Visualisation and analysis of large-scale vortex structures in three-dimensional turbulent lid-driven cavity flow

In this paper, large eddy simulation (LES) of a three-dimensional turbulent lid-driven cavity (LDC) flow at Re = 10,000 has been performed using the multiple relaxation time lattice Boltzmann method. A Smagorinsky eddy viscosity model was used to represent the sub-grid scale stresses with appropriate wall damping. The prediction for the flow field was first validated by comparing the velocity profiles with previous experimental and LES studies, and then subsequently used to investigate the large-scale three-dimensional vortical structures in the LDC flow. The instantaneous three-dimensional coherent structures inside the cavity were visualised using the second invariant (Q), Δ criterion, λ₂ criterion, swirling strength (λ_ci) and streamwise vorticity. The vortex structures obtained using the different criteria in general agree well with each other. However, a cleaner visualisation of the large vortex structures was achieved with the λ_ci criterion and also when the visualisation is based on the vortex identification criteria expressed in terms of the swirling strength parameters. A major objective of the study was to perform a three-dimensional proper orthogonal decomposition (POD) on the fluctuating velocity fields. The higher energy POD modes efficiently extracted the large-scale vortical structures within the flow which were then visualised with the swirling strength criterion. Reconstruction of the instantaneous fluctuating velocity field using a finite number of POD modes indicated that the large-scale vortex structures did effectively approximate the large-scale motion. However, such a reduced order reconstruction of the flow based on the large-scale vortical structures was clearly not as effective in predicting the small-scale details of the fluctuating velocity field which relate to the turbulent transport.     

The second Hopf bifurcation in lid-driven square cavity

To date, there are very few studies on the second Hopf bifurcation in a driven square cavity, although there are intensive investigations focused on the first Hopf bifurcation in literature, due to the difficulties of theoretical analyses and numerical simulations. In this paper, we study the characteristics of the second Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme recently developed by us. We numerically identify the critical Reynolds number of the second Hopf bifurcation located in the interval of(11093.75, 11094.3604) by bisection. In addition, we find that there are two dominant frequencies in its spectral diagram when the flow is in the status of the second Hopf bifurcation, while only one dominant frequency is identified if the flow is in the first Hopf bifurcation via the Fourier analysis. More interestingly, the flow phase portrait of velocity components is found to make transition from a regular elliptical closed form for the first Hopf bifurcation to a non-elliptical closed form with self-intersection for the second Hopf bifurcation. Such characteristics disclose flow in a quasi-periodic state when the second Hopf bifurcation occurs.     

Transition to chaos in lid-driven square cavity flow

To date, there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity, due to the difficulties in theoretical analysis and numerical simulations. In this paper, we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us. We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of (13944.7021,13946.5333) by the method of bisection. Through Fourier analysis, it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval. Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram, Kolmogorov entropy and maximal Lyapunov exponent. The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic.     

Numerical heat transfer analysis in turbulent channel flow over a side-by-side triangular prism pair

Heat transfer and flow behavior in a channel fitted with a transverse triangular prism pair is numerically investigated in the turbulent flow regime for the Reynolds number ranging from 10000 to 50000. The aspect ratio of channel height to the prism base is fixed at 4.0 throughout the study. The Navier-Stokes equation, along with the energy equation, is solved using a finite volume method with the SIMPLE technique and the QUICK numerical scheme for coupling the discretized equations while the standard k-ɛ turbulence model is used for closure of the problem. The numerical result reveals that heat transfer augmentation in the channel with the built-in prism pair can be obtained. It is observed that as compared to a channel, the heat transfer is enhanced by about 17% for a single triangular prism and by some 85% for a triangular prism pair mounted on the channel wall. Effects of the clearance between the prisms on the heat transfer augmentation are presented. The heat transfer enhancement is due to the vortex formation or recirculation zone downstream of the prism elements. However, the presence of the prisms also leads to higher values of friction loss over the channel.     

Numerical simulations of electro-thermo-convection and heat transfer in 2D cavity

In this article the electro-thermo-convective phenomena in a dielectric liquid enclosed in a 2D cavity and subjected to the simultaneous action of an electric field and a thermal gradient is studied. We solved directly the full set of coupled equations of Electro-Hydro-Dynamic (EHD) and energy equation using a finite volume method. In order to characterize the influence of the electric field on heat transfer the liquid is first heated (from a lateral wall) till the thermal steady state is obtained and then the electric potential and injection of electric charge is applied. Two cases of injection are considered: from the lower electrode and from a lateral wall (left or right). The flow pattern and Nusselt number strongly depend on the non-dimensional characteristic parameters: electrical parameter, Rayleigh number, Prandtl number and mobility parameter M. The convective motion passing from a purely thermal convection to a purely electrical convection and the number of electro-thermo-convective rolls patterns are investigated.As a consequence of the analysis of the combined effect of electric and thermal fields on the flow structure and on Nusselt number, we have also evaluated the heat transfer enhancement due to electroconvection. It is shown that the injection of electric charge increases the heat transfer and Nusselt number is independent of Rayleigh number for high enough values of T.     

Numerical investigation of heat transfer augmentation through geometrical optimization of vortex generators

In this paper a two-dimensional numerical simulation of a steady incompressible and turbulent model has been carried out to study the effects of vortex generators in a compact heat exchanger in a curvilinear coordinate system. The mesh which is applied in this study is boundary fitted and has been smoothed by a Laplace operator. Experimental data of a former study has been applied to validate the numerical results. The effects of geometrical variation are studied by adjusting vortex generators’ inclination and relative cross location. The major issue of this study is the optimal trade-off by selecting an optimal geometric, considering the opposite influences of geometrical variation on Nusselt number and pressure drop.     

带有纵向涡发生器的翅片管的流动与传热数值研究

用三维数值的研究方法对带有纵向涡发生器的翅片管流动和传热进行了数值研究。研究发现,使用了45°冲角的矩形小翼纵向涡发生器可以使得翅片管的传热增加10.4-24.6%,同时相应的压力损失增加30.5-57.2%。研究了不同的冲角(a=30,45,60)对于管翅间换热和流动的影响,结果显示冲角为30°时效果最好。     

Numerical visualization of vortex flow behavior in square jets in cross-flow

Direct numerical simulations have been performed in this study to visualize the flow behavior of single and multiple square jets issuing normally into a cross-flow. Three configurations are considered, a single jet located in the centre of the domain, twin jets in side-by-side (SBS) arrangement in the spanwise direction and triple jets in tandem arrangement with twin jets at the front and a third jet in downstream along the centre line. Simulation uses a jet to cross-flow velocity ratio of 2.5 and the Reynolds number 225, based on the free-stream quantities and the jet width. While the vortical structures predicted from single jet case were in good qualitatively agreement with the findings of other researchers, our results show that the process of merging between two counter-rotating vortex pairs (CRVP) in twin jets configurations is strongly dependent on the jet-to-jet edge distance. Further downstream in the far-field, results from the SBS twin jets show a most dominating larger CRVP accompanied with a smaller inner vortex pair. The observations are in good qualitative agreement with the experimental findings in the literature. The resulting flow structures of triple jets in tandem configuration have revealed, for the first time, more complicated flow interactions between individual jets and cross-flow, providing further insights of complex flow physics and its potential engineering applications.     

螺旋槽管管内湍流流动与换热的三维数值模拟

利用Fluent对5种不同槽深的螺旋槽管进行了模拟求解,得出了湍流状态下螺旋槽管内流体的速度场和温度场,从微观上说明了螺旋槽管的强化传热机理。分析了槽深对螺旋槽管阻力性能和换热性能的影响。数值计算结果表明,该类螺旋槽管在湍流工况下的平均Nu数大约是光管的1.6—2.1倍,平均阻力系数f大约是光管1.5—4.5倍。与实验数据进行比较发现,数值模拟具有相当的可靠性。     

湍流热对流中的动力学和传热研究

文章介绍了湍流热对流中流动结构和动力学的实验研究. 本文作者通过流动示标和粒子成像测速系统（PIV）的测量,清晰地揭示了对流系统的三维流动结构,发现大尺度环流的角向运动在不同的时间尺度上有不同的表现. 通过统计分析,本文作者进一步发现大尺度环流方位角的变化具有布朗棘齿的特性,并且从实验上证明在湍流热对流系统中不同的流动模式的确可以得到不同的传热效率.     

湍流热对流中的动力学和传热研究

文章介绍了湍流热对流中流动结构和动力学的实验研究．本文作者通过流动示标和粒子成像测速系统（PIV）的测量，清晰地揭示了对流系统的三维流动结构，发现大尺度环流的角向运动在不同的时间尺度上有不同的表现．通过统计分析，本文作者进一步发现大尺度环流方位角的变化具有布朗棘齿的特性，并且从实验上证明在湍流热对流系统中不同的流动模式的确可以得到不同的传热效率．     

On nonquasineutrality and turbulent heat transfer in a tokamak

A new approach is proposed for describing a steady turbulent state formed far from thermodynamic equilibrium in the plasma column of a tokamak as a result of the development of microinstabilities. A fundamental feature of such a highly nonequilibrium plasma is its nonquasineutrality, i.e., the plasma properties are largely determined by electric fields localized on a scale of the order of the Debye radius. It is established that the transverse thermal diffusivity is determined by the expression

Numerical analysis of roughness effect on microtube heat transfer

Roughness effect on the heat transfer and pressure loss performances of microscale tubes and channels are investigated through a finite element CFD code. Surface roughness is explicitly modelled through a set of random generated peaks along the ideal smooth surface. Different peak shapes and distributions are considered; geometrical parameters are representative of tubes in the diameter range from 50 to 150 μm. The use of a fine enough mesh allows the direct computation of tube performances under the assumption of incompressible fully developed flow. As a result, a significant increase in Poiseuille number is detected for all of the configurations considered, while the effect of roughness on heat transfer rate is smaller and highly dependent on the tube shape.     

Numerical study of unsteady MHD oblique stagnation point flow and heat transfer due to an oscillating stream

The unsteady stagnation point flow impinging obliquely on a flat plate in presence of a uniform applied magnetic field due to an oscillating stream has been studied. The governing partial differential equations are transformed into dimensionless form and the stream function is expressed in terms of Hiemenz and tangential components. The dimensionless partial differential equations are solved numerically by using well-known implicit finite difference scheme named as Keller-box method. The obtained results are compared with those available in the literature. It is observed that the results are in excellent agreement with the previous studies. The effects of pertinent parameters involved in the problem namely magnetic parameter, Prandtl number and impinging angle on flow and heat transfer characteristics are illustrated through graphs. It is observed that the influence of magnetic field strength increases the fluid velocity and by the increase of obliqueness parameter, the skin friction increases.