Roughness induced forced convective laminar-transitional micropipe flow: energy and exergy analysis

Variable fluid property continuity, Navier–Stokes and energy equations are solved for roughness induced forced convective laminar-transitional flow in a micropipe. Influences of Reynolds number, heat flux and surface roughness, on the momentum-energy transport mechanisms and second-law of thermodynamics, are investigated for the ranges of Re = 1–2,000, Q = 5–100 W/m² and ε = 1–50 μm. Numerical investigations put forward that surface roughness accelerates transition with flatter velocity profiles and increased intermittency values (γ); such that a high roughness of ε = 50 μm resulted in transitional character at Re _tra = 450 with γ = 0.136. Normalized friction coefficient (C _f^*) values showed augmentation with Re, as the evaluated C _f^* are 1.006, 1.028 and 1.088 for Re = 100, 500 and 1,500, respectively, at ε = 1 μm, the corresponding values rise to C _f^* = 1.021, 1.116 and 1.350 at ε = 50 μm. Heat transfer rates are also recorded to rise with Re and ε; moreover the growing influence of ε on Nusselt number with Re is determined by the Nu _ε=50 μm/Nu _ε=1 μm ratios of 1.086, 1.168 and 1.259 at Re = 500, 1,000 and 1,500. Thermal volumetric entropy generation values decrease with Re and ε in heating; however the contrary is recorded for frictional volumetric entropy generation data, where the augmentations in are more considerable when compared with the decrease rates of      

On a Generalized Nonlinear K–ε Model and the Use of Extended Thermodynamics in Turbulence

A resent extension of the nonlinear K–ε model is critically discussed from a basic theoretical standpoint. While it was said in the paper that this model was formulated to incorporate relaxation effects, it will be shown that the model is incapable of describing one of the most basic such turbulent flows as is obvious but is described for clarity. It will be shown in detail that this generalized nonlinear K–ε model yields erroneous results for the Reynolds stress tensor when the mean strains are set to zero in a turbulent flow – the return-to-isotropy problem which is one of the most elementary relaxational turbulent flows. It is clear that K–ε type models cannot describe relaxation effects. While their general formalism can describe relaxation effects, the nonlinear K–ε model – which the paper is centered on – cannot. The deviatoric part of the Reynolds stress tensor is predicted to be zero when it actually only gradually relaxes to zero. Since this model was formulated by using the extended thermodynamics, it too will be critically assessed. It will be argued that there is an unsubstantial physical basis for the use of extended thermodynamics in turbulence. The role of Material Frame-Indifference and the implications for future research in turbulence modeling are also discussed. Received 19 February 1998 and accepted 23 October 1998     

An experimental study of a two-dimensional plane turbulent wall jet

 Laser-Doppler measurements were conducted in a plane turbulent wall jet at a Reynolds number based on inlet velocity, Re ₀, of 9600. The initial development as well as the fully developed flow was studied. Special attention was given to the near-wall region, including the use of small measuring volumes and the application of specific near-wall data corrections, so that wall shear stresses were determined directly from the mean velocity gradient at the wall using only data below y ⁺=4. It was possible to resolve the inner peak in the streamwise turbulence intensity as well as the inner (negative) peak in the shear stress. Limiting values of (u′)⁺ and uv ⁺ were determined. Turbulence data from the outer region of the flow were compared to earlier hot wire measurements and large differences in the normal turbulence intensity and the shear stress were found. These differences can be attributed to high turbulence intensity effects on the hot-wires. Received: 17 October 1996 / Accepted: 8 December 1997     

Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers

 The lift force experienced by a spinning sphere moving in a viscous fluid, with constant linear and angular velocities, is measured by means of a trajectographic technique. Measurements are performed in the range of dimensionless angular velocities γ=aω/V lying between 1 and 6, and in the range of Reynolds numbers Re=2aV/ν lying between 10 and 140 (a sphere radius, ω angular velocity, V relative velocity of the sphere centre, ν fluid kinematic viscosity). A notable departure from the theoretical relationship at low Reynolds number, C _L =2γ, is obtained, the ratio C _L /γ being found to significantly decrease with increasing γ and increasing Re. The following correlation is finally proposed to estimate the lift coefficient in the range 10<Re<140: C _L ≅0.45+(2γ−0.45) exp (−0.075γ^0.4 Re ^0.7) Received: 20 May 1996/Accepted: 9 November 1997     

Some Reynolds number effects on two- and three-dimensional turbulent boundary layers

Experimental data for a two-dimensional (2-D) turbulent boundary layer (TBL) flow and a three-dimensional (3-D) pressure-driven TBL flow outside of a wing/body junction were obtained for an approach Reynolds number based on momentum thickness of Re _θ =23,200. The wing shape had a 3:2 elliptical nose, NACA 0020 profiled tail, and was mounted on a flat wall. Some Reynolds number effects are examined using fine spatial resolution (Δy ⁺=1.8) three-velocity-component laser-Doppler velocimeter measurements of mean velocities and Reynolds stresses at nine stations for Re _θ =23,200 and previously reported data for a much thinner boundary layer at Re _θ =5,940 for the same wing shape. In the 3-D boundary layers, while the stress profiles vary considerably along the flow due to deceleration, acceleration, and skewing, profiles of the parameter correlate well and over available Reynolds numbers. The measured static pressure variations on the flat wall are similar for the two Reynolds numbers, so the vorticity flux and the measured mean velocities scaled on wall variables agree closely near the wall. The stresses vary similarly for both cases, but with higher values in the outer region of the higher Re _θ case. The outer layer turbulence in the thicker high Reynolds number case behaves similarly to a rapid distortion of the flow, since stream-wise vortical effects from the wall have not diffused completely through the boundary layer at all measurement stations. Received: 9 June 2000/Accepted: 26 January 2001     

Investigation of the vortex induced unsteadiness of a separation bubble via time-resolved and scanning PIV measurements

A transitional separation bubble on the suction side of an SD7003 airfoil is considered. The transition process that forces the separated shear layer to reattach seems to be governed by Kelvin–Helmholtz instabilities. Large scale vortices are formed due to this mechanism at the downstream end of the bubble. These vortices possess a three-dimensional structure and detach from the recirculation region, while other vortices are formed within the bubble. This separation of the vortex is a highly unsteady process, which leads to a bubble flapping. The structure of these vortices and the flapping of the separation bubble due to these vortices are temporally and spatially analyzed at angles of attack from 4° to 8° and chord-length based Reynolds numbers Re _c = 20,000–60,000 using time-resolved PIV measurements in a 2D and a 3D set-up, i.e., stereo-scanning PIV measurements are done in the latter case. These measurements complete former studies at a Reynolds number of Re _c = 20,000. The results of the time-resolved PIV measurements in a single light-sheet show the influence of the angle of attack and the Reynolds number. The characteristic parameters of the separation bubble are analyzed focusing on the unsteadiness of the separation bubble, e.g., the varying size of the main recirculation region, which characterizes the bubble flapping, and the corresponding Strouhal number are investigated. Furthermore, the impact of the freestream turbulence is investigated by juxtaposing the current and former results. The stereo-scanning PIV measurements at Reynolds numbers up to 60,000 elucidate the three-dimensional character of the vortical structures, which evolve at the downstream end of the separation bubble. It is shown that the same typical structures are formed, e.g., the c-shape vortex and the screwdriver vortex at each Reynolds number and angle of attack investigated and the occurrence of these patterns in relation to Λ-structures is discussed. To evidence the impact of the freestream turbulence, these results are compared with findings of former measurements.     

Approach to local axisymmetry in a turbulent cylinder wake

The objective of this experimental study is to characterise the small-scale turbulence in the intermediate wake of a circular cylinder using measured mean-squared velocity gradients. Seven of the twelve terms which feature in ε, the mean dissipation rate of the turbulent kinetic energy, were measured throughout the intermediate wake at a Reynolds number of Re _d  ≈ 3000 based on the cylinder diameter (d). Earlier measurements of the nine major terms of ε by Browne et al. (J Fluid Mech 179: 307–326 1987) at a downstream distance (x) of x = 420d and Re _d  ≈ 1170 are also used. Whilst departures from local isotropy are significant at all locations in the wake, local axisymmetry of the small-scale turbulence with respect to the mean flow direction is first satisfied approximately at x = 40d. The approach towards local axisymmetry is discussed in some detail in the context of the relative values of the mean-squared velocity gradients. The data also indicate that axisymmetry is approximately satisfied by the large scales at x/d ≥ 40, suggesting that the characteristics of the small scales reflect to a major extent those of the large scales. Nevertheless, the far-wake data of Browne et al. (1987) show a discernible departure from axisymmetry for both small and large scales.     

Reynolds Number Effects on the Coherent Dynamics of the Turbulent Horseshoe Vortex System

The adverse pressure gradient induced by a surface-mounted obstacle in a turbulent boundary layer causes the approaching flow to separate and form a dynamically rich horseshoe vortex system (HSV) in the junction of the obstacle with the wall. The Reynolds number of the flow (Re) is one of the important parameters that control the rich coherent dynamics of the vortex, which are known to give rise to low-frequency, bimodal fluctuations of the velocity field (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). We carry out detached eddy simulations (DES) of the flow past a circular cylinder mounted on a rectangular channel for Re = 2.0 × 10⁴ and 3.9 × 10⁴ (Dargahi, Exp Fluids 8:1–12, 1989) in order to systematically investigate the effect of the Reynolds number on the HSV dynamics. The computed results are compared with each other and with previous experimental and computational results for a related junction flow at a much higher Reynolds number (Re = 1.15 × 10⁵) (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). The computed results reveal significant variations with Re in terms of the mean-flow quantities, turbulence statistics, and the coherent dynamics of the turbulent HSV. For Re = 2.0 × 10⁴ the HSV system consists of a large number of necklace-type vortices that are shed periodically at higher frequencies than those observed in the Re = 3.9 × 10⁴ case. For this latter case the number of large-scale vortical structures that comprise the instantaneous HSV system is reduced significantly and the flow dynamics becomes quasi-periodic. For both cases, we show that the instantaneous flowfields are dominated by eruptions of wall-generated vorticity associated with the growth of hairpin vortices that wrap around and disorganize the primary HSV system. The intensity and frequency of these eruptions, however, appears to diminish rapidly with decreasing Re. In the high Re case the HSV system consists of a single, highly energetic, large-scale necklace vortex that is aperiodically disorganized by the growth of the hairpin mode. Regardless of the Re, we find pockets in the junction region within which the histograms of velocity fluctuations are bimodal as has also been observed in several previous experimental studies.     

Conjugate heat transfer study of incompressible turbulent offset jet flows

In the present case, the conjugate heat transfer involving a turbulent plane offset jet is considered. The bottom wall of the solid block is maintained at an isothermal temperature higher than the jet inlet temperature. The parameters considered are the offset ratio (OR), the conductivity ratio (K), the solid slab thickness (S) and the Prandtl number (Pr). The Reynolds number considered is 15,000 because the flow becomes fully turbulent and then it becomes independent of the Reynolds number. The ranges of parameters considered are: OR = 3, 7 and 11, K = 1–1,000, S = 1–10 and Pr = 0.01–100. High Reynolds number two-equation model (k–ε) has been used for turbulence modeling. Results for the solid–fluid interface temperature, local Nusselt number, local heat flux, average Nusselt number and average heat transfer have been presented and discussed.     

Testing of Model Equations for the Mean Dissipation using Kolmogorov Flows

Direct Numerical Simulations (DNS) of Kolmogorov flows are performed at three different Reynolds numbers Re _λ between 110 and 190 by imposing a mean velocity profile in y-direction of the form U(y) = F sin(y) in a periodic box of volume (2π)³. After a few integral times the turbulent flow turns out to be statistically steady. Profiles of mean quantities are then obtained by averaging over planes at constant y. Based on these profiles two different model equations for the mean dissipation ε in the context of two-equation RANS (Reynolds Averaged Navier–Stokes) modelling of turbulence are compared to each other. The high Reynolds number version of the k-ε-model (Jones and Launder, Int J Heat Mass Transfer 15:301–314, 1972), to be called the standard model and a new model by Menter et al. (2006), to be called the Menter–Egorov model, are tested against the DNS results. Both models are solved numerically and it is found that the standard model does not provide a steady solution for the present case, while the Menter–Egorov model does. In addition a fairly good quantitative agreement of the model solution and the DNS data is found for the averaged profiles of the kinetic energy k and the dissipation ε. Furthermore, an analysis based on flow-inherent geometries, called dissipation elements (Wang and Peters, J Fluid Mech 608:113–138, 2008), is used to examine the Menter–Egorov ε model equation. An expression for the evolution of ε is derived by taking appropriate moments of the equation for the evolution of the probability density function (pdf) of the length of dissipation elements. A term-by-term comparison with the model equation allows a prediction of the constants, which with increasing Reynolds number approach the empirical values.     

Tailoring turbulence with an active grid

Using an active grid in a wind tunnel, we generate homogeneous shear turbulence and initiate turbulent boundary layers with adjustable properties. Homogeneous shear turbulence is characterized by a constant gradient of the mean velocity and a constant turbulence intensity. It is the simplest anisotropic turbulent flow thinkable, and it is generated traditionally by equipping a wind tunnel with screens which have a varying transparency and flow straighteners. This is not done easily, and the reachable turbulence levels are modest. We describe a new technique for generating homogeneous shear turbulence using an active grid only. Our active grid consists of a grid of rods with attached vanes which can be rotated by servo motors. We control the grid by prescribing the time-dependent angle of each axis. We tune the vertical transparency profile of the grid by setting appropriate angles of each rod such as to generate a uniform velocity gradient, and set the rods in flapping motion around these angles to tailor the turbulence intensity. The Taylor Reynolds number reached was R _λ = 870, the shear rate S = ∂U/∂y = 9.2 s⁻¹, the nondimensional shear parameter S ^*≡ Sq ²/ε = 12 and u = 1.4 ms⁻¹. As a further application of this idea we demonstrate the generation of a simulated atmospheric boundary layer in a wind tunnel which has tunable properties. This method offers a great advantage over the traditional one, in which vortex-generating structures need to be placed in the wind tunnel to initiate a fat boundary layer.     

Coherent Structures and their Frequency Signature in the Separated Shear Layer on the Sides of a Square Cylinder

The purpose of the present work is to study the various specific time scales of the turbulent separating flow around a square cylinder, in order to determine the Reynolds number effect on the separating shear layer, where occurs a transition to turbulence. Unsteady analysis based on large eddy simulation (LES) at intermediate Reynolds numbers and laser doppler velocimetry (LDV) measurements at high Reynolds numbers are carried out. The Reynolds number, based on the cylinder diameter D and the inflow velocity U _o , is ranging from Re?=?50 to Re?=?300,000. A special focus is performed on the coherent structures developing on the sides and in the wake of a square cylinder. For a large Reynolds number range above Re?≈?1,000, both signatures of Von Karman (VK) and Kelvin–Helmholtz (KH) type vortical structures are found on velocity time samples. The combination of their frequency signature is studied based on Fourier and wavelet analysis. In the present study, We observe the occurrence of KH pairings in the separating shear layer on the side of the cylinder, and confirm the intermittency nature of such a shear flow. These issues concerning the structure of the near wake shear layer which were addressed for the round cylinder case in a recent experimental publication (Rajagopalan and Antonia, Exp Fluids 38:393–402, 2005) are of interest in the present flow configuration as well.     

Comparison of turbulent channel and pipe flows with varying Reynolds number

Single normal hot-wire measurements of the streamwise component of velocity were taken in fully developed turbulent channel and pipe flows for matched friction Reynolds numbers ranging from 1,000 ≤ Re _τ ≤ 3,000. A total of 27 velocity profile measurements were taken with a systematic variation in the inner-scaled hot-wire sensor length l ⁺ and the hot-wire length-to-diameter ratio (l/d). It was observed that for constant l ⁺ = 22 and l/d >~200l/d \gtrsim 200, the near-wall peak in turbulence intensity rises with Reynolds number in both channels and pipes. This is in contrast to Hultmark et al. in J Fluid Mech 649:103–113, (2010), who report no growth in the near-wall peak turbulence intensity for pipe flow with l ⁺ = 20. Further, it was found that channel and pipe flows have very similar streamwise velocity statistics and energy spectra over this range of Reynolds numbers, with the only difference observed in the outer region of the mean velocity profile. Measurements where l ⁺ and l/d were systematically varied reveal that l ⁺ effects are akin to spatial filtering and that increasing sensor size will lead to attenuation of an increasingly large range of small scales. In contrast, when l/d was insufficient, the measured energy is attenuated over a very broad range of scales. These findings are in agreement with similar studies in boundary layer flows and highlight the need to carefully consider sensor and anemometry parameters when comparing flows across different geometries and when drawing conclusions regarding the Reynolds number dependency of measured turbulence statistics. With an emphasis on accuracy, measurement resolution and wall proximity, these measurements are taken at comparable Reynolds numbers to currently available DNS data sets of turbulent channel/pipe flows and are intended to serve as a database for comparison between physical and numerical experiments.     

LES Study of Turbulent Boundary Layer Over a Smooth and a Rough 2D Hill Model

Large eddy simulation (LES) is carried out to investigate the turbulent boundary-layer flows over a hill-shaped model with a steep or relatively moderate slope at moderately high Reynolds numbers (Re = O(10³)) defined by the hill height and the velocity at the hill height. The study focuses on the effects of surface roughness and curvature. For Sub-grid Scale (SGS) modeling of LES, both the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM) are applied. The behavior of the separated shear layer and the vortex motion are affected by the oncoming turbulence, such that the shear layer comes close to the ground surface, or the size of a separation region becomes small because of the earlier instability of the separated shear layer. Appropriate measures are required to generate the inflow turbulence. The methods of Lund et al. (J. Comput. Phys., 140:233–258, 1998) and Nozawa and Tamura (J. Wind Eng. Ind. Aerodyn., 90:1151–1162, 2002; The 4th European and African Conference on Wind Engineering, 1–6, 2005) are employed to simulate the smooth- and rough-wall turbulent boundary layers in order to generate time-sequential data of inflow turbulence. This paper discusses the unsteady phenomena of the wake flows over the smooth and rough 2D hill-shaped obstacles and aims to clarify the roughness effects on the flow patterns and the turbulence statistics distorted by the hill. Numerical validation is conducted by comparing the simulation results with wind tunnel experiment data for the same hill shape at almost the same Re. The applicability of DSM and DMM are discussed, focusing on the recirculation region behind a steep hill.     

Turbulent wake and vortex shedding for a stack partially immersed in a turbulent boundary layer

The effect of the jet-to-cross-flow velocity ratio, R, on the turbulent wake and Kármán vortex shedding for a cylindrical stack of aspect ratio AR=9 was investigated in a low-speed wind tunnel using thermal anemometry. The cross-flow Reynolds number was Re_D=2.3×10⁴, the jet Reynolds number ranged from Re_d=7.6×10³ to 4.7×10⁴, and R was varied from 0 to 3. The stack was partially immersed in a flat-plate turbulent boundary layer, with a boundary layer thickness-to-stack-height ratio of δ/H=0.5 at the location of the stack. From the behaviour of the turbulent wake and the vortex shedding, the flow around the stack could be classified into three regimes depending on the value of R, which were the downwash (R<0.7), cross-wind-dominated (0.7R<1.5), and jet-dominated (R1.5) flow regimes. Each flow regime had a distinct structure to the mean velocity (streamwise and wall-normal directions), turbulence intensity (streamwise and wall-normal directions), and Reynolds shear stress fields, as well as the variation of the Strouhal number and the power spectrum along the stack height.     

Effects of wall permeability on turbulence

In order to understand the effects of the wall permeability on turbulence near a porous wall, flow field measurements are carried out for turbulent flows in a channel with a porous bottom wall by a two-component particle image velocimetry (PIV) system. The porous media used are three kinds of foamed ceramics which have almost the same porosity (0.8) but different permeability. It is confirmed that the flow becomes more turbulent over the porous wall and tends to be turbulent even at the bulk Reynolds number of Re_b=1300 in the most permeable wall case tested. Corresponding to laminar to turbulent transition, the magnitude of the slip velocity on the porous wall is found to increase drastically in a narrow range of the Reynolds number. To discuss the effects of the wall roughness and the wall permeability, detailed discussions are made of zero-plane displacement and equivalent wall roughness for porous media. The results clearly indicate that the turbulence is induced by not only the wall roughness but the wall permeability. The measurements have also revealed that as Re_b or the wall permeability increases, the wall normal fluctuating velocity near the porous wall is enhanced due to the effects of the wall permeability. This leads to the increase of the turbulent shear stress resulting in higher friction factors of turbulence over porous walls.     

Laminarisation and re-transition of a turbulent boundary layer subjected to favourable pressure gradient

 Experimental results are reported for the response of an initially turbulent boundary layer (Re _θ≈1700) to a favourable pressure gradient with a peak value of K≡(−υ/ρU ³ _E ) dp/dx equal to 4.4×10^-6. In the near-wall region of the boundary layer (y/δ<0.1) the turbulence intensity u′ scales roughly with the free-stream velocity U _E until close to the location where K is a maximum whereas in the outer region u′ remains essentially frozen. Once the pressure gradient is relaxed, the turbulence level increases throughout the boundary layer until K falls to zero when the near wall u′ levels show a significant decrease. The intermittency γ is the clearest indicator of a fundamental change in the turbulence structure: once K exceeds 3×10^-6, the value of γ in the immediate vicinity of the wall γ _s falls rapidly from unity, reaches zero at the location where K again falls below 3×10^-6 and then rises back to unity. Although γ is practically zero throughout the boundary layer in the vicinity of γ _s =0, the turbulence level remains high. The explanation for what appears to be a contradiction is that the turbulent frequencies are too low to induce turbulent mixing. The mean velocity profile changes shape abruptly where K exceeds 3×10^-6. Values for the skin friction coefficient, based upon hot-film measurements, peak at the same location as K and fall to a minimum close to the location where K drops back to zero. Received: 28 January 1998/Accepted: 8 April 1998     

A rotating elliptic airfoil in fluid at rest and in a parallel freestream

This paper reports results of DPIV measurements on a two-dimensional elliptic airfoil rotating about its own axis of symmetry in a fluid at rest and in a parallel freestream. In the former case, we examined three rotating speeds (Re _c,Ω = 400, 1,000 and 2,000), and in the later case, four rotating speeds (Ro _c,Ω = 2.4, 1.2, 0.6 and 0.4), together with two freestream velocities (Re _c,u  = 200 and 1,000) and two starting configurations of the airfoil (i.e., chord parallel to (α ₀ = 0°) or normal (α ₀ = 90°) to the freestream). Results show that a rotating airfoil in a stationary fluid produces two distinct types of vortex structures depending on the Reynolds number. The first type occurs at the lowest Reynolds number (Re _c,Ω = 400), where vortices shed from the two edges or tips of the airfoil dissipated quickly, resulting in the airfoil rotating in a layer of diffused vorticity. The second type occurs at higher Reynolds numbers (i.e., Re _c,Ω = 1,000 and 2,000), where the corresponding vortices rotated together with the airfoil. Due to the vortex suction effect, the torque characteristics are likely to be heavily damped for the first type because of the rapidly subsiding vortex shedding, and more oscillatory for the second type due to persistent presence of tip vortices. In a parallel freestream, increasing the tip-speed ratio (V/U) of the airfoil (i.e., decreasing the Rossby number, Ro _c,Ω) transformed the flow topology from periodic vortex shedding at Ro _c,Ω = 2.4 to the generation of a “hovering vortex” at Ro _c,Ω = 0.6 and 0.4. The presence of the hovering vortex, which has not been reported in literature before, is likely to enhance the lift characteristics of the airfoil. Freestream Reynolds number is found to have minimal effect on the vortex formation and shedding process, although it enhances shear layer instability and produces more small-scale flow structures that affect the dynamics of the hovering vortex. Likewise, initial starting configuration of the airfoil, while affecting the flow transient during the initial phase of rotation, has insignificant effect on the overall flow topology. Unfortunately, technical constraint of our apparatus prevented us from carrying out complimentary force measurements; nevertheless, the results presented herein, which are more extensive than those computed by Lugt and Ohring (1977), will provide useful benchmark data, from which more advanced numerical calculations can be carried out to ascertain the corresponding force characteristics, particularly for those conditions with the presence of hovering vortex.     

AN EXTENDED k-ε MODEL FOR NUMERICAL SIMULATION OF WIND FLOW AROUND BUILDINGS

It is assumed in this paper that for a high Reynolds number nearly homogeneouswind flow, the Reynolds stresses are uniquely related to the mean velocity gradientsand the two independent turbulent scaling parameters k and E. By applying dimensionalanalysis and owing to the Cayley-Hamilton theorem for tensors, a new turbulenceenclosure model so-called the axtended k-ε model has been developed. The coefficientsof the model expression were detemined by the wind tunnel experimental data ofhomogeneous shear turbulent flow. The model was compared with the standard k-εmodel in in composition and the prediction of the Reynold’s normal Stresses. Using thenew model the numerical simulation of wind flow around a square cross-section tallbuilding was performed. The results show that the extended k-ε model improves theprediction of wind velocities around the building the building and wind pressures on the buildingenvelope.