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.     

几何尺寸对矩形微通道液体流动和传热性能的影响

基于连续介质方法数值研究液体在不同几何结构微通道中的流动和传热性能。在相同热边界条件下,通过比较水力直径、通道长度和宽高比等几何参数对液体微流动的影响,得到各参数对泊肃叶数(Po)和努塞尔数(Nu)的影响关系。研究发现,截面宽高比越大,Po数越小,且雷诺数对泊肃叶数基本无影响;雷诺数(Re)小于500情况下,水力直径小于0.545 mm时,Po数随水力直径减小而减小,水力直径大于0.545 mm时,水力直径变化对Po数基本无影响;Po数不随通道长度变化而变化,但略受流动雷诺数影响;在Re=20～1 800时,Nu数正比于水力直径和宽高比,但是通道长度对Nu数的作用受流动Re数的影响;在通道材料和流动介质相同的条件下,Nu数和Re数之间的关系受通道几何参数的影响,并且拟合得到其关系式。     

Pollutant dispersion over two-dimensional hilly terrain

Numerical prediction of the wind flow and pollutant dispersion over two-dimensional hilly terrain is presented. The wind tunnel experiments are conducted to validate the numerical results of the flow field. Measured mean velocity profiles, turbulence characteristics, and surface pressure distributions show good agreement with the numerical predictions. The hypothesis of Reynolds number independency for an atmospheric boundary layer flow over aerodynamically rough terrain is numerically confirmed. The linear theory provides generally good prediction of speed-up characteristics for gently sloped low hills. The effect of two-dimensional double hills on the dispersion of pollutants from continuously or temporally released line source of different emission heights and locations is also investigated. The ground-level concentrations are considerably reduced as emission heights are increased. The variances of ground-level concentration with respect to time from a temporally released source are strongly influenced by the flow separation.     

Performance analysis of four-pad hydrostatic squeeze film dampers loaded between pads under laminar and turbulent flow conditions

This paper presents a theoretical study of the effects of Poiseuille Reynolds number and eccentricity ratio on the performance of four-pad hydrostatic squeeze film dampers. The finite difference method has been used to solve Reynolds equation based on Constantinescu’s turbulent lubrication theory. The numerical results obtained are analysed and compared between three and four-lobe hybrid journal bearings. The computed results indicate that the performance of a hydrostatic squeeze film damper loaded between pads is significantly influenced by the flow regimes. The results presented in this work can be useful to the bearing designers.     

Two-dimensional aperiodic flows in a rectangle subject to a harmonic forcing

An unsteady two-dimensional incompressible flow inside a rectangular container under a torsional oscillation has been numerically obtained. Effect of three parameters, the aspect ratio, the dimensionless angular frequency, and the Reynolds number, on the flow pattern’s development is studied. The flow is irregular and aperiodic at the Reynolds number 5000. Some aspects of the vortical flow dynamics are investigated. Observed in the numerical experiment are stretching, folding, splitting, merging, and curling etc.     

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     

CFD analysis of the performance of elbow-meter with high concentration coal ash slurries

Elbow meter is a simple flow measuring device and its characteristics for the flow of single-phase fluids are reasonably well understood and the functional dependence of elbow meter coefficient (C_k) on parameters like Reynolds Number, radius ratio, pipe roughness etc. Is well documented in literature. Elbow meters are also being used for solid liquid flow in many industries. The present study aims to establish the characteristics of an elbow meter for high concentration coal ash slurry pipelines using validated CFD. High concentration coal ash slurries are known to behave as homogeneous fluids exhibiting behavior as Bingham plastic fluids. The validated CFD methodology has been used to predict the values of C_k for the flow of Bingham plastic fluid and establish its dependence on radius ratio, Hedstrom Number and Bingham Reynolds Number. Further, for the flow of high concentration fly ash slurry flows, C_k for any given radius ratio is observed to be independent of Hedstrom Number (over the range investigated He ≤ 10⁵). Further, in fully turbulent flows, beyond a critical Reynolds number (Re_B ≥ 5.3 × 10³), C_k remains constant and is dependent only on the radius ratio.     

Numerical modeling of combustion processes and pollutant formations in direct-injection diesel engines

The Representative Interactive Flamelet (RIF) concept has been applied to numerically simulate the combustion processes and pollutant formation in the direct injection diesel engine. Due to the ability for interactively describing the transient behaviors of local flame structures with CFD solver, the RIF concept has the capabilities to predict the auto-ignition and subsequent flame propagation in the diesel engine combustion chamber as well as to effectively account for the detailed mechanisms of soot formation, NO_X formation including thermal NO path, prompt and nitrous NO_X formation, and reburning process. Special emphasis is given to the turbulent combustion model which properly accounts for vaporization effects on the mixture fraction fluctuations and the pdf model. The results of numerical modeling using the RIF concept are compared with experimental data and with numerical results of the commonly applied procedure which the low-temperature and high-temperature oxidation processes are represented by the Shell ignition model and the eddy dissipation model, respectively. Numerical results indicate that the RIF approach including the vaporization effect on turbulent spray combustion process successfully predicts the ignition delay time and location as well as the pollutant formation.     

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.     

矩形进料体高宽比对旋流器流场和分离性能影响的数值模拟

横截面为矩形的进料体比圆形的分离性能更好,但是一直没有找出矩形进料体合适的高宽比.本文采用数值分析法研究了矩形进料体的高宽比对直径为75 mm旋流器分离性能的影响,将数值结果与Hsieh经典试验结果进行了对比,发现两者有良好的一致性,验证了该方法的有效性.探究了进料体不同高宽比下的压力场、速度场、湍流场和分离效率.结果...     

Taylor Vortices–Induced Instability (Transition Flow) versus “Turbulence” in Concentric Cylinders Separated by Microscale Clearances

This paper is concerned with the relationship between the onset and the development of the Taylor instabilities and their treatment as turbulent flows in the most accepted turbulence models (Constantinescu (1); Ng-Pan (2); Hirs (3)) used with the Reynolds equation, in the range of 41.3√R/C < Re < 2000. The authors show that in between these limits there is a transition regime where the velocity and pressure profiles are fundamentally different from either a Couette flow or a fully developed turbulent flow. Thus the issue under consideration is whether the flow formations observed during Taylor instability regimes should be simulated using the widely accepted turbulence models as they presently are modeled in microscale clearance flows. We are considering the flow of light silicone oil in gaps varying from 3.302 mm (0.13 in.) to 0.127 mm (0.005 in.) between two concentric cylinders, with the inner cylinder rotating. The computational engine used in this study is a well-established and a tried software package: CFD-ACE+. It was found that the Taylor vortices (cells) begin to form at certain, but different, “critical” speeds, function of clearance size, and as the speed grows, the vortices become fully developed and evolve further into wavy vortices. Calculations show that both the 1st and 2nd critical Taylor numbers and Reynolds numbers are functions of the clearance size. The Taylor numbers decrease, while the Reynolds numbers increase with the decrease in clearance size. The onset of both instabilities is clearly characterized by the discontinuities in the Torque-√Ta (or Torque – Re) curve slope. The calculations presented here show that the slope changes in the above-mentioned graphs are due to the changes in the average velocity gradient on the outer cylinder and not to a change in the actual viscosity as it is implemented by the turbulence models mentioned above. Finally a comparison is made between present calculations and the data of Roberts (4), Cole (5), Walowit et al. (6), Weinstein (7), Koschmieder (8), and DiPrima (9).     

A near-wall reynolds stress model for backward-facing step flows

A near-wall Reynolds stress model has been used in numerical computations for two-dimensional, incompressible turbulent flows over backward-facing steps. Numerical results are compared with Direct Numerical Simulation data as well as experimental data for flow quantities such as the skin friction, wall pressure,U-velocity and the Reynolds stress. Budgets of the transport equations for theU-velocity, turbulence kinetic energy,k and the Reynolds shear stress,— are also calculated and compared with the Direct Numerical Simulation data. The comparison reveals that the near-wall Reynolds stress model predicts the reattachment length fairly accurately. The near-wall Reynolds stress model also predicts the development of the boundary layer downstream of the reattachment point correctly when the Reynolds number is low. However, the model generally predicts a weak separation bubble and a slowly developing boundary layer when the Reynolds number is high.     

Spatial resolution effects on unsteady turbulent flow computations for the rectangular cylinders byκ-ε turbulence models

In predicting unsteady turbulent flows around a square cylinder usingκ-ε turbulence models, choice of right turbulence models was found to be critical. If a proper care is taken to choose a convection scheme and near-wall resolution, the conventional turbulence models may predict an unsteady turbulent flow at low Reynolds numbers with reasonable accuracy. A systematic computation is carried out to identify the effects of the aspect ratio of a rectangular cylinder and of the flow Reynold number on the spatial resolution requirement. It is found in general that the grid resolution requirement is more stringent for a cylinder with a smaller aspect ratio. By investigating high Reynolds number computations, the grid refinement in terms of viscous wall units is found unimportant in accurately predicting the unsteady aerodynamic forces on the cylinder. Instead, resolution of shear layers formed at the forward separation corners is found to be more critical.     

Numerical simulation of flow past rectangular cylinders with different aspect ratios using the incompressible lattice Boltzmann method

This paper presents a numerical study of a uniform flow past a rectangular cylinder using the incompressible lattice Boltzmann method (ILBM). Firstly, we use the ILBM to simulate the flow past a square cylinder symmetrically placed in a two-dimensional channel and results are validated against the well-resolved results obtained using finite-difference method and finite-volume method. Secondly, the effects of the aspect ratio defined as R = width/height on the fluid forces, vortex shedding frequency and the flow structures in the wake are investigated. Aspect ratios ranging from 0.15 to 4.00 and four Reynolds numbers Re = 100, 150, 200 and 250 are selected for the investigation. The results show that the effects of aspect ratio on physical quantities such as drag and lift coefficients, Strouhal number and the vortex shedding mechanism are very notable in the range between 0 and 2. In general, the drag coefficient decreases with the aspect ratio and the decreasing rate is more distinct in the range of 0.15 ≤ R ≤ 2.0. There is no local maximum found at around R = 0.6 in the drag coefficient as reported for higher Reynolds numbers in the literature. However the root-mean-square value of the lift coefficient shows a maximum value at R ≈ 0.5 for all Reynolds numbers selected. The variation of Strouhal number with R appears to be different for four selected Reynolds numbers. Especially for Re = 250, a discontinuity in St, as has been observed for higher Reynolds numbers, is observed at around R = 1.45 where multiple peaks are found in the result of Fourier spectrum analysis of the lift force and irregular vortex shedding behavior with no fixed shedding frequency is observed from the instantaneous vorticity contours. Such discontinuity is not observed for Re = 100, 150 and 200. The present results using the LBM are compared with some existing experimental data and numerical studies. The comparison shows that the LBM can capture the characteristics of the bluff body flow well and is a useful tool for bluff body flow studies.     

Comparison of DNS and Reynolds stress modelling of flow around a rotating cylinder

The low Reynolds number stress-omega model is applied to flow associated with a rotating cylinder operating in a larger, stationary cylinder. The working fluid fills the gap between the cylinders. Direct numerical simulation data are used to test the predictions by this turbulence model. Previous work has shown that simpler models are unable to predict with reasonable accuracy the wall shear stress experienced by the rotating cylinder. The present study with a more complex turbulence model shows that the wall shear stress on the rotating cylinder is underestimated significantly. Examination of turbulence velocity fluctuation intensity distributions points to underprediction of the streamwise turbulence level and excessive values of the wall normal turbulence level. Results are given for no shear and a wall shear at the outer cylinder surface but no effect on the inner cylinder statistics was found. An examination of the Reynolds stress anisotropy tensor components highlights a significant deficiency in this parameter which is an essential component of the pressure-strain modelling of Reynolds stress models. The most significant aspect is a rapid decrease of the streamwise component of the Reynolds stress anisotropy tensor relative to the direct numerical simulation results and values which are too low for the other two components.     

A comparison study between navier-stokes equation and reynolds equation in lubricating flow regime

For practical calculations, the Reynolds equation is frequently used to analyze the lubricating flow. The full Navier-Stokes Equations are used to find validity limits of Reynolds equation in a lubricating flow regime by result comparison. As the amplitude of wavy upper wall increased at a given average channel height, the difference between Navier-Stokes and lubrication theory decreased slightly ; however, as the minimum distance in channel throat increased, the differences in the maximum pressure between Navier-Stokes and lubrication theory became large.     

A turbulent friction and heat transfer study of dispersed fluids with ultra-micronized metallic particles

Turbulent friction and heat transfer behaviors of dispersed fluids with ultra-micronized metallic particles are experimentally investigated in a circular pipe. Viscosity measurements are also conducted by using a viscometer. Aqueous mixtures with γ-Al₂O₃ and TiO₂ particles of which the mean diameters are 13 and 27 nm, respectively, are used to represent the dispersed fluids. The ranges of Reynolds and Prandtl numbers tested are 10⁴～10⁵ and 5.6～10.7, respectively. The relative viscosity of the dispersed fluid with γ-Al₂O₃ particles is about two hundred at the 10% volume concentration, while that of the dispersed fluid with TiO₂ particles is about twenty at the same volume concentration. Both of the relative viscosities are the unexpected results compared with predictions from classical theory of suspension rheology. Darcy friction factors for the comparatively dilute dispersion fluids used in present study coincide well with Kays correlation for tubulent flow of a single phase fluid, which implies that additional pumping power is not required despite adding solid particles into water. The Nusselt number of both the dispersed fluids for fully developed turbulent flow increases with increasing the volume concentration as well as the Reynolds number as expected. At the maximum volume concentration of 3% approximately, the percentage heat transfer enhancement due to addition of particles for the γ-Al₂O₃ and TiO₂ dispersing fluid systems are 60% and 30%, respectively. Under the range of volume concentration in the present study, the new correlation for turbulent convective heat transfer for both of the dispersed fluids is given by the following equation: Nu=0.021Re^0.8Pr.^0.5     

THD Effects of Static Performance Characteristics of Infinitely Wide Turbulent Journal Bearings

Formulas for static parameters were found for infinitely wide turbulent full journal bearings that correlate either load capacity or friction coefficient for thermohydrodynamics (THD) effects in terms of a single THD parameter. The database was built by numerical simulation of turbulent liquid lubricant flows with various eccentricity ratios in a wide range of the Reynolds number for both isoviscous and THD cases. The least-squares method was applied to the groups of parameters yielding the formulas of load capacity, friction coefficient, and attitude angle. The isoviscous attitude angle was fitted as a function of the maximum-to-minimum film thickness ratio, and the variation of attitude angle due to THD is linearly dependent on the THD-to-isoviscous load capacity ratio. With the formulas provided in this study, designers can quickly determine static parameters of turbulent journal bearings without the burden of labor-intensive numerical computation of the governing differential equations.     

A novel comprehensive correlation for discharge coefficient of square-edged concentric orifice plate at low Reynolds numbers

Among various differential pressure flow meters, the orifice meter has gained its publicity in applications where cost, space, and ease of maintenance are of high priority. A major problem associated with the use of orifice flow meters at low Reynolds number flows is the significant variation of discharge coefficient (C_d) as a function of orifice geometry and the Reynolds number. In this work, a two-dimensional axisymmetric numerical model was applied to the investigation of viscous, incompressible flow through square-edged concentric orifice plate for the purpose of studying the performance of discharge coefficient consequent to variations of Reynolds number (Re), orifice/pipe diameter ratio (β), and orifice thickness ratio (t*). The analysis of numerical results by means of multiple regression method has yielded a new correlation incorporating the effect of the parameters under study on orifice meter discharge coefficient for orifice bore Reynolds numbers (Re_o) < 250. Results of relevant investigations from the literature are used in the present work as references for the validation of the numerical model as well as the proposed correlation for discharge coefficient.     

A thermohydrodynamic analysis of journal bearings operating under turbulent conditions

An estimate of temperatures and pressures of a hydrodynamic journal bearing operating in the turbulent range has been obtained by the simultaneous numerical solution of the energy and Reynolds equations accounting for the variation of lubricant properties. The method has been applied to a particular bearing geometry and lubricant, and it is demonstrated that large reductions in load-carrying capacity result which are accompanied by, to a lesser extent, reduced bearing power loss.