Turbulent natural convection flow and heat transfer in an inclined square enclosure

Numerical analysis was performed for the two-dimensional turbulent natural convection in an inclined enclosure. The enclosure has two walls which one is heated and the other cooled, and has the other two walls of the linear temperature distributions. The inclined angle is equal to zero when the wall of linear temperature was horizontal and increases counter-clockwise. The mean continuity, mean momentum and mean energy equations have been obtained by using the conventional time-averaging procesure. The turbulent model has been applied ak-ε two equation model of turbulence similar to the one proposed by the Launder and Spalding. Numerical results were studied for a series of inclined angle, ranging from 0° to 60° and for a Grashof number range of 6×10⁶∼10⁸. The average heat transfer rate on hot wall is shown maximum value at 30° regardless of Grashof number taken here. When Gr≥5×10⁷ and θ≥45°, the flow region of whole enclosure became a significant turbulence. This paper was presented at the International Symposium on the Refined Flow Modeling and Turbulent Measurement. Iowa City, Iowa, U.S.A., 1985     

A numerical study of shock wave/boundary layer interaction in a supersonic compressor cascade

A numerical analysis of shock wave/boundary layer interaction in transonic/supersonic axial flow compressor cascade has been performed by using a characteristic upwind Navier-Stokes method with various turbulence models. Two equation turbulence models were applied to transonic/supersonic flows over a NACA 0012 airfoil. The results are superion to those from an algebraic turbulence model. High order TVD schemes predicted shock wave/boundary layer interactions reasonably well. However, the prediction of SWBLI depends more on turbulence models than high order schemes. In a supersonic axial flow cascade at M=1.59 and exit/inlet static pressure ratio of 2.21, k-μ and Shear Stress Transport (SST) models were numerically stables. However, the k-μ model predicted thicker shock waves in the flow passage. Losses due to shock/shock and shock/boundary layer interactions in transonic/supersonic compressor flowfields can be higher losses than viscous losses due to flow separation and viscous dissipation.     

Analysis of two dimensional and three dimensional supersonic turbulence flow around tandem cavities

The supersonic flows around tandem cavities were investigated by two-dimensional and three-dimensional numerical simulations using the Reynolds-Averaged Navier-Stokes (RANS) equation with thek-ω turbulence model. The flow around a cavity is characterized as unsteady flow because of the formation and dissipation of vortices due to the interaction between the freestream shear layer and cavity internal flow, the generation of shock and expansion waves, and the acoustic effect transmitted from wake flow to upstream. The upwind TVD scheme based on the flux vector split with van Leer’s limiter was used as the numerical method. Numerical calculations were performed by the parallel processing with time discretizations carried out by the 4th-order Runge-Kutta method. The aspect ratios of cavities are 3 for the first cavity and 1 for the second cavity. The ratio of cavity interval to depth is 1. The ratio of cavity width to depth is 1 in the case of three dimensional flow. The Mach number and the Reynolds number were 1.5 and 4.5 × 10⁵, respectively. The characteristics of the dominant frequency between twodimensional and three-dimensional flows were compared, and the characteristics of the second cavity flow due to the first cavity flow was analyzed. Both two dimensional and three dimensional flow oscillations were in the ‘shear layer mode’, which is based on the feedback mechanism of Rossiter’s formula. However, three dimensional flow was much less turbulent than two dimensional flow, depending on whether it could inflow and outflow laterally. The dominant frequencies of the two dimensional flow and three dimensional flows coincided with Rossiter’s 2nd mode frequency. The another dominant frequency of the three dimensional flow corresponded to Rossiter’s 1st mode frequency.     

Effect of boundary layer swirl on supersonic jet instabilities and thrust

This paper reports the effects of nozzle exit boundary layer swirl on the instability modes of underexpanded supersonic jets emerging from plane rectangular nozzles. The effects of boundary layer swirl at the nozzle exit on thrust and mixing of supersonic rectangular jets are also considered. The previous study was performed with a 30° boundary layer swirl (S=0.41) in a plane rectangular nozzle exit. At this study, a 45° boundary layer swirl (S=1.0) is applied in a plane rectangular nozzle exit. A three-dimensional unsteady compressible Reynolds-Averaged Navier-Stokes code with Baldwin-Lomax and Chien’sk-ε two-equation turbulence models was used for numerical simulation. A shock adaptive grid system was applied to enhance shock resolution. The nozzle aspect ratio used in this study was 5.0, and the fully-expanded jet Mach number was 1.526. The “flapping” and “pumping” oscillations were observed in the jet’s small dimension at frequencies of about 3,900Hz and 7,800Hz, respectively. In the jefs large dimension, “spanwise” oscillations at the same frequency as the small dimension’s “flapping“ oscillations were captured. As reported before with a 30° nozzle exit boundary layer swirl, the induction of 45° swirl to the nozzle exit boundary layer also strongly enhances jet mixing with the reduction of thrust by 10%.     

Numerical analysis of the subsonic flow around a three-dimensional cavity

Flight vehicles such as wheel wells and bomb bays have many cavities. The flow around a cavity is characterized as an unsteady flow because of the formation and dissipation of vortices brought about by the interaction between the free stream shear layer and the internal flow of the cavity. The resonance phenomena can damage the structures around the cavity and negatively affect the aerodynamic performance and stability of the vehicle. In this study, a numerical analysis was performed for the cavity flows using the unsteady compressible three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equation with Wilcox’s turbulence model. The Message Passing Interface (MPI) parallelized code was used for the calculations by PC-cluster. The cavity has aspect ratios (L/D) of 2.5 ∼ 7.5 with width ratios (W/D) of 2 ∼ 4. The Mach and Reynolds numbers are 0.4 ∼ 0.6 and 1.6×10 ⁶ , respectively. The occurrence of oscillation is observed in the “shear layer and transient mode” with a feedback mechanism. Based on the Sound Pressure Level (SPL) analysis of the pressure variation at the cavity trailing edge, the dominant frequencies are analyzed and compared with the results of Rossiter’s formula. The dominant frequencies are very similar to the result of Rossiter’s formula and other experimental data in the low aspect ratio cavity (L/D = ∼ 4.5). In the large aspect ratio cavity, however, there are other low dominant frequencies due to the leading edge shear layer with the dominant frequencies of the feedback mechanism. The characteristics of the acoustic wave propagation are analyzed using the Correlation of Pressure Distribution (CPD). This paper was recommended for publication in revised form by Associate Editor Do Hyung Lee Hong-il CHOI received the B.S and M.S degrees in Aerospace Engineering from Chosun University, Korea in 2005 and 2008, respectively. He currently work at KOREA Electric Power Research Institute in Korea Pa-ul MUN received the B.S in Aerospace Engineering from Chosun University, Korea in 2008. He is currently Candidate for the degree of master of Aerospace Engineering at Chosun University in Korea. Jae-soo KIM received the B.S in Aerospace Engineering from Seoul National University in Korea in 1981. He then received his M.S and Ph.D. degree in Aerospace Engineering from KAIST in Korea in 1983 and 1987, respectively. He spent one year at Cornell university(USA) as a Post Doc. He worked at Korea Aerospace Research Institute for eight years. Dr. Kim is currently a Professor at the Department of Aerospace Engineering at Chosun University in Korea     

Effect of turbulence models on predicting HAWT rotor blade performances

The effect of turbulence models on predicting the aerodynamic performance of horizontal-axis wind turbine (HAWT) rotor blades has been investigated. The flow fields around the 2-D airfoil and the 3-D blade of the NREL phase VI wind turbine rotor have been analyzed, and the results are compared between a correlation-based transition model and two other fully turbulent models. The turbulence models selected are the Spalart-Allmaras fully turbulent one-equation model, the k-ω SST fully turbulent two-equation model, and the transition model. A vertex-centered finite-volume method based on an unstructured mesh technique was used to discretize the governing Navier-Stokes equations. The inviscid fluxes were calculated by using 2^nd order Roe’s FDS, and the viscous fluxes were evaluated in a central-differencing manner. For the time integration, an implicit method based on the Gauss-Seidel iteration was used. The results showed that the transition model well captures the laminar separation bubbles on the surface of the airfoil and the blade, and these separation bubbles trigger the separation-induced transition as the laminar flow separates and re-attaches as turbulent. The separation bubbles change the flow pattern on the surface of the airfoil and on the blade, and the pressure and skin-friction distributions are also changed abruptly across the laminar-turbulent transition. With properly predicted boundary-layer transition, the results of the transition model match well with the experiment. However, the results of the fully turbulent models deviate from the experiment due to the lack of the ability of capturing the boundary-layer transition. The adoption of a proper transition turbulence model is essential for the accurate prediction of the aerodynamic loads and also the rotor performance for horizontal-axis wind turbines.     

Turbulence modeling of natural convection in enclosures: A review

In this paper a review of recent developments of turbulence models for natural convection in enclosures is presented. The emphasis is placed on the effect of the treatments of Reynolds stress and turbulent heat flux on the stability and accuracy of the solution for natural convection in enclosures. The turbulence models considered in the preset study are the two-layer k − ɛ model, the shear stress transport (SST) model, the elliptic-relaxation (V2-f) model and the elliptic-blending second-moment closure (EBM). Three different treatments of the turbulent heat flux are the generalized gradient diffusion hypothesis (GGDH), the algebraic flux model (AFM) and the differential flux model (DFM). The mathematical formulation of the above turbulence models and their solution method are presented. Evaluation of turbulence models are performed for turbulent natural convection in a 1:5 rectangular cavity ( Ra= 4.3×10¹⁰) and in a square cavity with conducting top and bottom walls ( Ra= 9 1.58×10⁹) and the Rayleigh-Benard convection ( Ra = 2 × 10⁶ ∼ Ra = 10⁹). The relative performances of turbulence models are examined and their successes and shortcomings are addressed.     

Numerical simulation of flows around axisymmetric inlet with bleed regions

A numerical simulation of flows in an axisymmetric supersonic inlet with bleed regions is performed. An existing code which solves the Reynolds Averaged Navier-Stokes equations and the two-equation turbulence model equations is converted into an axisymmetric code. In addition, a bleed boundary condition model has been applied to the code. In this paper, the modified code is validated by comparing numerical results against experimental data and other computational results for flows on a bump and over an oblique shock with bleed region. Using the code, numerical simulation is performed for the flows in an inlet with multiple bleed regions.     

Mathematical modelling and experimental investigation on sun and solar drying of white mulberry

The drying kinetics of white mulberry was investigated in a solar dryer with forced convection and under open sun with natural convection. The constant rate period is absent from the drying curve. The drying process took place in the falling rate period. The drying data were fitted to the different mathematical models. The performance of these models was investigated by comparing the determination of coefficient (R), reduced chi-square (χ ²) and root mean square error (RMSE) between the observed and predicted moisture ratios. Among these models, the drying model developed by Logarithmic model showed good agreement with the data obtained from the experiments in the solar dryer with forced convection drying mode. The Verma et al. model has shown a better fit to the experimental mulberries data for open sun drying with natural convection mode than the other models. The effective moisture diffusivity values were estimated from Fick’s diffusional model. These values were 3.56×10⁻⁹ m²/s for solar drying and 2.40×10⁻⁹ m²/s for open sun drying.     

Assessment of a turbulence model for numerical predictions of sheet-cavitating flows in centrifugal pumps?

Various approaches have been developed for numerical predictions of unsteady cavitating turbulent flows. To verify the influence of a turbulence model on the simulation of unsteady attached sheet-cavitating flows in centrifugal pumps, two modified RNG k-? models (DCM and FBM) are implemented in ANSYS-CFX 13.0 by second development technology, so as to compare three widespread turbulence models in the same platform. The simulation has been executed and compared to experimental results for three different flow coefficients. For four operating conditions, qualitative comparisons are carried out between experimental and numerical cavitation patterns, which are visualized by a high-speed camera and depicted as isosurfaces of vapor volume fraction α _v = 0.1, respectively. The comparison results indicate that, for the development of the sheet attached cavities on the suction side of the impeller blades, the numerical results with different turbulence models are very close to each other and overestimate the experiment ones slightly. However, compared to the cavitation performance experimental curves, the numerical results have obvious difference: the prediction precision with the FBM is higher than the other two turbulence models. In addition, the loading distributions around the blade section at midspan are analyzed in detail. The research results suggest that, for numerical prediction of cavitating flows in centrifugal pumps, the turbulence model has little influence on the development of cavitation bubbles, but the advanced turbulence model can significantly improve the prediction precision of head coefficients and critical cavitation numbers.     

Analysis of the Pump-turbine S Characteristics Using the Detached Eddy Simulation Method

Current research on pump-turbine units is focused on the unstable operation at off-design conditions, with the characteristic curves in generating mode being S-shaped. Unlike in the traditional water turbines, pump-turbine operation along the S-shaped curve can lead to difficulties during load rejection with unusual increases in the water pressure, which leads to machine vibrations. This paper describes both model tests and numerical simulations. A reduced scale model of a low specific speed pump-turbine was used for the performance tests, with comparisons to computational fluid dynamics(CFD) results. Predictions using the detached eddy simulation(DES) turbulence model, which is a combined Reynolds averaged Naviers-Stokes(RANS) and large eddy simulation(LES) model, are compared with the two-equation turbulence mode results. The external characteristics as well as the internal flow are for various guide vane openings to understand the unsteady flow along the so called S characteristics of a pump-turbine. Comparison of the experimental data with the CFD results for various conditions and times shows that DES model gives better agreement with experimental data than the two-equation turbulence model. For low flow conditions, the centrifugal forces and the large incident angle create large vortices between the guide vanes and the runner inlet in the runner passage, which is the main factor leading to the S-shaped characteristics. The turbulence model used here gives more accurate simulations of the internal flow characteristics of the pump-turbine and a more detailed force analysis which shows the mechanisms controlling of the S characteristics.     

Geometrical effects on spray characteristics of air-pressurized swirl flows

In an effort to obtain the significant features associated with the ALR and length/diameter ratio of the final discharge orifice in swirling flows, experimental observations using a 3-D PDPA system were carried out. Profiles of SMD distributions depending on l _o /d _o , correlation between SMD and turbulence intensities in terms of l _o /d _o and correlations between droplet size and turbulence components were quantitatively analyzed. As discussed in a previous literature, an axisymmetric swirl angle of 30° was selected for this investigation because of its strong turbulence levels in the flow-field and finer droplet disintegrations. Three ALRs of 0.093, 0.106, and 0.122 as well as the length/diameter ratio of 0.15, 0.45, and 0.60 were chosen as parameters. Due to the complex interactions in swirling flows under these variables, this experimental observation will be of fundamental importance to the understanding of geometrical effects on spray trajectory. From the observations, it is indicated that increasing the ALR causes the spray development to be more dependent on number density and volume flux. The results indicated that the SMD decreases discernibly with smaller l _o /d _o , substantiating the fact that turbulence intensities are inversely proportional to the SMD. But, l _o /d _o is quite proportional to the SMD.     

Total pressure fluctuations and two-phase flow turbulence in self-aerated stepped chute flows

Current knowledge in high-velocity self-aerated flows continues to rely upon physical modelling. Herein a miniature total pressure probe was successfully used in both clear-water and air-water flow regions of high-velocity open channel flows on a steep stepped channel. The measurements were conducted in a large size facility (θ=45°, h=0.1 m, W=0.985 m) and they were complemented by detailed clear-water and air-water flow measurements using a Prandtl-Pitot tube and dual-tip phase-detection probe respectively in both developing and fully-developed flow regions for Reynolds numbers within 3.3×10⁵ to 8.7×10⁵. Upstream of the inception point of free-surface aeration, the clear-water developing flow was characterised by a developing turbulent boundary layer and an ideal-flow region above. The boundary layer flow presented large total pressure fluctuations and turbulence intensities, with distributions of turbulence intensity close to intermediate roughness flow data sets: i.e., intermediate between d-type and k-type. The total pressure measurements were validated in the highly-aerated turbulent shear region, since the total pressure predictions based upon simultaneously-measured void fraction and velocity data agreed well with experimental results recorded by the total pressure probe. The results demonstrated the suitability of miniature total pressure probe in both monophase and two-phase flows. Both interfacial and water phase turbulence intensities were recorded. Present findings indicated that the turbulence intensity in the water phase was smaller than the interfacial turbulence intensity.     

Three-dimensional effects of supersonic cavity flow due to the variation of cavity aspect and width ratios

Unlike the steady closed-type supersonic cavity flow, open-type cavity flow is divided into internal and external flows by turbulent shear layer. The cavity flow may cause resonance phenomena due to pressure oscillation, depending on the cavity geometry and the flow conditions. These phenomena may induce noise generation, structural damage, and aerodynamic instability. In this research, the flow characteristics of three-dimensional supersonic cavity flow of Mach number 1.5 were analyzed with the variations of aspect ratio and width ratio. Three-dimensional unsteady compressible Reynolds-averaged Navier-Stokes (RANS) equations were used with a turbulence model. For numerical calculations, the 4th-order Runge-Kutta method and the FVS method with van Leer’s flux limiter were applied. The numerical calculations were performed by using a parallel processing program with 16 CPUs. The sound pressure level (SPL) spectra of pressure variations were analyzed at the point of cavity leading edge. The correlation of pressure distribution (CPD) was also analyzed for the propagation of dominant oscillation pressure waves with respect to the reference point of the cavity leading edge. The dominant oscillation frequency was compared with the oscillation modes of Rossiter’s formula. Oscillation Mode 2 appeared as a dominant oscillation frequency regardless of the aspect ratio of cavity in the two-dimensional flow. Oscillation Modes1 and 2 appeared in three-dimensional cavities of small aspect ratios. However, as the aspect or the width ratio increases, only the mode 2 or 3 frequency appeared as a dominant oscillation frequency.     

Numerically analyzed supersonic flow structure behind the exit of a two-dimensional micro nozzle

The compressible flow field is numerically analyzed in a two-dimensional converging-diverging nozzle of which the area ratio, exit to throat, is 1.8. The solver is FLUENT and the embedded RNG k − ε model is adopted to simulate turbulent flow. The plume characteristics such as shock-cell structure are discussed when nozzle pressure ratio and stagnation temperature at the nozzle entrance are varied. The downstream flow field can be classified into two types based on the shock shapes generated near the nozzle exit. First, a reiterative pattern in the plume is not formed between the slip streams in case that a strong lambda-type shock wave exists. Second, when oblique shock waves are crossing each other on the nozzle centerline, a shock cell structure appears in the plume field. Even when the flow field is changed due to stagnation temperature, the upstream of the shock wave is little affected. Especially, the pressure distributions on the nozzle centerline behind the shock wave are rarely influenced by the stagnation temperature, that is, the product of density and temperature is nearly constant provided that the working fluid is a perfect gas. Therefore, the pressure field shows quasi-isobaric behavior far downstream.     

An analysis of turbulent flow around a NACA4412 airfoil by using a segregated finite element method

A turbulent flow around a NACA4412 airfoil is simulated by a segregated finite element method based on the SIMPLE algorithm and the low Reynolds numberk-ω turbulence model. The originalk-ω model and a modified version of thek-ω, model (shear stress transport model) are adopted, for which grid independent solutions are obtained, respectively. From the present numerical experiment, it has been shown that the segregated finite element method with thek-ω turbulence model can predict the turbulent flow leading to separation satisfactorily with apparently reduced memories compared with the mixed integrated formulation. It is also recommended that for the analysis of external flows a modifiedk-ω model should be used instead of the originalk-ω model, which combines the features of both the standardk-ε model and the originalk-ω model.     

Multiple source modeling of low-reynolds-number dissipation rate equation with aids of DNS data

The paper reports a multiple source modeling of low-Reynolds-number dissipation rate equation with aids of DNS data. The key features of the model are to satisfy the wall limiting conditions of the individual source terms in the exact dissipation rate equation using the wall damping functions. The wall damping functions are formulated in term of dimensionless dissipation length scalel _D ⁺(≡l _D (νε)^1/4/ν) and the invariants of small and large scale turbulence anisotropy tensors,a_ij ( = [`(u_i u_j )] /k - 2d_ij /3)a_{ij} ( = \overline {u_i u_j } /k - 2\delta _{ij} /3) ande _ij (=ε _ij /ε-2δ _ij /3). The model constants are optimized with aids of DNS data in a plane channel flow. Adopting the dissipation length scale as a parameter of damping function, the applicabilities ofk-ε model are extended to the turbulent flow calculation of complex flow passages.     

Experimental and numerical study of heat transfer downstream of an axisymmetric abrupt expansion and in a cavity of a circular tube

This research is an experimental and numerical investigation of heat transfer and fluid flow characteristics in separated, recirculated and reattached regions created by an axisymmetric abrupt expansion and by an abrupt expansion followed by an abrupt contraction (called a “cavity”) in a circular tube at a uniform wall temperature. The flow just upstream of the expansion was unheated and proved to be fully-developed at the entrance to the heated cavity region. Local heat transfer coefficients were measured using a balance-type isothermal heat flux gage. Measurements were made at a small-to-large tube diameter ratio of d/D = 0.4 and downstream Reynolds numbers ranging from Re_D = 4,300 to 44,500. Generally, the maximum Nusselt numbers downstream of an axisymmetric abrupt expansion at a uniform wall temperature occur between 9 and 12 step heights from the expansion step. Numerical simulation has been carried out by a two-equation turbulence model and its results such as mean velocity profiles and local Nusselt numbers are in good agreement with experimental results.     

Unsteady numerical analysis of the liquid-solid two-phase flow around a step using Eulerian-Lagrangian and the filter-based RANS method

The present study adopts the filter-based RANS (k-ε) method to analyze unsteady liquid-solid two-phase flow around a step in a rectangle channel. Numerical simulation was carried out in three dimensions using Eulerian-Lagrangian approach, in which the continuous phase is treated by Eulerian method and the motions of the dispersed phases are solved by Lagrangian method. The filter-based unsteady RANS (k-ε) model was implemented via user-defined functions in ANSYS Fluent 14.0. The flow field measurement by PIV experiment and the pressure fluctuation downstream the step were carried out for validation. Based on the comparison between the numerical and experimental data, results show that the pressure and velocity distributions were successfully reproduced. Compared with the standard k-ε model, the filter-based model can improve the prediction accuracy for wake flow and particle motion downstream the step. Furthermore, the numerical simulation reveals that the vorticity described by Q-criterion, promotes the particle motion at the wake area. However, the significant discrepancy of the particle distribution in the wake indicates the importance of turbulence modeling method for liquid-solid two-phase flow simulation.

     

Extended two-fluid model applied to analysis of bubbly flow in multiphase rotodynamic pump impeller

This paper presents an extended two-fluid model based on the Navier-Stokes equations and the standard κ — ε turbulence model, to simulate the threedimensional air-water bubbly flow in turbo machinery. In the governing equations, the drag force and added mass force are added and the additional source terms arising from fluctuations of gas volume fraction are considered. The discrete equations are solved using a developed twophase semi-implicit method for pressure-linked equations, consistent (SIMPLEC) algorithm in body-fitted coordinates with a staggered grid system. Simulation is then carried out for the pure liquid flow and air-water two-phase flow with the inlet gas volume fraction being 15% in a multiphase rotodynamic pump impeller and the pump head performance is predicted. Comparison with experimental results shows the reliability and commonality of the numerical model.