence. Although this term appears to be small in the average, it turns out that it can reach very large values instantaneously and intermittently, and the energy transfer from polymer to turbulence is located in very well defined areas inside the channel. This implies that locally there is a strong interaction between the polymer and the turbulent flow structure, and this strong interaction is mostly seen in areas of high velocity fluctuations.     

Turbulence,vortex and external explosion induced by venting

The process of explosion venting to air in a cylindrical vent vessel connected to a duct, filling with a stoichiometric methane-oxygen gas mixture, was simulated numerically by using a colocated grid SIMPLE scheme based on k-epsilon turbulent model and Eddydissipation combustion model. The characteristics of the combustible cloud, flame and pressure distribution in the external flow field during venting were analyzed in terms of the predicted results. The results show that the external explosion is generated due to violent turbulent combustion in the high pressure region within the external combustible cloud ignited by a jet flame. And the turbulence and vortex in the external flow field were also discussed in detail. After the jet flame penetrating into the external combustible cloud, the turbulent intensity is greater in the regions with greater average kinetic energy gradient, rather than in the flame front ; and the vortex in the external flow field is generated primarily due to the baroclinic effect, which is greater in the regions where the pressure and density gradients are nearly perpendicular.     

A pore scale study on turbulent combustion in porous media

This paper presents pore scale simulation of turbulent combustion of air/methane mixture in porous media to investigate the effects of multidimensionality and turbulence on the flame within the pores of porous media. In order to investigate combustion in the pores of porous medium, a simple but often used porous medium consisting of a staggered arrangement of square cylinders is considered in the present study. Results of turbulent kinetic energy, turbulent viscosity ratio, temperature, flame speed, convective heat transfer and thermal conductivity are presented and compared for laminar and turbulent simulations. It is shown that the turbulent kinetic energy increases from the inlet of burner, because of turbulence created by the solid matrix with a sudden jump or reduction at the flame front due to increase in temperature and velocity. Also, the pore scale simulation revealed that the laminarization of flow occurs after flame front in the combustion zone and turbulence effects are important mainly in the preheat zone. It is shown that turbulence enhances the diffusion processes in the preheat zone, but it is not enough to affect the maximum flame speed, temperature distribution and convective heat transfer in the porous burner. The dimensionless parameters associated with the Borghi–Peters diagram of turbulent combustion have been analyzed for the case of combustion in porous media and it is found that the combustion in the porous burner considered in the present study concerns the range of well stirred reactor very close to the laminar flame region.