The correction of longitudinal heat flux in turbulence measurement

In this paper the influence of temperature on velocity signal in hot-wire measurement of turbulence is analysed. It is pointed out that when the temperature influence is small, the temperature influence on measured intensity of velocity fluctuations is second order small and negligible. However, the temperature influence on measuring longitudinal heat flux is of first order quantity, and must be corrected, or large error will occur. The method to correct the temperature influence on measuring ρ _θu and the procedure to decide experimentally temperature influence coefficient have been given.     

Numerical simulation of shock tube generated vortex: effect of numerics

Vortices generated at the open end of a planar shock tube are numerically simulated using the AUSM+ scheme. This scheme is known to have low numerical dissipation and therefore is suitable for capturing unsteady vortex motion. However, this low numerical dissipation can also cause oscillations in the vorticity field. Numerical experiments presented here highlight the effect of numerical dissipation on the simulated vortex, as well as the role played by turbulence models. Two turbulence models – the shear-stress-transport (SST) and its modified version for unsteady flows (SST-SAS) – are employed to observe the effect of including turbulence models in such complex flows where the vortex has an embedded shock.     

Direct numerical simulation of turbulent heat transfer in annuli: Effect of heat flux ratio

Fully developed turbulent flow and heat transfer in a concentric annular duct is investigated for the first time by using a direct numerical simulation (DNS) with isoflux conditions imposed at both walls. The Reynolds number based on the half-width between inner and outer walls, δ=(r₂-r₁)/2, and the laminar maximum velocity is Re_δ=3500. A Prandtl number Pr=0.71 and a radius ratio r^*=0.1 were retained. The main objective of this work is to examine the effect of the heat flux density ratio, q^*=q₁/q₂, on different thermal statistics (mean temperature profiles, root mean square (rms) of temperature fluctuations, turbulent heat fluxes, heat transfer, etc.). To validate the present DNS calculations, predictions of the flow and thermal fields with q^*=1 are compared to results recently reported in the archival literature. A good agreement with available DNS data is shown. The effect of heat flux ratio q^* on turbulent thermal statistics in annular duct with arbitrarily prescribed heat flux is discussed then. This investigation highlights that heat flux ratio has a marked influence on the thermal field. When q^* varies from 0 to 0.01, the rms of temperature fluctuations and the turbulent heat fluxes are more intense near the outer wall while changes in q^* from 1 to 100, lead to opposite trends.     

Numerical simulation of quasi-streamwise hairpin-like vortex generation in turbulent boundary layer

A mechanism for generation of near wall quasi-streamwise hairpin-like vortex （QHV） and secondary quasi-streamwise vortices （SQV） is presented. The conceptual model of resonant triad in the theory of hydrodynamic instability and direct numerical simulation of a turbulent boundary layer were applied to reveal the formation of QHV and SQV. The generation procedures and the characteristics of the vortex structures are obtained, which share some similarities with previous numerical simulations. The research using resonant triad conceptual model and numerical simulation provides a possibility for investigating and controling the vortex structures, which play a dominant role in the evolution of coherent structures in the near-wall region.     

Numerical analysis on longitudinal location optimization of vortex generator in compact heat exchangers

In this paper, numerical, curvilinear and turbulent model has been used to investigate the effect of vortex generator's longitudinal displacement on heat transfer and fluid flow in different Reynolds numbers ranging from 500 to 3000. The numerical model has been validated with experimental results of a former study, which is resembled in a particular case. Numerical simulation shows that the vorticity enhancement would increase both Nusselt number and pressure drop. Proposed trend is not constant and the pattern in which parameters change is dependent on Reynolds number. Finally, a conjugated optimization of pressure drop and the Nusselt number has been suggested based on the order of parameter changes. Copyright © 2010 John Wiley & Sons, Ltd.     

Direct numerical simulation of turbulent heat transfer on the Reynolds analogy over irregular rough surfaces

The effect of rough surface topography on heat and momentum transfer is studied by direct numerical simulations of turbulent heat transfer over uniformly heated three-dimensional irregular rough surfaces, where the effective slope and skewness values are systematically varied while maintaining a fixed root-mean-square roughness. The friction Reynolds number is fixed at 450, and the temperature is treated as a passive scalar with a Prandtl number of unity. Both the skin friction coefficient and Stanton number are enhanced by the wall roughness. However, the Reynolds analogy factor for the rough surface is lower than that for the smooth surface. The semi-analytical expression for the Reynolds analogy factor suggests that the Reynolds analogy factor is related to the skin friction coefficient and the difference between the temperature and velocity roughness functions, and the Reynolds analogy factor for the present rough surfaces is found to be predicted solely based on the equivalent sand-grain roughness. This suggests that the relationship between the Reynolds analogy factor and the equivalent sand-grain roughness is not affected by the effective slope and skewness values. Analysis of the heat and momentum transfer mechanisms based on the spatial- and time-averaged equations suggests that two factors decrease the Reynolds analogy factor. One is the increased effective Prandtl number within the rough surface in which the momentum diffusivity due to the combined effects of turbulence and dispersion is larger than the corresponding thermal diffusivity. The other is the significant increase in the pressure drag force term above the mean roughness height.     

Coherent structures in trailing-edge cooling and the challenge for turbulent heat transfer modelling

The present paper tests the capability of a standard Reynolds-Averaged Navier–Stokes (RANS) turbulence model for predicting the turbulent heat transfer in a generic trailing-edge situation with a cutback on the pressure side of the blade. The model investigated uses a gradient-diffusion assumption with a scalar turbulent-diffusivity and constant turbulent Prandtl number. High-fidelity Large-Eddy Simulations (LES) were performed for three blowing ratios to provide reliable target data and the mean velocity and eddy viscosity as input for the heat transfer model testing. Reasonably good agreement between the LES and recent experiments was achieved for mean flow and turbulence statistics. The LES yielded coherent structures which were analysed, in particular with respect to their effect on the turbulent heat transfer. For increasing blowing ratio, the LES replicated an also experimentally observed counter-intuitive decrease of the cooling effectiveness caused by the coherent structures becoming stronger. In contrast, the RANS turbulent heat transfer model failed in predicting this behaviour and yielded significantly too high cooling effectiveness. It is shown that the model cannot predict the strong upstream and wall-directed turbulent heat fluxes caused by large coherent structures, which were found to be responsible for the counter-intuitive decrease of the cooling effectiveness.     

Longitudinal vortex pair imbedded in a turbulent boundary layer: Comparative performances of several turbulence models

Four turbulence models, namely, the basic and nonlinear stress-transport models and the basic and anisotropick-ε models, have been tested in the case of interaction between a longitudinal vortex pair and a flat-plate boundary layer. The results of their predictions were compared with Mehta and Bradshaw's measurements. In this paper, part of the results involving those of the nonlinear stress-transport model and anisotropick-ε model are presented and discussed. The project supported by the National Natural Science Foundation of China under Contract No. 19132012     

Effect of free-stream turbulence on conical vortex dynamics

The influence of Free-Stream Turbulence (FST) on the space–time dynamics of a conical vortex developing along a A-pillar is studied experimentally. Measurements of unsteady wall pressure and velocity by High Speed-Stereo PIV highlight the important effects of turbulence on the mean and instantaneous properties of the vortex. Very significant increases in Reynolds stresses into the vortex region and in wall fluctuating pressure are observed in the presence of FST. In smooth flow, the frequency content of the pressure and velocity fields is very rich with low and high frequency contributions due to the meandering of the vortex and instabilities in the vortex core. Meandering shows, for the different integral length scales and intensities of turbulence tested, a great receptivity to the presence of a FST and we observe a global motion of the vortex structure at low frequency. This frequency is modulated by the value of the integral length scale of the FST. We show that the mean conical structure is a wave guide for the perturbations of the core but that, with FST, the spatio-temporal evolution of the envelope overwhelms the intrinsic instability of the vortex core observed in smooth flow.     

Dynamic pressure based prediction of spray cooling heat transfer coefficients

An important goal of spray cooling research is the ability to predict local heat transfer from the spray hydrodynamics. It is postulated that the local normal pressure exerted by the spray onto the heated surface can be used to obtain the local heat transfer coefficient. This hypothesis was tested using data obtained from hollow cone, full cone, and linear sprays at four nozzle pressures and three stand-off distances. A correlation between the pressure and heat transfer coefficient was determined from the data, then used to “predict” the heat transfer coefficient to verify the accuracy of the correlation. The area averaged heat transfer coefficient could be predicted within 25%, indicating that pressure can be used to predict the local heat transfer coefficient in the single-phase regime.     

LBE simulation of coherent vortex motion and heat transfer in jets of cross flow

Lattice Boltzmann equation method is used to simulate the coherent vortex motions and interactions and the heat transfer characteristics of jets in cross flow (JICFs) via TD2G9 model. After validation, the characteristics of cross flow under different Reynolds numbers are illustrated, including the mean profiles, the Reynolds stress tensor, the vortex and temperature fields, the temperature gradients near the walls, and the coherent correlation of vortex motions. The results show that the velocity profiles in JICF can be characterized by three basic regions, which are mainly caused by the mergence of JICF with the main flow. The temperature gradient near the walls can also be categorized by four basic regions, which are caused mainly by the impulse of JICFs too. Coherent vortex motions are found in JICF for Re = 3000, which are proved by strong periodic correlation of flow variables over a fixed area.     

Influence of turbulence intensity and free stream velocity oscillations on stagnation point heat transfer

A model is proposed for the momentum eddy diffusivity induced by free stream turbulence intensity and integral length scale. The eddy diffusivity model is applied to the stagnation point of a cylinder situated in a steady uniform crossflow in the presence of free stream turbulence. A numerical solution of the governing steady-state momentum and energy equations with the proposed eddy diffusivity model yielded results for the skin friction coefficient and the Nusselt number. Agreement between the numerical predictions of this work and experimental data is very good. The experimental data concerning the unsteady stagnation point heat transfer under the combined influence of free stream velocity oscillations and turbulence intensity have been successfully correlated by means of a new turbulence parameter     

Simulation of vortex shedding past a square cylinder with different turbulence models

This paper presents the results of numerical simulations of vortex shedding past a free-standing square cylinder at Re_D=22 000, obtained with different turbulence models. Using wall functions, the standard k–ε model is compared with a modification suggested by Kato and Launder (Proc. 9th Symp. Turbulent Shear Flows, Kyoto, 10-4-1 (1993)). In addition, both versions are used in a two-layer approach, in which the flow close to the cylinder is computed with a locally more suitable one-equation turbulence model and only outside the viscous near-wall layer with the two mentioned high-Re model versions. To allow a comparison, the simulations are performed first using the same computational domain and boundary conditions as in previous investigations. Then results are presented that were obtained on a computational domain and with boundary conditions more suitable for a comparison with the experiments. © 1998 John Wiley & Sons, Ltd.     

A model of stratified entrainment using vortex persistence

A new model is proposed for the entrainment rate by vortices across stratified interfaces. In the model, different entrainment regimes are distinguished by the conventional parameters Richardson, Reynolds, and Schmidt number as well as a new parameter, the “vortex persistence”. Vortex persistence is defined as the number of rotations a vortex makes during the time it moves its own diameter with respect to the interface. It is further proposed that the concept of vortex persistence is important whenever a vortex is near any kind of surface, either stratified or solid. The model is in accord with most field and laboratory observations in a variety of stratified and bounded flows, including measurements of wall heat transfer and vortex formation in starting jets.     

An explicit algebraic Reynolds stress and heat flux model for incompressible turbulence: Part I Non-isothermal flow

Tensor representation theory is used to derive an explicit algebraic model that consists of an explicit algebraic stress model (EASM) and an explicit algebraic heat flux model (EAHFM) for two-dimensional (2-D) incompressible non-isothermal turbulent flows. The representation methodology used for the heat flux vector is adapted from that used for the polynomial representation of the Reynolds stress anisotropy tensor. Since the methodology is based on the formation of invariants from either vector or tensor basis sets, it is possible to derive explicit polynomial vector expansions for the heat flux vector. The resulting EAHFM is necessarily coupled with the turbulent velocity field through an EASM for the Reynolds stress anisotropy. An EASM has previously been derived by Jongen and Gatski [10]. Therefore, it is used in conjunction with the derived EAHFM to form the explicit algebraic model for incompressible 2-D flows. This explicit algebraic model is analyzed and compared with previous formulations including its ability to approximate the commonly accepted value for the turbulent Prandtl number. The effect of pressure-scrambling vector model calibration on predictive performance is also assessed. Finally, the explicit algebraic model is validated against a 2-D homogeneous shear flow with a variety of thermal gradients. Dedicated to the memory of the late Professor Charles G. Speziale of Boston University     

Simulation on motion of particles in vortex merging process

In a two-phase flow, the vortex merging influences both the flow evolution and the particle motion. With the blobs-splitting-and-merging scheme, the vortex merging is calculated by a corrected core spreading vortex method （CCSVM）. The particle motion in the vortex merging process is calculated according to the particle kinetic model. The results indicate that the particle traces are spiral lines with the same rotation direction as the spinning vortex. The center of the particle group is in agreement with that of the merged vortex. The merging time is determined by the circulation and the initial ratio of the vortex radius and the vortex center distance. Under a certain initial condition, a stretched particle trail is generated, which is determined by the viscosity, the relative position between the particles and the vortex, and the asymmetrical circulation of the two merging vortices.     

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.     

An explicit algebraic Reynolds stress and heat flux model for incompressible turbulence: Part II Buoyant flow

This paper presents a derivation of an explicit algebraic model for two-dimensional (2-D) buoyant flows. It is an extension of the work reported in Part I (So et al. [27]). The tensor representation method of Jongen and Gatski [14] is extended to derive an explicit algebraic Reynolds stress model (EASM) for 2-D buoyant flow invoking the Boussinesq approximation. The projection methodology is further extended to treat the heat flux transport equation in the derivation of an explicit algebraic heat flux model (EAHFM) for buoyant flow. Again, the weak equilibrium assumption is invoked for the scaled Reynolds stress and scaled heat flux equation. An explicit algebraic model for buoyant flows is then formed with the EASM and EAHFM. From the derived EAHFM, an expression for the thermal diffusivity tensor in buoyant shear flows is deduced. Furthermore, a turbulent Prandtl number (Pr_T) for each of the three heat flux directions is determined. These directional Pr_T are found to be a function of the gradient Richardson number. Alternatively, a scalar Pr_T can be derived; its value is compared with the directional Pr_T. The EASM and EAHFM are used to calculate 2-D homogeneous buoyant shear flows and the results are compared with direct numerical simulation data and other model predictions, where good agreement is obtained. Dedicated to the memory of the late Professor Charles G. Speziale of Boston University