Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 2. Flows with heat transfer and combustion

The objective of this part of the paper is to summarize the information concerning the authors' works in the field of simulation of two-phase gas-particle turbulent flows with heat transfer and combustion. A kinetic equation had been derived for the probability density function (PDF) of the particle velocity, temperature, and mass distributions in turbulent flows. This PDF equation is used for the construction of the governing conservation equations of mass, momentum, and heat transfer in the dispersed particle phase.The numerical scheme incorporates two-phase fluid dynamics, convective and radiative heat transfer, and combustion. The proposed models have been applied to the calculation of various particle-laden turbulent flows in jets, combustion and gasification chambers, and furnaces.     

Nonlinear stability of two-phase jets

The effect of solid particles on the flow stability and secondary regime branching in plane submerged jets is studied. The presence of the particles has an important influence on the macrostructure and microstructure of the jet flows, modifying the rate of turbulent momentum, heat and mass transfer [1,2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 50–55, May–June, 1985.The authors are grateful to V. N. Shtern for useful comments.     

Motion and heat and mass transfer in a disperse admixture in turbulent nonisothermal jets of a gas and a low-temperature plasma

The motion and heat and mass transfer of particles of a disperse admixture in nonisothermal jets of a gas and a low-temperature plasma are simulated with allowance for the migration mechanism of particle motion actuated by the turbophoresis force and the influence of turbulent fluctuations of the jet flow velocity on heat and mass transfer of the particle. The temperature distribution inside the particle at each time step is found by solving the equation of unsteady heat conduction. The laws of scattering of the admixture and the laws of melting and evaporation of an individual particle are studied, depending on the injection velocity and on the method of particle insertion into the jet flow. The calculated results are compared with data obtained with ignored influence of turbulent fluctuations on the motion and heat and mass transfer of the disperse phase. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 95–108, May–June, 2008.     

湍流冲击射流流动与传热的数值研究进展

湍流冲击射流由于其冲击表面时具有很高的局部传热率和冲击力,被广泛应用于如表面的加热、电子元件的冷却、纸张的干燥和材料的切割等工程应用和工业过程中.由于其流动的复杂性,也常被作为一种理想的测试实例来评价湍流模型的性能.此外,湍升力射流与地面之间的空气动力作用对V/STOL (垂直或短距离起落)飞机的性能具有很大的影响.长期以来,人们从理论分析、实验测量和数值模拟方面对冲击射流进行了广泛而系统的研究,积累了丰富的资料.本文在分析了湍流冲击射流的数值研究现状的基础上,对近年来有关湍流冲击射流流动与传热的数值研究方面的文献有选择地进行了综述,重点评述了不同湍流模型对冲击射流流动与传热的预测能力,讨论了存在的问题并对该领域今后的研究方向进行了展望.      

Radiative heat transfer calculations in real gases

A general formulation for radiative heat transfer calculations is presented, based on integrated quantities such as total emissivities and absorptivities. The procedure is intended particularly for combustion chamber applications of varying degree of complexity, the radiative active medium consisting of gases such as H₂O and CO₂ and of soot. First, some preliminary calculations are given for the often treated radiative equilibrium cases of plane parallel plates and infinite concentric cylinders. Then an example of a combustion chamber calculation is studied where the radiative heat transfer calculation is included in a system of partial differential equations describing momentum, heat and mass transfer with combustion.     

Gas–Dynamic Structures in Supersonic Combustion of Hydrogen in a System of Plane Jets in a Supersonic Flow

Results of numerical and theoretical studies of supersonic diffusive combustion of a system of plane hydrogen jets in a supersonic air flow are described. It is shown that large–scale vortex structures appear in the mixing zone of the system of hydrogen jets and the cocurrent flow. These vortex structures affect the mechanism of turbulent exchange between the fuel and the oxidizer.     

An analytical wall-function for recirculating and impinging turbulent heat transfer

The performance of the analytical wall-function (AWF) of Craft et al. [Craft, T.J., Gerasimov, A.V., Iacovides, H., Launder, B.E., 2002, Progress in the generalisation of wall-function treatments. Int. J. Heat Fluid Flow 23, 148–160.] is improved for predicting turbulent heat transfer in recirculating and impinging flows. Since constant parameters of the eddy viscosity formula were used to derive the AWF, the prediction accuracy of the original AWF tends to deteriorate in complex flows where those parameters need changing according to the local turbulence. To overcome such shortcomings, the present study introduces a functional behaviour on the strain parameter into the coefficient of the eddy viscosity of the AWF. The presently modified version of the AWF is validated in turbulent heat transfer of pipe flows, channel flows, back-step flows, pipe flows with abrupt expansion and plane impinging slot jets. The results confirm that the present modification successfully improves the performance of the original AWF for all the flows and heat transfer tested.     

Multiple-plane-jet turbulent mixing analysis via a kinetic theory approach

Turbulent mixing of a single jet, twin jets, triple jets and multiple jets is synthetically analysed in this paper. Chung's kinetic theory of turbulence and a modified Green's function are employed to solve this problem. The probability density function of fluid elements in the velocity space of multiple plane jets and the corresponding turbulence correlations are revealed in this analysis. The calculated results are found to be in good agreement with the available experimental data. The internal physical structure of the turbulent mixing mechanism seems better understood via the kinetic theory approach. The present study provides the fundamentals for theoretical understanding of multiple-jet turbulent mixing and further application to multiple-jet turbulent combustion analysis.     

PIV study of large-scale flow organisation in slot jets

The paper reports on particle image velocimetry (PIV) measurements in turbulent slot jets bounded by two solid walls with the separation distance smaller than the jet width (5–40%). In the far-field such jets are known to manifest features of quasi-two dimensional, two component turbulence. Stereoscopic and tomographic PIV systems were used to analyse local flows. Proper orthogonal decomposition (POD) was applied to extract coherent modes of the velocity fluctuations. The measurements were performed both in the initial region close to the nozzle exit and in the far fields of the developed turbulent slot jets for Re ⩾ 10,000. A POD analysis in the initial region indicates a correlation between quasi-2D vortices rolled-up in the shear layer and local flows in cross-stream planes. While the near-field turbulence shows full 3D features, the wall-normal velocity fluctuations day out gradually due to strong wall-damping resulting in an almost two-component turbulence. On the other hand, the longitudinal vortex rolls take over to act as the main agents in wall-normal and spanwise mixing and momentum transfer. The quantitative analysis indicates that the jet meandering amplitude was aperiodically modulated when arrangement of the large-scale quasi-2D vortices changed between asymmetric and symmetric pattern relatively to the jet axis. The paper shows that the dynamics of turbulent slot jets are more complex than those of 2D, plane and rectangular 3D jets. In particular, the detected secondary longitudinal vortex filaments and meandering modulation is expected to be important for turbulent transport and mixing in slot jets. This issue requires further investigations.     

Flow and Heat Transfer in Underexpanded Air Jets Issuing from the Sonic Nozzle of a Plasma Generator

We present the results of an experimental investigation and numerical simulation of the gasdynamic structure of underexpanded dissociated-air jets and the heat transfer in these strongly nonequilibrium flows under the test conditions realized in the 100-kW electrodeless VGU-4 plasma generator of the Institute for Problems in Mechanics of the Russian Academy of Sciences (IPM RAS). The flow and heat transfer analysis is carried out on the basis of measurements of the static pressure in the plenum chamber, at the sonic nozzle exit, and on the low-pressure chamber wall, the stagnation pressure on the jet axis using a Pitot tube, and the heat transfer at the stagnation points of water-cooled models placed along the jet axis. The numerical simulation, based on complete Navier-Stokes equations, includes the calculation of (1) equilibrium air plasma flows in the discharge channel of the VGU-4 plasma generator; (2) underexpanded nonequilibrium dissociated-air jet outflow into the ambient space; and (3) axisymmetric jet flow past cylindrical models.     

Einleitung nichtisothermer ebener Strahlen tangential und normal zu einer turbulenten Querströmung zum Zweck der Filmkühlung

The injection of plane cold air jets tangential or/and normal to a turbulent crossflow for the purpose of film cooling of combustion chamber walls is treated by developing a model based on the conservation equations which allows the calculation of the adiabatic wall temperature distribution. Starting with the differential equations of Prandtls boundary layer theory, Gaussian similarity profiles are assumed for the time averaged quantities of velocity and temperature. The different spread of heat and momentum for the jets is considered in the similarity profiles by an experimental expression for the turbulent Prandtl-number. The resulting linear differential equation system is closed by an entrainment hypothesis which pays attention to the suction effect of the jet. An additional ideal model conception is used to define the coupling conditions necessary for the interaction between tangentially and normally injected cold air streams. In order to demonstrate the capability of the mathematical model own experimental results as well as those of other authors are used for comparison with the calculations. The variety of investigated film cooling configurations reaches from pure tangential over pure normal up to the combination of both injection systems.     

Predictive Capabilities of an Improved Cubic k–ε Model for Inert Steady Flows

Through an improved ε transport equation, a major quality enhancement of the cubic k–ε model, earlier developed in[13], is obtained. The ε-equation of [13],yielding good results for wall-bounded and rotating flows, is combined with the one derived by Shih et al. [20], which produces good results for free shear flows (e.g. the plane jet–round jet anomaly is resolved).Results are presented for the following flows: fully developed stationary and rotating channel and pipe, backward-facing step, sudden pipe expansion, smooth channel expansion and contraction, plane and round jet. Heat transfer predictions in turbulent impinging jets are also discussed. Accurate results are obtained for the mean flow quantities for all test cases, without case dependent model tuning. This revised version was published online in July 2006 with corrections to the Cover Date.     

Scaling investigation of plasma-induced flows over curved and flat surfaces: Comparison to the wall jet

The present investigation deals with Dielectric Barrier Discharge (DBD) induced jets flowing over curved surfaces and studied in the framework of a circulation control application, carried out by acting near the rounded trailing-edge of an airfoil. These jets are characterized experimentally via Particle Image Velocimetry (PIV) in quiescent air conditions. The study assesses the evolution of these flows in terms of self-similarity of the mean flow and of its turbulent components. DBD wall jets evolution in the streaming direction is also analyzed through the rate of spread and the maximum velocity decay evolution as commonly done for fluidic wall jets, and also through several normalized quantities deriving from different length and velocity scales. A comparison with a canonical flow, such as the classical wall jet flowing over plane or curved surfaces, is made in order to find out the similarities and the discrepancies between these two flows. Results reveal that DBD wall jets and canonical fluidic wall jets show comparable properties in the diffusion zone. Compared to the plane DBD wall jet, centrifugal forces are responsible of the greater spread of curved DBD wall jets and are likely the source of instabilities leading to their transitional state. The momentum flux of the induced jet and the radius of curvature of the surface are two relevant scales for DBD induced flows developing over curved surfaces.     

Calculation of the momentum and heat transfer in turbulent gas-particle jet flows

The equations for the second moments of the dispersed-phase velocity and temperature fluctuations are used for calculating gas-suspension jet flows within the framework of the Euler approach. The advantages of introducing the equations for the second moments of the particle velocity fluctuations has previously been quite convincingly demonstrated with reference to the calculation of two-phase channel boundary flows [9–11]. The flows considered below have a low solid particle volume concentration, so that interparticle collisions can be neglected and, consequently, the stochastic motion of the particles is determined exclusively by their involvement in the fluctuating motion of the carrier flow. In addition to the equations for the turbulent energy of the gas and its dissipation, the calculation scheme includes the equations for the turbulent energy and turbulent heat transfer of the solid phase; however, the model constructed does not contain additional empirical constants associated with the presence of the particles in the flow.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 69–80, May–June, 1992.     

Drag reduction and heat transfer in surfactant solutions with excess counterion

We present the results of a study of turbulent drag reduction in a small circulating loop using surfactant solutions with excess counterion. In addition, these solutions were used in measurements of heat transfer, both in pipe flow and in an impinging jet. Both frictional drag and heat transfer were reduced in the pipe flow experiments. Measurements of heat transfer in the impinging jet revealed a dependence on the molar concentration ratio of the counterion. When the counterion was added at a molar concentration 30 times higher than that of the surfactant, the resulting surfactant solution did not reduce the rate of heat transfer in the impinging jet. By using this surfactant system in an impinging jet, we show both a reduction in pipe friction and normal heat transfer potential in a circulating heat exchange system. In order to investigate this difference in heat transfer between pipe flows and impinging jet flows, a comparison was made of the wall shear stress between these two flow regimes. The estimated wall shear stress was of the same order in both flows, and thus was not considered to be the primary cause of the difference in heat transfer. It is instead suggested that the micellar structure of the surfactant is influenced by a compressive deformation of the impinging flow in a manner that is different from the shear deformation observed in pipe flow.     

Calculation of an axisymmetric turbulent wall jet over a surface of convex curvature

One of the many applications of curved wall jets of engineering importance is the Coanda Flare, which is used for burning waste gases in the petroleum industry and which gave rise to this work. The gas jet flows over an axisymmetric tulip shaped body, entraining ambient air and so promoting clean combustion. The object of this work was to calculate the development of the jet with the extra rates of strain imposed by both longitudinal curvature and divergence. A differential ‘partially-parabolic’ technique was used with uncoupling of the streamwise and cross-stream momentum equations, leading to an efficient computer program. The extra rates of strain were modelled by corrections to a mixing length model with the two effects being assumed to be additive. The calculation method was compared with seven test ccases of experimental data. The first five were from published literature, and included the plane wall jet and axisymmetric free jet, and the separate effects of longitudinal curvature and divergence. The lost two cases were measurements of the wall jet flow over a model Coanda Flare. The calculation method gave generally good results for the main features of the flow such as growth rate and velocity decay. Details of the flow were not so well predicted, particularly the turbulent shear stress, as a result of the relatively simple turbulence model employed. The calculation method should provide a useful engineering tool, but some profitable developments could be made, particularly in the area of turbulence modelling.     

Numerical Study of Turbulent Jet Ignition in a Lean Premixed Configuration

Direct numerical simulations (DNS) of a hot combustion product jet interacting with a lean premixed hydrogen-air coflow are conducted to fundamentally investigate turbulent jet ignition (TJI) in a three-dimensional configuration. TJI is an efficient method for initiating and controlling combustion in ultra-lean combustion systems. Fully compressible gas dynamics and species equations are solved with high order finite difference methods. The hydrogen-air reaction is simulated with a reliable detailed chemical kinetics mechanism. The physical processes involved in the TJI-assisted combustion are investigated by considering the flame heat release, temperature, species concentrations, vorticity, and Baroclinc torque. The complex turbulent flame and flow structures are delineated in three main: i) hot product jet, ii) burned-mixed, and iii) flame zones. In the TJI-assisted combustion, the flow structures and the flame features such as flame speed, temperature, and species distribution are found to be quite different than those in “standard” turbulent premixed combustion due to the existence of a high energy turbulent hot product jet. The flow structures and statistics are also found to be different than those normally seen in non-isothermal non-reacting jets.     

Large eddy simulation of vertical turbulent jets under JONSWAP waves

The effect of random waves on vertical plane turbulent jets is studied numerically and the mechanism behind the interaction of the jet and waves is analyzed. The large eddy simulation method is used and the σ-coordinate system is adopted. Turbulence is modeled by a dynamic coherent eddy model. The σ-coordinate transformation is introduced to map the irregular physical domain with a wavy free surface and an uneven bottom onto a regular computational domain. The fractional step method is used to solve the fil...     

Development of a swirling jet in infinite space

We examine the problem of swirling-jet development in an infinite space filled with the same fluid. The fourth term of the asymptotic expansion of the tangential-velocity component is obtained. The constant appearing in the solution is obtained semlempirically. Results are presented of calculations of the velocities and pressure in swirling jets and of experimental studies.Swirling jet flows play an important role in the process of combustion intensification and stabilization and are widely used in engineering.The formulation and first solution of the problem of swirling-jet development in an infinite space filled with the same fluid at rest were accomplished by Loitsyanskii [1], who found the first two terms of the asymptotic expansion of the solution of the boundary-layer equations. The third and fourth terms of the asymptotic expansion of the axial-velocity component were found in [2], which made it possible to study the effect of jet swirl on the axial-velocity-component profile.In the present study we obtain the fourth term of the asymptotic expansion of the tangential-velocity component and present results of experimental studies on swirling jets.The authors wish to thank L. G. Loitsyanskii for valuable comments.