Large eddy simulation of hot and cold fluids mixing in a T-junction for predicting thermal fluctuations

Temperature fluctuations in a mixing T-junction have been simulated on the FLUENT platform using the large eddy simulation （LES） turbulent flow model and a sub-grid scale Smagorinsky-Lilly model. The normalized mean and root mean square temperatures for describing time-averaged temperature and temperature fluctuation intensity, and the velocity are obtained. The power spectrum densities of temperature fluctuations, which are key parameters for thermal fatigue analysis and lifetime evaluation, are analyzed. Simulation results are consistent with experimental data published in the literature, showing that the LES is reliable. Several mixing processes under different conditions are simulated in order to analyze the effects of varying Reynolds number and Richardson number on the mixing course and thermal fluctuations.     

Experimental and numerical analyses on the effect of increasing inflow temperatures on the flow mixing behavior in a T-junction

Thermal degradation of piping induced by high cycle thermal fatigue (HCTF) is of significant importance as operating Nuclear Power Plants (NPP) become older and lifetime extension activities are initiated. In particular, HCTF incidents related to turbulent thermal mixing of fluids in a T-junction piping system are not well understood and could not be adequately monitored using common thermocouple instrumentation. To investigate this phenomenon, an experimental T-junction test facility was commissioned at the University of Stuttgart, known as the Fluid Structure Interaction (FSI) test facility. The paper presents the experimental investigation and the corresponding numerical validation using the large eddy simulation (LES) method to study T-junction flow mixing. Three experimental test cases are investigated with temperature differences (∆T) of 51.5 K (Case 1), 76 K (Case 2) and 97 K (Case 3) between the mixing fluids. A constant mass flow rate ratio (main/branch) of 4:1 is maintained in all the investigated cases. Flow mixing is observed to be incomplete in all the cases, resulting in a thermally stratified flow with an oscillating stratification layer downstream of the T-junction. Mean temperature and root mean square (RMS) temperature fluctuations predicted by LES in the mixing region are found to be in good agreement with measurement data, with the exception of few positions. Amplitudes of temperature fluctuations are observed to be higher near the stratification layer, ranging from 6.3–9.9% of ∆T. Power spectral density (PSD) analyses of temperature fluctuations indicate no dominant frequency (spectral peak) under prevailing flow conditions, an important factor in thermal fatigue analysis, and the energy of these fluctuations are mainly contained in the frequency range of 0.1–2 Hz for all the investigated cases. LES is performed using the CFD software ANSYS CFX 14.0.     

Measurements on supersonic free jets

Summary An experimental study of round supersonic air jets discharging into quiescent air is described. The initial stagnation enthalpy of the jets was equal to that of the atmosphere. Most of the experiments concerned a fully expanded jet with initial Mach number M _I =1.74. From the experimental results the turbulent Prandtl number and the turbulent coefficient of momentum transfer could be calculated in a large part of the mixing zone of the jets. A mixing parameter K has been introduced and calculated for the jets. The results of this investigation are compared with those obtained for low-speed jets.     

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 Measurements in the Near and Intermediate Field Regions of Jets Issuing from Eight Different Nozzle Geometries

An experimental study was conducted to investigate the effect of nozzle geometry on the mixing characteristics and turbulent transport phenomena in turbulent jets. The nozzle geometry examined were round, square, cross, eight-corner star, six-lobe daisy, equilateral triangle as well as ellipse and rectangle each with aspect ratio of 2. The jets were produced from sharp linear contoured nozzles which may be considered intermediate to the more widely studied smooth contraction and orifice nozzles. A high resolution particle image velocimetry was used to conduct detailed velocity measurements in the near and intermediate regions. It was observed that the lengths of the potential cores and the growth rates of turbulence intensities on the jet centerline are comparable with those of the orifice jets. The results indicate that the decay and spreading rates are lower than reported for orifice jets but higher than results for smooth contoured jets. The jets issuing from the elliptic and rectangular nozzles have the best mixing performance while the least effective mixing was observed in the star jet. The distributions of the Reynolds stresses and turbulent diffusion clearly showed that turbulent transport phenomena are quite sensitive to nozzle geometry. Due to the specific shape of triangular and daisy jets, the profiles of mean velocity and turbulent quantities are close to each other in their minor and major planes while in the elliptic and rectangular jets are considerably different. They also exhibit more isotropic behavior compared to the elliptic and rectangular jets. In spite of significant effects of nozzle geometry on mean velocity and turbulent quantities, the integral length scales are independent of changes in nozzle geometry.     

Flow and mixing characteristics of pulsed confined opposed jets in turbulent flow regime

A numerical study is performed on a two-dimensional confined opposed-jet configuration to gain basic understanding of the flow and mixing characteristics of pulsed turbulent opposed-jet streams. The sinusoidal pulsating flows with different temperature are imposed at opposed-jet inlets, which are mixed with each other in a confined flow channel. The current mathematical model taking the effect of temperature-dependent thermo-physical properties of fluid into account can present a good prediction for opposed-jet streams compared with experimental data. The numerical results indicate that introduction of temperature difference between opposed jet flows can lead to an asymmetric flow field immediately after jet impact, and the sinusoidal flow pulsations can effectively enhance mixing rate of opposed jets. Parameter studies are conducted for optimization of pulsed opposed jets. The effect of Reynolds number and flow pulsation as well as the configuration geometry on the mixing performance are discussed in detail. Examination of the flow and thermal field shows that the mixing rate is highly dependent on the vortex-induced mixing and residence time of jet fluid in the exit channel.     

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.     

Analysis of the nozzle exit flow parameter effect on the turbulence characteristics and the noise level in jets issuing from nozzles of different types

The flow, turbulence, and noise parameters of cold and hot jets flowing out of nozzles of different types at subsonic and supersonic velocities are calculated using the high-resolution RANS/ILES method. The effect of the Mach number and the temperature at the nozzle exit on the flow features, the turbulent fluctuations of the velocity, the static pressure, and the temperature, together with the overall noise level is analyzed for all the jets considered. The accuracy of the calculations is confirmed by means of comparing with the available experimental data concerning certain parameters.     

大速差射流燃烧室中烟煤与贫煤燃烧的数值模拟

本文基于颗粒相的轨道模型,对大速差射流燃烧室中烟煤粉与贫煤粉的二维流动,混合及燃烧进行了数值模拟,模拟结果从两相耦合的角度,阐明了煤粉颗粒在燃烧室中运动的规律,煤粉与大速差射流诱导的中心气体逆流之间的混合及其对煤粉火焰稳定的影响,指出此种燃烧室中煤粉火焰稳定的回流区燃烧机理,气相流场及回流区的预报结果与实验符合良好。     

Large-eddy simulation of thermal fatigue in a mixing tee

Temperature fluctuations occur due to thermal mixing of hot and cold streams in the T-junctions of the piping system in nuclear power plants, which may cause thermal fatigue of piping system. In this paper, three-dimensional, unsteady numerical simulations of coolant temperature fluctuations at a mixing T-junction of equal diameter pipes were performed using the large eddy simulation (LES) turbulent model. The experiments used in this paper to benchmark the simulations were performed by Hitachi Ltd. The calculated normalized mean temperatures and fluctuating temperatures are in good agreement with the measurements. The influence of the time-step ranging from 100 Hz to 1000 Hz on the numerical simulation results was explored. The simulation results indicate that all the results with different frequencies agree well with the experimental data. Finally, the attenuation of fluctuation of fluid temperature was also investigated. It is found that, drastic fluctuation occurs within the range of less than L/D = 4.0; the fluctuation of fluid temperature does not always attenuate from the pipe center to the wall due to the continuous generation of vortexes. At the top wall, the position of L/D = 1.5 has a minimum normalized mean temperature and a peak value of root-mean square temperature, whereas at the bottom wall, the position having the same characteristics is L/D = 2.0.     

Large-eddy simulation in a mixing tee junction: High-order turbulent statistics analysis

This study analyses the mixing and thermal fluctuations induced in a mixing tee junction with circular cross-sections when cold water flowing in a pipe is joined by hot water from a branch pipe. This configuration is representative of industrial piping systems in which temperature fluctuations in the fluid may cause thermal fatigue damage on the walls. Implicit large-eddy simulations (LES) are performed for equal inflow rates corresponding to a bulk Reynolds number Re = 39,080. Two different thermal boundary conditions are studied for the pipe walls; an insulating adiabatic boundary and a conducting steel wall boundary. The predicted flow structures show a satisfactory agreement with the literature. The velocity and thermal fields (including high-order statistics) are not affected by the heat transfer with the steel walls. However, predicted thermal fluctuations at the boundary are not the same between the flow and the solid, showing that solid thermal fluctuations cannot be predicted by the knowledge of the fluid thermal fluctuations alone. The analysis of high-order turbulent statistics provides a better understanding of the turbulence features. In particular, the budgets of the turbulent kinetic energy and temperature variance allows a comparative analysis of dissipation, production and transport terms. It is found that the turbulent transport term is an important term that acts to balance the production. We therefore use a priori tests to evaluate three different models for the triple correlation.     

Coherent structures and wavepackets in subsonic transitional turbulent jets

A large eddy simulation (LES) is performed for two subsonic jets with a Reynolds number of Re = 105, which have different core temperatures, i.e., the cold and hot jet. The far-field overall sound pressure levels (OASPL) and noise spectra are well validated against previous exper-imental results. It is found that the OASPL is raised by heating at shallow angles. The most energetic coherent struc-tures are extracted with specified frequencies using the filter based on the frequency domain variant of the snapshot method of proper orthogonal decomposition (POD). The m = 0, 1 modes have high coherence of near-field pres-sure for both jets, while the coherence of m = 0 modes is enhanced greatly by heating. Based on the coherent struc-tures, spatial wavepackets are educed and the characteristics of growth, saturation and decay are analyzed and compared between the two jets in detail. The results show that heat-ing would enhance the linear growth rate for high frequency components, and nonlinear growth rates for low frequency components in general, which are responsible for higher OASPL in the hot jet. The far-field sound generated by wavepackets is computed using the Kirchhoff extrapolation, which matches well with that of LES at shallow angles. This indicates that the wavepackets associated with coherent structures are dominant sound sources in forced transitional turbulent jets. Additionally, the present POD method is proven to be a robust tool to extract the salient features of the wavepackets in turbulent flows.     

A numerical study of turbulent opposed impinging jets issuing from triangular nozzles with different geometries

In present research, two turbulent opposed impinging air jets issuing from triangular nozzles with fixed and variable exit velocity ratios and different nozzle-to-nozzle distances have been studied numerically and then compared with rectangular and circular nozzles. The finite volume method has been applied for solving mass and momentum equations. The turbulence model being used here is k-ε RNG. Distributions of pressure, turbulence, kinetic energy and its dissipation rate in various regions especially on the impingement regions have been obtained with high accuracy. Study of the nozzle geometries has shown the advantage of triangular nozzles over other geometries. First, the triangle’s base in nozzle geometry has an important role in our study case which, mixing two flows and regions with high turbulence intensity, directly depends on it. Second, our results show that circular and rectangular nozzles have less efficiency than triangular nozzles in mixing applications. Third and last, it was found that the radial jet being created by opposed jets has some similarities to free jets. In this investigation, air in standard atmospheric pressure has been applied as working fluid.     

Density and compressibility effects in turbulent subsonic jets part 1: mean velocity field

The behavior of compressible jets originated from initially turbulent pipe flows issuing in still air has been investigated at three different subsonic Mach numbers, 0.3, 0.6 and 0.9. Helium, nitrogen and krypton gases were used to generate the jet flows and investigate the additional effects of density on the flow structure. Particle image velocimetry, high-frequency response pressure transducers and thermocouples were used to obtain velocity, Mach number and total temperature measurements inside the flow field. The jets were formed at the exit of an adiabatic compressible frictional turbulent pipe flow, which was developing toward its corresponding sonic conditions inside the pipe, and continued to expand within the first four diameters distance after it exited the pipe. Theoretical considerations based on flow self-similarity were used to obtain the decay of Mach number along the centerline of the jets for the first time. It was found that this decay depends on two contributions, one from the velocity field which is inversely proportional to the distance from the exit and one from the thermal field which is proportional to this distance. As a result, a small non-linearity in the variation of the inverse Mach number with downstream distance was found. The decay of the Mach number at the centerline of the axisymmetric jets increases by increasing the initial Mach number at the exit of the flow for all jets. The decay of mean velocity at the centerline of the jets is also higher at higher exit Mach numbers. However, the velocity non-dimensionalized by the exit velocity seems to decrease faster at low exit Mach numbers, suggesting a reduced mixing with increasing exit flow Mach numbers. Helium jets were found to have the largest spreading rate among the three different gas jets used in the present investigation, while krypton jets had the lowest spreading rate. The spreading rate of each gas decreases with increasing its kinetic energy relatively to its internal energy.     

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.     

Mixing characteristics of turbulent water vapour jets measured using an isokinetic sampling probe

 Horizontal turbulent water vapour (steam) jets were discharged into ambient air from a circular convergent nozzle under unchoked/choked and saturated/superheated nozzle exit conditions, resulting in two-phase (liquid and vapour), two-fluid (air and water) condensing free jets. Flow properties and mixing characteristics have been measured with the aid of an isokinetic sampling probe arrangement. Radial and axial profiles of air and steam mass flow rates and mass fractions were measured from which entrainment, centreline decay and half-width spreading rates were calculated and compared with data from the literature. Overall, the mixing characteristics of the condensing jets are very similar to those of non-condensing jets extensively reported in the literature. Received: 30 September 1996 / Accepted: 19 May 1997     

Evidences of persisting thermal structures in Couette flows

DNS of passive thermal turbulent Couette flow at several friction Reynolds numbers (180, 250, and 500), and the Prandtl number of air are presented. The time averaged thermal flow shows the existence of long and wide thermal structures never described before in Couette flows. These thermal structures, named CTFS (Couette Thermal Flow Superstructures), are defined as coherent regions of hot and cold temperature fluctuations. They are intrinsically linked to the velocity structures present in Couette flows. Two different 2D symmetries can be recognized, which get stronger with the Reynolds number. These structures do not affect the mean flow or mean quantities as the Nusselt number. However, turbulent intensities and thermal fluxes depend on the width of the structures, mainly far from the walls. Since the width of the structures is related to the channel width, the statistics of thermal Couette flow are to some point box-dependent.     

Development of a submerged turbulent isothermal jet and the minimum entropy-production principle

It is shown in the example of a submerged turbulent isothermal jet that the process of turbulent mixing of gas jets can evolve in accordance with, the principle of minimum entropy production.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 52–58, July–August, 1978.     

Numerical investigation of turbulent free jet flows issuing from rectangular nozzles: the influence of small aspect ratio

In this research, the fluid and thermal characteristics of a rectangular turbulent jet flow is studied numerically. The results of three-dimensional jet issued from a rectangular nozzle are presented. A numerical method employing control volume approach with collocated grid arrangement was employed. Velocity and pressure fields are coupled with SIMPLEC algorithm. The turbulent stresses are approximated using k–e{\varepsilon} model with two different inlet conditions. The velocity and temperature fields are presented and the rates of their decay at the jet centerline are noted. The velocity vectors of the main flow and the secondary flow are illustrated. Also, effect of aspect ratio on mixing in rectangular cross-section jets is considered. The aspect ratios that were considered for this work were 1:1 to 1:4. The results showed that the jet entrains more with smaller AR. Special attention has been drawn to the influence of the Reynolds number (based on hydraulic diameter) as well as the inflow conditions on the evolution of the rectangular jet. An influence on the jet evolution is found for smaller Re, but the jet is close to a converged state for higher Reynolds numbers. The inflow conditions have considerable influence on the jet characteristics.     

An investigation into the interaction of closely-spaced starting jets

The transient, three-dimensional scavenging flow inside a novel two-stroke engine has been investigated both experimentally in a scaled water model as well as numerically using a commercial CFD code incorporating an unsteady Reynolds averaged Navier–Stokes (URANS) formulation. The scavenging flow consists of 16 round jets in close proximity of each other and the cylinder wall, developing from the top of the combustion chamber down towards the exhaust ports located along the wall at the bottom of the cylinder. Flow visualization of the scavenging flow was performed using a scaled fixed-piston water model and was used as a means of validating the URANS simulations themselves. The flow visualization experiments provided insight into the complex jet–jet and jet–wall interactions within the engine cylinder. These interactions were not as well predicted by the CFD simulations. In fact, the CFD simulations were found to significantly under-predict the turbulent mixing between the jets. This suggests that unsteady-RANS formulations are incapable of reproducing the large-scale and unsteady mixing structures associated with the vortex shedding between the closely-spaced jets.