Inlet Flow Angle Research Articles

Area Schedule Based Design of High-Pressure Recovery Radial Diffusion Systems

High-pressure ratio centrifugal compressors require advanced diffusion systems to achieve enhanced efficiencies set by future turbocharger applications. To address the shortcomings of the commonly used channel diffuser and airfoil cascade design perspectives, a streamtube based area schedule is adopted paying special attention to the diffuser entry region. It is shown that the diffusion in the semivaneless space, controlled chiefly by inlet flow angle and the vane suction side geometry, plays a key role in improving diffuser performance. Removing excess thickness from the suction side eliminates flow overspeed, increases effective diffusion length, and leads to higher pressure recovery at reduced stagnation pressure loss. The pressure side thickness distribution controls the channel area schedule. Thin leading edges (LEs) ensure smooth flow area transition into the channel and reduce the vane upstream influence, mitigating high-cycle fatigue related mechanical issues.

Thermal design exploration of a swirl flow microchannel heat sink for high heat flux applications based on numerical simulations

Numerical simulations of velocity and temperature fields to explore the design of a single phase microchannel cooling system with spiraling radial inflow for high heat flux applications are presented. Total pressure drop and average wall heat flux are calculated for different flow rates and the effects of changing the microchannel height, flow inlet angle, and working fluid are investigated. Rotation of the fluid induces a crossflow and entrainment, this is found to enhance convective heat transfer considerably due to motion of fluid towards the heat exchange surface. The strength of this effect depends on the structure of hydrodynamic boundary layers, which is characterized by the Reynolds number and the flow inlet angle. The effect of reducing the Prandtl number is evaluated changing the working fluid from water to a 2vol% and a 4vol% water-Cu nanofluid suspension. For the cases studied, it is found that heat transfer enhancement by increasing the inlet swirl is greater than that of decreasing the Prandtl number using a nanofluid, though at a much higher pumping cost. In order to improve the performance of the device for high heat flux applications, admission of the flow should be as tangential as practically possible. It is found that, when reducing the microchannel height, boundary layers may merge and the entrainment effect is lost, therefore the total heat flux may not always increase with a decrease of the flow passage area, as opposed to conventional microchannels. The swirl flow microchannel heat sink showed promising cooling characteristics for applications such as thermal management of electronics or concentrated photovoltaics, with a ratio of pumping cost to heat rate of 0.02% for the base design studied.

Investigation of aerodynamic and energy characteristics of L.P.C. compartment of stages with inlet pipe and leak system for powerful steam turbine unit

The results of computational and engineering developments and numerical studies of the inlet pipe compartment with the first three stages are represented, taking into account the steam extraction, leak ages under the diaphragms, shroud seals and discharge openings in the disks of low pressure cylinder of the turbine K-1250-6,9/25. All the computations were based on the model of one speed wet steam flow without droplets and supercooling was not taken into account. The sectorial approach was applied to description of the interaction of the inlet pipe and the group stages. The stages were considered in steady state formulation. The initial data and boundary conditions were taken basing on thermal design of ²TURBOATOM². Some methodological aspects and the results of improving of studied facilities by numerical experiment by MTFS® code are discussed. It is shown that the main total pressure loss in inlet pipe arises in collector and in place of its connection with tube. The improvement of inlet pipe annular collector due to the profiled sheets and input tube knee reduces the internal loss coefficient in 2 times. The axial length of the radial-axial outlet channel increase and the height of the splitter reduction almost no effect on the internal losses, but significantly (by 45%) reduce the coefficient of circumferential non-uniformity of static pressure at the stage inlet. Based on the item-evaluation of the effectiveness the final version of the inlet (M7) is developed. It is revealed that the inlet flow angles on the nozzle edges in the left and right sides of the inlet pipe are substantially symmetrical, i.e. the back effect of stages on the inlet pipe is small. The KE loss on the nozzles of 1st stage in the different sectors is different; on sectors of 1st blade row the loss and load are uniform. This effect persists for the next stages. Studies of the first three stages of the compartment based on leaks through the seal and discharge openings, sucking and suction, steam extraction showed that the root suctions behind the nozzles comply with the recommendations of MEI. Design of new seal for blade rows of 1st and 2nd stages in real boundary conditions showed a relatively high efficiency and the weak dependence on flow rate for axial position of the rotor relatively to the stator. // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o

An Experimental Investigation of the Performance Impact of Swirl on a Turbine Exhaust Diffuser/Collector for a Series of Diffuser Strut Geometries

A comprehensive experimental investigation was initiated to evaluate the aerodynamic performance of a gas turbine exhaust diffuser/collector for various strut geometries over a range of inlet angle. The test was conducted on a 1/12th scale rig developed for rapid and accurate evaluation of multiple test configurations. The facility was designed to run continuously at an inlet Mach number of 0.40 and an inlet hydraulic diameter-based Reynolds number of 3.4 × 105. Multihole pneumatic pressure probes and surface oil flow visualization were deployed to ascertain the effects of inlet flow angle and strut geometry. Initial baseline diffuser-only tests with struts omitted showed a weakly increasing trend in pressure recovery with increasing swirl, peaking at 14 deg before rapidly dropping. Tests on profiled struts showed a similar trend with reduced recovery across the range of swirl and increased recovery drop beyond the peak. Subsequent tests for a full diffuser/collector configuration with profiled struts revealed a rising trend at lower swirl when compared to diffuser-only results, albeit with a reduction in recovery. When tested without struts, the addition of the collector to the diffuser not only reduced the pressure recovery at all angles but also resulted in a shift of the overall characteristic to a peak recovery at a lower value of swirl. The increased operation range associated with the implementation of struts in the full configuration is attributed to the deswirling effects of the profiled struts. In this case, the decreased swirl reduces the flow asymmetry responsible for the reduction in pressure recovery attributed to the formation of a localized reverse-flow vortex near the bottom of the collector. This research indicates that strut setting angle and, to a lesser extent, strut shape can be optimized to provide peak engine performance over a wide range of operation.

吹き出し角によるサイクロンセパレータの空力騒音特性の考察

吹き出し角によるサイクロンセパレータの空力騒音特性の考察

Aerodynamic Characteristics of Steam Turbine Prismatic Blade Section

For the needs of high-performance steam turbines producer the data of a blade section measurement have been analyzed in detail using an experimental and numerical approach. The blade section is used on prismatic blades in high and medium pressure steam turbine parts. The linear blade cascade was tested at four pitch/chord ratios at two different stagger angles. The blade cascade was tested under two levels of Reynolds number in the range of output izentropic Mach numbers from 0.4 to 0.9.The inlet of the test section was measured pitch-wise by five-hole probe to determine the inlet flow angle. The free stream turbulence of inlet flow was determined at 2.5% what is very close to the operating conditions on first high pressure stages. Two-dimensional flow field at the center of the blades was traversed pitch-wise downstream the cascade by means of a five-hole needle pressure probe to find out the overall integral characteristics. The blade loading was measured throughout surface pressure taps at the blade center. An in-house code based on a system of Favre-averaged Navier-Stokes equation closed by non-linear two-equation EARSM k-ω turbulence model was adopted for the predictions. The code utilizes an algebraic model of bypass transition valid for both attached and separated flows taking into account the effect of free-stream turbulence and pressure gradient. Results are presented by integral characteristic in means of kinetic energy loss coefficient and velocity or pressure distribution in the blade wakes or on the blade surface. In this article, the effect of investigated criteria and comparison of experimental and numerical approach are presented and discussed.

Experimental and numerical investigation of outlet guide vane and endwall heat transfer with various inlet flow angles

This paper investigates the heat transfer on the outlet guide vane (OGV) surface and its endwall region. The Reynolds number is fixed at 300,000 and the flow is subsonic. The inlet flow angle is varied from +25° (on-design), to +40° and −25° (off-design). Experiments were conducted in a linear cascade test facility using thermochromic liquid crystal technique. Numerical simulations using RANS were carried out with three turbulence models, i.e., standard k–ω model (k–ω), baseline k–ω model (BSL), and shear stress transport k–ω model (SST). Both the experimental and numerical results are provided and compared. On the OGV surface, boundary layer transition and separation affect the heat transfer significantly and they vary with the inlet flow angle. The abilities of the three models to predict these heat transfer behaviors are revealed. For the on-design case, both BSL and SST models capture the main feature of the heat transfer variations due to transition, but the k–ω model fails. For off-design cases where separation occurs, there are discrepancies found between the calculations and experimental data. On the endwall region, the effects of a horseshoe vortex (HV) on the heat transfer are clearly noticed at the leading edge (LE). The three models perform well to simulate the pitchwise averaged Nusselt number while they always over-predict the strength and size of the HV, which leads to higher heat transfer there compared to the measurements. For off-design conditions, the HV becomes more energetic than that of the on-design condition and the pressure side leg departs from the OGV at the inlet flow angle α=−25°.

A high-order sensitivity method for multi-element high-lift device optimization

A complete procedure to study and optimize a multi-element high-lift device is presented and applied to the L1T2 test case. The direct Reynolds-Averaged Navier–Stokes (RANS) simulations of the reference configuration first reveal the importance of the size of the computational domain to correctly capture the potential effects generated by the L1T2 configuration. A parameterized Navier–Stokes approach based on a high-order sensitivity technique is then used as a surrogate model for solution reconstructions. This approach has the advantage to ask for only one parameterized RANS simulation around a reference configuration. The results stress the importance to account for higher derivatives and turbulence effects for such non linear parameters as the drag. They also help assess the strong coupling between certain parameters such as the flap and slat rotations. Then, the high-lift device is optimized according to two illustrative objectives: maximize the lift and minimize the drag. A genetic algorithm is applied to construct the Pareto front. Optimizations using only the geometric parameters (geometrical optimization) or the geometric parameters and the inlet flow Mach number and angle of attack (total optimization) are performed. Both optimizations show quite similar optimal geometric positions: a flap rotation inducing the maximum camber to increase the lift and an upward slat rotation to reduce the drag according to the parameter coupling study. In the total optimization, configurations with higher lift coefficients are found by setting the angle of attack and the Mach number to their maximum values. This optimization allows obtaining more important variations of the lift and the drag from the baseline configuration than the geometrical optimization.

Numerical study of centrifugal compressor stage vaneless diffusers

The authors analyzed CFD calculations of flow in vaneless diffusers with relative width in range from 0.014 to 0.100 at inlet flow angles in range from 100 to 450 with different inlet velocity coefficients, Reynolds numbers and surface roughness. The aim is to simulate calculated performances by simple algebraic equations. The friction coefficient that represents head losses as friction losses is proposed for simulation. The friction coefficient and loss coefficient are directly connected by simple equation. The advantage is that friction coefficient changes comparatively little in range of studied parameters. Simple equations for this coefficient are proposed by the authors. The simulation accuracy is sufficient for practical calculations. To create the complete algebraic model of the vaneless diffuser the authors plan to widen this method of modeling to diffusers with different relative length and for wider range of Reynolds numbers.

Experimental Analysis of the Global Performance and the Flow Through a High-Bypass Turbofan in Windmilling Conditions

A detailed study of the air flow through the fan stage of a high-bypass, geared turbofan in windmilling conditions is proposed, to address the key performance issues of this severe case of off-design operation. Experiments are conducted in the turbofan test rig of ISAE, specifically suited to reproduce windmilling operation in an ambient ground setup. The engine is equipped with conventional measurements and radial profiles of flow quantities are measured using directional five-hole probes to characterize the flow across the fan stage and derive windmilling performance parameters. These results bring experimental evidence of the findings of the literature that both the fan rotor and stator operate under severe off-design angle-of-attack, leading to flow separation and stagnation pressure loss. The fan rotor operates in a mixed fashion: spanwise, the inner sections of the rotor blades add work to the flow while the outer sections extract work and generate a pressure loss. The overall work is negative, revealing the resistive loads on the fan, caused by the bearing friction and work exchange in the different components of the fan shaft. The parametric study shows that the fan rotational speed is proportional to the mass flow rate, but the fan rotor inlet and outlet relative flow angles, as well as the fan load profile, remain constant, for different values of mass flow rate. Estimations of engine bypass ratio have been done, yielding values higher than six times the design value. The comprehensive database that was built will allow the validation of 3D Reynolds-averaged Navier–Stokes (RANS) simulations to provide a better understanding of the internal losses in windmilling conditions.

Influence of pulsating flow frequencies towards the flow angle distributions of an automotive turbocharger mixed-flow turbine

This paper aims to provide a detailed understanding of the flow interaction within the complex geometry of turbine stage coupled with reflection and superposition of the imposed unsteady pressure waves. The defining performance characteristic of a turbomachines is the inlet flow angle at its leading edge, which in most cases limit its optimum operational range. Pulsating flow field, typical to turbocharger turbine due to opening and closing of the exhaust valves, further deteriorates the flow angle distribution around its circumference, hence performance. To investigate this phenomena and how it differs from the steady state equivalent, a fully validated ‘cold flow’ Computational Fluid Dynamics (CFD) analysis was carried out. For this purpose, 4 unsteady CFD simulations of 20Hz, 40Hz, 60Hz and 80Hz together with the steady state simulations have been conducted at 30,000rpm turbine speed. Discussions in this paper aim to provide a better insight on the flow angle behaviour in pulsating flow field. Evidences are shown where flow angle swings over a wide range (300% more than the steady state condition) in pulsating flow field as it propagates through the guide vanes. It was also found that the flow angle fluctuations during pressure drop period is significantly lower as compared to that during pressure increment period by (19°). This work also leads to a recommendation of correction factor in applying quasi-steady assumption of the rotor wheel. Without this correction, the prediction results could lead to underestimation of mass flow parameter up to 8% at high pressure ratio.

Gasdynamic characteristics of outlet straightener of gte low pressure compressor at underexpunded angles of flow inlet

The main hydrodynamic characteristics of the outlet straightener (OS) between LPC and HPC of the GTE have been discussed. OS is a stationary cage of the strait radial profiles which has the functions of the barring set and the guide grid simultaneously. From the hydrodynamics point of view OS should produce the homogeneous outlet flow with the least possible resistance. The main hydrodynamic characteristics of OS may change when the parameters of the outlet flow deviate from the calculated ones which is caused by the GTE operation in transient modes and as well as the heterogeneity of the velocity field at the outlet of the LPC [1] . The aim of the research is to receive a data about the variations of the main hydrodynamic characteristics of the OS as a result of deviation of the inlet flow angle in order to have the possibility to make the highly-efficient straightener and to estimate the efficiency of the gas turbine engine in general. The hydrodynamic characteristics of the OS were numerically investigated using the FLOW VISION fundamentals. The segment of the fully dimensional OS of the stationary gas turbine engine was used as a calculation object. It had two neighboring blades passage with strait radial blade between them. The axis x,y,z of the right angle coordinate system were coincided with circumferential, radial and axial directions, respectively. The calculations were provided by using the datum- model of the FLOW VISION turbulent flow - “ weakly-compressible liquid “ which is based on the standard “k-e model of turbulence”. The obtained results of the numerical calculation reflect the common tendency of debasement of almost all the hydrodynamic characteristics of OS such as the total pressure recovery coefficient, coefficient of the full hydrodynamic losses, condition of the velocity field at the exit and others when the angle of inlet flow slightly increases. They can be useful for the estimation of the reduction of efficiency the gas turbine engine in general.

Theoretical, Experimental and Numerical Investigations of the Effect of Inlet Blade Angle on the Performance of Regenerative Blowers

Regenerative machines allow high heads at small flow rates and present performance curves with very stable features. This research includes a study of the effect of four inlet flow angles (90°, 115°, 125° and 135°) of the blade at outlet flow angle of 90° on the performance of regenerative blower at rotation speed of 3000 rpm and at different flow rates. Investigation and comparison of the experimental results with both one-dimensional theoretical model and numerical CFD technique using CFX-ANSYS 16.1 are done. The numerical CFD analysis show that the flow enters the impeller from the blade side (about 65% of the blade side area) and leaves from the blade tip and blade side (the remaining 35% from the blade side area). According to this observation, a mathematical model that is based on momentum exchange theory to handle one inlet angle and two exit angles for the regenerative blower impeller blades is proposed. Consequently, the experimental work is carried out by two steps. The first step is done by studying the effect of inlet blade angle of 90° and analyzing the results by using the CFD analysis. The CFD results show shock losses and vortices behind each blade at the inlet flow regions. To reduce these losses, an increase of the inlet blade angle in a range between 25° to 45° is proposed. The second step is the splitting of this angle range to three inlet blade angles of 115°, 125° and 135° in order to study and analyze the CFD results for these angels. The CFD analysis shows the disappearance of the shock losses and vortices that are formed behind the blade of angle 90°. The experimental results show that the pressure head and the efficiency depend strongly on the blade inlet and outlet flow angles as well as on the blade geometry. The results also show that the best blower performance can be obtained at an inlet flow angle of 125°, and this is confirmed by CFD simulation analysis. Finally, it is shown that the proposed one-dimensional model yield results that are in a good agreement with the experimental results.

OPTIMIZATION OF THE BLADE PROFILE AND COOLING STRUCTURE IN A GAS TURBINE STAGE CONSIDERING BOTH THE AERODYNAMICS AND HEAT TRANSFER

The need to design high performance of a cooled gas turbine is considered with emphasis made on coupled aerodynamic and heat transfer optimization of the vane, blade, and single stage cooled gas turbine by using a multiobjective optimization method. The aerodynamic profile is designed to have three sections and the cooling structure to consist of a serpentine passage, with a tail transverse channel and trailing edge slots. The optimization platform is built up in an in-house code using a cooling structure parametric method based on MATLAB, as well as automatic grid generation methods, a blade profile parametric program in FORTRAN, the soft ware ISIGHT and ANSYS-CFX. The optimization platform evaluates the aerodynamic effects through the aerodynamic efficiency and presents the cooling effect by the high-temperature coefficient. The pressure drop is described by a pressure drop function. The multiobjective optimization method is accomplished by optimizing the inlet flow angle, installation angle, and the post-corner angle of the vane and blade profiles, while the position of partition is the optimized variable of the cooling structure. The results show that there exists an optimum case in aerodynamic efficiency, high-temperature coefficient, and pressure drop in a Pareto-optimal front. (Less)

Spanwise Penetration Depth with Turbine Disk Inclination

Spanwise penetration depth as a new correlating parameter was introduced in the cascade profile loss correlation of a new loss breakdown scheme for turbine cascade reported in the literature. For the case of an inclined turbine disk, when a turbine disk is inclined to its design position, the blade incidence or inlet flow angle varies with the position of blade on the turbine disk circumference, leading to the variation of spanwise penetration depth. To examine the influences of turbine disk inclination on the spanwise penetration depth, new correlations were developed and numerical simulations were performed with MATLAB. The role that turbine disk inclination plays in the spanwise penetration depth is manifested in a modified inlet flow angle expression on account of turbine disk inclination. It is concluded that the turbine disk inclination has considerable influences on the spanwise penetration depth in the turbine cascade passage.

Profile Loss Correlations Accounting for Turbine Disk Inclination

Incidence can significantly affect turbine cascade aerodynamic losses, including profile, secondary and tip-clearance losses. In previous works, correlations for these losses were developed on a convention that the whole cascade has a universal incidence angle. But in reality, there exist exceptional situations when a turbine disk is inclined to its design position. In such cases, the incidence varies with the location of blade on the circumference, leading to loss deviation from its design value. The present paper is motivated to work out new correlations for the profile losses with turbine disk inclinations and examine the effects of turbine disk inclination. Based on the state-of-the-art works, new correlations are developed to take into account the incidence variation by redefining the inlet flow angle in terms of turbine disk inclination angle and location angle of blade on turbine disk circumference. The effects of turbine disk inclination on profile losses were examined through numerical simulations. It is concluded that the turbine disk inclination has considerable influences on the profile losses of turbine cascade.

Two- and Three-Dimensional Prescribed Surface Curvature Distribution Blade Design (CIRCLE) Method for the Design of High Efficiency Turbines, Compressors, and Isolated Airfoils

The prescribed surface curvature distribution blade design (CIRCLE) method is presented for the design of two-dimensional (2D) and three-dimensional (3D) blades for axial compressors and turbines, and isolated blades or airfoils. The original axial turbine blade design method is improved, allowing it to use any leading-edge (LE) and trailing-edge (TE) shapes, such as circles and ellipses. The method to connect these LE and TE shapes to the remaining blade surfaces with curvature and slope of curvature continuity everywhere along the streamwise blade length, while concurrently overcoming the “wiggle” problems of higher-order polynomials is presented. This allows smooth surface pressure distributions, and easy integration of the CIRCLE method in heuristic blade-optimization methods. The method is further extended to 2D and 3D compressor blades and isolated airfoil geometries providing smooth variation of key blade parameters such as inlet and outlet flow angles, stagger angle, throat diameter, LE and TE radii, etc. from hub to tip. One sample 3D turbine blade geometry is presented. The efficacy of the method is examined by redesigning select blade geometries and numerically evaluating pressure-loss reduction at design and off-design conditions from the original blades: two typical 2D turbine blades; two typical 2D compressor blades; and one typical 2D isolated airfoil blade geometries are redesigned and evaluated with this method. Further extension of the method for centrifugal or mixed-flow impeller geometries is a coordinate transformation. It is concluded that the CIRCLE method is a robust tool for the design of high-efficiency turbomachinery blades.

Design and Performance Prediction of an Axial Flow Compressor

The main objective of this paper is to create a method for designing and studying the performance of a multistage axial flow compressor. A mathematical methodology based on aerothermodynamics is used to study the on /off design performance of the compressor. Performance curves are obtained by changing the performance parameters in terms of design parameters (diffusion factor, solidity, Mach number, and inlet flow angle). Results show the great effect of diffusion factor on increasing efficiency than that of solidity, also the effect of both (diffusion factor and solidity) in increasing the amount of compression and efficiency of the compressor. Higher efficiency was found at the mean line between the root and tip of the blade. Best lift to drag ratio is found at inlet flow angle of (55o).

NUMERICAL STUDY OF 3D THERMAL AND HYDRAULIC CHARACTERISTICS OF WAVY FIN-AND-TUBE HEAT EXCHANGER

This numerical analysis presents the airside performance of a wavy fin-and-tube heat exchanger having 4 row configurations considering steady, incompressible and 3D flow using Commercial CFD Code ANSYS CFX 12.0. Results are presented in the form of friction factor (f), Colburn factor (j) and efficiency index (j/f). The numerical procedure has been validated by comparison with published numerical and experimental results and good agreement has been observed. A series of numerical calculations have been carried out in order to analyze the influence of various geometric characteristics on different fields as well as on the heat transfer and pressure drop and efficiency within a heat exchanger. The effects of longitudinal pitch (Ll), transverse pitch (Lt), Fin Pitch (Fp), wavy angle (Wa) and inlet flow angle (α) on wavy fin-and-tube heat exchanger are studied. Different inlet flow angles such as 0 ˚, + 17.5˚, -17.5˚, +35˚ and -35˚ are employed normal to the face of the heat exchanger in order to investigate the performance of inlet flow angles. There is a strong correlation between the response of the flow efficiency, pressure drop and heat transfer performance to these parameters.

Control of the Separation Flow in a Sudden Enlargement

In the present paper, an experimental and numerical investigation of fluid flow and heat transfer in the case of wall injection besides main flow through a circular sudden enlargement are studied. The injected flow is achieved through an annular slot placed around the inner side wall of the step. The static pressure variation along the sudden enlargement length is measured and calculated at different values of injection ratio ( Q ) and injection flow angles. The average heat transfer with Reynolds number (ReJ) of injected flow at different values of the inlet flow angle is obtained. The velocity, turbulent kinetic energy and temperature contours are presented in this study. Reynolds number of injected flow is varied between 320 and 840, Reynolds number of main flow is between 5895 and 8450 and the injection flow angles are 0 o , 15 o , 30 o , 45 o and 60 o . In the injection case, the results indicate that, the pressure recovery coefficient increases by decreasing the injection ratio and increasing the flow angle. The average heat transfer coefficient increases as both injection Reynolds number and the injection flow angle increase. The numerical results showed that two recirculation zones generate behind the step between the injection flow and the main flow. The size of these recirculation zones decreases by increasing the injection flow rate. The turbulent kinetic energy increases within region between the recirculation zones and main zone also, it decays by injecting flow in the recirculation zone. The length for higher value of flow temperature decreases by injecting flow in the recirculation zone, and that length increases as the injection flow rate increases. The comparison between the experimental results and the numerical results gives good agreement using the k-e model with Leschziner and Rodi correction.