Measurements in a heated turbulent wall jet on a concave wall

The paper contains the results of extensive single-point hot-wire and resistance-thermometer measurements in a wall jet on a heated concave wall with an external free stream. It is found that the turbulence in the inner (wall) and outer layers is sensitive to the distortion produced by the curved wall, broadly confirming current views of these effects. The effect on the turbulence of streamline curvature is stabilising in the outer layer, destabilising in the inner. Consequently the point of zero shear stress is closer to the point of maximum mean velocity than in flat and convex wall jets with which these new results are compared. The rate of growth is about 80% of that of the equivalent flat wall flow, and about half that of the convex wall flow. Changes in the wall shear stress and heat flux, which are increased relative to the flat wall flow, are significant but less than the changes in the corresponding convex wall flow. The greatest changes occur in the triple products.     

An experimental investigation of the combined effects of surface curvature and streamwise pressure gradients both in laminar and turbulent flows

Flow and heat transfer characteristics over flat, concave and convex surfaces have been investigated in a low speed wind tunnel in the presence of adverse and favourable pressure gradients (k), for a range of –3.6 × 10^–6 ≤ k ≤ +3.6 × 10^–6. The laminar near zero pressure gradient flow, with an initial momentum thickness Reynolds number of 200, showed that concave wall boundary layer was thinner and heat transfer coefficients were almost 2 fold of flat plate values. Whereas for the same flow condition, thicker boundary layer and 35% less heat transfer coefficients of the convex wall were recorded with an earlier transition. Accelerating laminar flows caused also thinner boundary layers and an augmentation in heat transfer values by 28%, 35% and 16% for the flat, concave and convex walls at k = 3.6 × 10^–6. On the other hand decelerating laminar flows increased the boundary layer thickness and reduced Stanton numbers by 31%, 26% and 22% on the flat surface, concave and convex walls respectively. Turbulent flow measurements at k = 0, with an initial momentum thickness Reynolds number of 1100, resulted in 30% higher and 25% lower Stanton numbers on concave and convex walls, comparing to flat plate values. Moreover the accelerating turbulent flow of k = 0.6 × 10^–6 brought about 29%, 30% and 24% higher Stanton numbers for the flat, concave and convex walls and the decelerating turbulent flow of k = –0.6 × 10^–6 caused St to decrease up to 27%, 25% and 29% for the same surfaces respectively comparing to zero pressure gradient values. An empirical equation was also developed and successfully applied, for the estimation of Stanton number under the influence of pressure gradients, with an accuracy of better than 4%.     

NUMERICAL PREDICTION OF SEMI-CONFINED JET IMPINGEMENT AND COMPARISON WITH EXPERIMENTAL DATA

The standard k–ε eddy viscosity model of turbulence in conjunction with the logarithmic law of the wall has been applied to the prediction of a fully developed turbulent axisymmetric jet impinging within a semi-confined space. A single geometry with a Reynolds number of 20,000 and a nozzle-to-plate spacing of two diameters has been considered with inlet boundary conditions based on measured profiles of velocity and turbulence. Velocity, turbulence and heat transfer data have been obtained using laser–Doppler anemometry and liquid crystal thermography respectively. In the developing wall jet, numerical results of heat transfer compare to within 20% of experiment where isotropy prevails and the trends in turbulent kinetic energy are predicted. However, stagnation point heat transfer is overpredicted by about 300%, which is attributed directly to the turbulence model and inapplicability of the wall function.     

Effects of injection angle orientation on concave and convex surfaces film cooling

The present study employs a transient liquid crystal thermography to measure film cooling performance over constant curvature of concave and convex surfaces. This work investigates detailed distributions of both film cooling effectiveness and heat transfer coefficient on concave and convex surfaces with one row of injection holes inclined stream-wise at 35° at four blowing ratios (0.5, 1.0, 1.5 and 2.0) on four test pieces with different hole configurations. All test models have a row of discrete holes with a stream-wise injection angle (γ of 35° and a pitch-to-diameter ratio (P/d) of 3. The current work examines four different injection configurations, one with simple and three with 8° forward-expanded holes. Three compound angles of 0, 45 and 90° with air (ρ_c/ρ_m = 0.98) as coolants are tested under the mainstream Reynolds number (Re_d) of 2300 on concave surface, and 1700 on convex surface. Measured results of the concave surface show that both the span-wise averaged heat transfer coefficient and film cooling effectiveness increase with blowing ratios for all tested models. Higher heat transfer levels induced by large flow disturbance of compound-angle injection also lead to poorer overall film cooling performance, especially at high blowing ratio and large span-wise injection angle. Present results show that the best surface protection on the concave surface over the widest range of M can be provided by the forward-expanded holes with β = 0° (Model-B), followed by the forward-expanded holes with β = 45° (Model-C). Convex surface results show that the compound-angle injection indicates increases in both film cooling effectiveness and heat transfer at moderate and high blowing ratios. The forward-expanded hole with simple-angle injection provides the best film performance because of high film cooling effectiveness and low heat transfer coefficient at blowing ratio of 0.5.     

Forced-convection freezing heat transfer characteristics in a return bend with a rectangular cross section

Experiments have been performed to investigate the freezing heat transfer characteristics in a return bend with a rectangular cross section. The experiments were carried out for two kinds of duct heights of 30 and 50 mm under the fixed size of 300 mm in duct width and 159 mm in curvature radius of convex wall. Both the convex and concave walls of a return bend were kept less than the freezing temperature of water. It was found that the freezing characteristics on the convex wall are markedly different from those on the concave wall of a return bend, and that the cooling temperature ratio is one of the most important parameters on the forced-convection freezing heat transfer in a return bend.     

狭缝射流撞击圆柱表面的湍流特性实验研究

实验研究了狭缝射流撞击圆柱表面后壁面射流区的平均流动和湍流特 性. 考察了雷诺数 Re (6000-20000), 喷口到受撞表面距 离 Y/W (5-13), 喷口宽度 W (6.25mm, 9.38mm), 受撞表 面曲率(半圆柱体直径 D = 150mm)对流动和湍流结构的影响. 通过分析 X 热线 在壁面射流区的测量结果发现，在近壁区域，表面曲率、 Re_{w} , Y/W 和 S/W 等 参数对 \sqrt {\overline{u^2}} / U_m 的影响比对 \sqrt {\overline{v^2}} / U_m 强，并且切 应力 \overline {uv} /U_m^2 对表面曲率变化最敏感. 当喷口与受撞击表面之间的距 离 Y/W 在一定范围内增加时， 沿圆柱表面流动的流向和横向的湍流强度增强. 用平板射流和圆柱体表面壁面射流的数据进行比较，从而得到表面曲率对壁面射流特 性的影响. 结果表明，曲率对壁面射流的影响较强， 并随着 S/W 的增大而增强. 随着雷诺数的增大，壁面曲率的影响也有强化的趋势.     

Experimental study of turbulent round jet flow impinging on a square cylinder laid on a flat plate

A turbulent axisymmetric air jet impinging on a square cylinder mounted on a flat plate has been studied experimentally. Turbulence statistics and flow’s topology were investigated. When the surface was heated through uniform heat flux, local heat transfer coefficient was measured. The jet from a long round pipe, 75 pipe diameters (D) in length, at Reynolds number of 23,000, impinged vertically on the square cylinder (3D × 3D × 43D). Measurements were performed using particle image velocimetry, flow visualization using fluorescent dye and infrared thermography. The flow’s topology demonstrated a three-dimensional recirculation after separating from the square cylinder and a presence of foci between the bottom corner and the recirculation’s detachment line. The distribution of heat transfer coefficient was explained by the influence of these flow’s structures and the advection of kinetic energy. On the impingement wall of the square cylinder, a secondary peak in heat transfer coefficient was observed. Its origin can be attributed to very pronounced shear production coupled with the external turbulence coming from the free jet.     

Fluid flow and heat transfer in transitional boundary layers: effects of surface curvature and free stream velocity

Velocity and wall temperature measurements, over flat plate, concave and convex walls, were experimentally investigated in a low-speed wind tunnel with inlet velocities of 4 and 12 m/s encompassing the transitional region with streamwise distance Reynolds numbers from 3.15×10⁵ to 1.04×10⁶. As the velocity profiles, recorded by a semi-circular pitot tube and a digital constant-temperature hot-wire anemometer, were compared to exact Blasius profile and (1/7)th power law, experimental local Stanton numbers to analytical flat plate solution and turbulent correlation formula. Intermittency factors, derived from velocities and local Stanton numbers, were presented both in streamwise and pitchwise directions. It was found that the convex curvature delayed transition up to Re _x =1.04×10⁶, with a mean intermittency value of 0.61 and a shape factor of 1.81, where the similar intermittency and shape factors were determined at Re _x of 8.33×10⁵ and 4.25×10⁵ for the flat plate and concave wall, indicating the enhancing role of concave curvature on the transition mechanism. The thinner boundary layers of the concave surface resulted in higher intermittency values, corresponding to higher skin friction and Stanton numbers; moreover the lowest gap between the measured and derived Stanton numbers were also obtained over the concave surface. Destabilising role of the concave wall caused Stanton numbers to increase up to 22%, whereas the convex wall, due to its stabilising character, produced lower Stanton numbers by 12% with respect to those of the flat plate.     

Theoretical and experimental investigations of the flow of a viscous fluid near the line of intersection of a cylindrical surface and a flat surface

Flow along a corner was investigated at large Reynolds numbers in, for example, [1–3]. The present author [4] considered flow in the neighborhood of a corner formed by the intersection of a plane and a concave cylindrical surface, the main attention being devoted to the formation of the three-dimensional boundary layer on the plane near the corner. It was shown that the curvature of one of the intersecting surfaces changes the flow pattern qualitatively. In the present paper, we report an investigation of the formation of the flow on a concave cylindrical surface near such a corner and consider how the flow is rearranged in the neighborhood of a corner in, for example, a channel of rectangular cross section that has an initial straight section and then a bend with a discontinuity of the curvature of the line of intersection of the concave and flat sides of the channel. The results are given of some experimental investigations of flow near the line of intersection of a flat wall and a curved (concave and convex) wall at a bend in a rectangular channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 64–68, January–February, 1983.I thank G. M. Bam-Zelikovich for constant interest in the work and A. I. Ruban for a number of extremely helpful comments.     

The development of an axisymmetric curved turbulent wall jet

An experimental study has been carried out of the low speed Coanda wall jet with both streamwise and axisymmetric curvature. A single component laser Doppler technique was used, and by taking several orientations at a given point, values of the three mean velocities and five of the six Reynolds stresses were obtained. The lateral divergence and convex streamwise curvature both enhanced the turbulence in the outer part of the jet compared with a plane two-dimensional wall jet. The inner layer exhibited a large separation of the positions of maximum velocity and zero shear stress. It was found that the streamwise mean velocity profile became established very rapidly downstream of the slot exit. The profile appeared fairly similar at later downstream positions, but the mean radial velocity and turbulence parameters showed the expected nonself preservation of the flow. Removal of the streamwise curvature resulted in a general return of the jet conditions toward those expected of a plane wall jet. The range and accuracy of the data may be used for developing turbulence models and computational techniques for this type of flow.     

Comparative Study of DNS,LES and Hybrid LES/RANS of Turbulent Boundary Layer with Heat Transfer Over 2d Hill

This paper first presents the turbulent heat transfer phenomenon of the boundary layer over a 2-dimensional hill using the direct numerical simulation (DNS). DNS results reveal turbulent heat transfer phenomena in the boundary layer over a 2-dimensional hill affected by the flow acceleration and the concave wall at the foreface of a hill, the convex wall at the top of the hill, and the flow deceleration, separation, and reattachment and the concave wall at the back of the hill. The prediction of turbulent heat transfer, the turbulence models of LES and HLR should be assessed in such heat transfer because these models have seldom been evaluated in the complex turbulent heat transfer. Therefore, this paper also presents evaluations of predictions of LES and HLR in the complicated turbulent heat transfer which is the boundary layer with heat transfer over a 2-dimensional hill. Consequently, this paper obviously shows the detailed turbulent heat transfer phenomena of a boundary layer over a 2-dimensional hill via DNS, and the evaluation results of prediction accuracy of LES and HLR for the heat transfer. LES and HLR give good prediction in comparison with DNS results, but the predicted reattachment and separation points are slightly different from DNS.     

Wake-boundary layer interaction subject to convex and concave curvatures and adverse pressure gradient

Measurements of mean velocity and turbulent quantities have been carried out when the wake of a symmetrical airfoil interacts with the boundary layer on the (i) walls of a straight duct/diffuser and (ii) convex and concave walls of a curved duct/diffuser. The effects of adverse pressure gradient and of curvatures on the interaction are studied separately and in combination. Six cases are considered, viz. with (i) neither pressure gradient nor curvature, (ii) adverse pressure gradient and no curvature, (iii) and (iv) convex curvature with zero and adverse pressure gradients, respectively, (v) and (vi) concave curvature with zero and adverse pressure gradients, respectively. For the flows with curvature, the curvature parameter δ/R is 0.023, and for the flows with adverse pressure gradient, the Clauser pressure gradient parameter β is 0.62. The individual influences of adverse pressure gradient and convex and concave curvatures on the boundary layer are similar to those observed by earlier investigations. It is further observed that the combined effect of concave/convex curvature and the adverse pressure gradient causes higher turbulence intensities than the sum of the individual effects. The effect of curvature is to make the wake asymmetric, and in combination with adverse pressure gradient the asymmetry increases. It is observed that the adverse pressure gradient causes faster wake–boundary-layer interaction. Comparing measurements in a straight duct, a curved duct, a curved diffuser and a straight diffuser, it is seen that the convex curvature reduces the boundary layer thickness. The asymmetry in wake development compensates for this effect and the wake–boundary-layer interaction on a convex surface is almost the same as that on a straight surface. In the case of interaction with the boundary layer on a concave surface, the curvature increases the boundary layer thickness and causes enhanced turbulence intensities. However, the asymmetry in wake is such that the extent of wake is lower towards the boundary layer side. As a result, the wake–boundary-layer interaction on concave surface is almost the same as on a straight surface. The interaction is faster in the presence of adverse pressure gradient. Received: 16 June 2000 / Accepted: 17 May 2001     

Computations for a jet impinging obliquely on a flat surface

A SIMPLE-C algorithm and Jones-Launder k-ε two-equation turbulence model are used to simulate a two-dimensional jet impinging obliquely on a flat surface. Both the continuity and momentum equations for the unsteady state are cast into suitable finite difference equations. The pressure, velocity, turbulent kinetic energy and turbulent energy dissipation rate distributions are solved and show good agreement with various experimental data. The calculations show that the flow field structure of the jet impinging obliquely on a flat surface is strongly affected by the oblique impingement angle. The maximum pressure zone of the obliquely impinging jet flow field moves towards the left as the oblique impingement angle is decreased.     

An experimental investigation on flow structures of confined and unconfined impinging air jets

The flow characteristics of both confined and unconfined air jets, impinging normally onto a flat plate have been experimentally investigated. The mean and turbulence velocities, and surface pressures were measured for Reynolds numbers ranging from 30,000 to 50,000 and the nozzle-to-plate spacings in range of 0.2–6. Smoke-wire technique is used to visualize the flow behavior. The effects of Reynolds number, nozzle-to-plate spacing and flow confinement on the flow structure are reported. In the case of confined jet, subatmospheric regions occur on both impingement and confinement surfaces at nozzle-to-plate spacings up to 2 for all Reynolds numbers in consideration and they lie up to nearly the same radial location at both surfaces. However, there is no evidence of the subatmospheric region in unconfined jet. It is concluded that there exists a linkage among the subatmospheric region, turbulence intensity and the peaks in heat transfer coefficients for low spacings in impinging jets.     

Enhancement of turbulent heat transfer during interaction of an impinging axisymmetric mist jet with a target

The flow structure and heat transfer of a mist jet with a low mass concentration of droplets (within 1%) impinging onto a flat surface aligned normal to the jet are studied numerically. The mathematical model is based on solving a system of Reynolds-averaged Navier-Stokes equations for a two-phase flow with the kinetic equation of the probability density function for coordinates, velocity, and temperature of particles. Addition of droplets is demonstrated to enhance heat transfer substantially, as compared with an impinging single-phase air jet in the region directly adjacent to the stagnation point of the jet.     

Turbulent boundary layer on a mildly curved convex surface

Extensive single point turbulence measurements made in the boundary layer on a mildly curved heated convex wall show that the turbulence heat fluxes and Stanton number are more sensitive to a change in wall curvature than the Reynolds stresses and skinfriction coefficient, and that downstream, as the flow adjusts to new curved conditions, the St/c _f ratio of Reynolds analogy is appreciably lower than in plane wall flow for the same conditions. Details of the turbulence structure in unheated flow have been documented in an earlier paper; temperature field measurements now described comprise mean temperature distributions, the streamwise variation of wall heat flux, profiles of the temperature variance, transverse and streamwise heat fluxes, and triple correlations. Turbulent diffusion of heat flux is drastically reduced even by mild curvature; changes in the heat fluxes are of the same order as changes in the shear stress, that is, an order of magnitude greater than the ratio of boundary layer thickness to wall radius of curvature. The data include plane flow measurements taken in a developed boundary layer upstream of a change in wall curvature.     

Turbulent boundary layer on a mildly curved convex surface

Mean flow and turbulence measurements have been made in a boundary layer which grows first on a flat' wall and then on a convex wall of radius of curvature approximately 100 times the boundary layer thickness. The turbulence data include profiles of the four non-zero components of the Reynolds stress tensor and three triple velocity products obtained at five stream-wise positions. A number of measurements were also made for comparison in the boundary layer on a flat wall under the same conditions. The effects of convex curvature are to reduce turbulent intensities, shear stress and wall friction by approximately 10% of their plane flow values; the triple velocity products are halved in the curved layer. The measurements supplement the small quantity of previously published data available for testing mathematical models of turbulence. The results show the same general trends that have been observed in earlier investigations but there are significant differences in detail, notably in respect of levels of the normal stresses.     

Propagation of Rayleigh waves on curved surfaces

The propagation and properties of Rayleigh waves on curved surfaces are investigated theoretically. The Rayleigh wave dispersion equation for propagation on a curved surface is derived as a parabolic equation, and its penetration depth is analyzed using the curved surface boundary. Reciprocity is introduced to model the diffracted Rayleigh wave beams. Simulations of Rayleigh waves on some canonical curved surfaces are carried out, and the results are used to quantify the influence of curvature. It is found that the velocity of the surface wave increases with greater concave surface curvature, and a Rayleigh wave no longer exists once the surface wave velocity exceeds the bulk shear wave velocity. Moreover, the predicted wave penetration depth indicates that the energy in the Rayleigh wave is transferred to other modes and cannot propagate on convex surfaces with large curvature. A strong directional dependence is observed for the propagation of Rayleigh waves in different directions on surfaces with complex curvatures. Thus, it is important to include dispersion effects when considering Rayleigh wave propagation on curved surfaces.     

Stereo-PIV measurements of vapor-induced flow modifications in confined jet impingement boiling

A single subcooled jet of water which undergoes boiling upon impingement on a discrete heat source is studied experimentally using time-resolved stereo particle image velocimetry (PIV). The impinging jet issues from a 3.75 mm diameter sharp-edged orifice in a confining orifice plate positioned 4 orifice diameters from the target surface. The behavior at jet Reynolds numbers of 5,000 and 15,000 is compared for a constant jet inlet subcooling of 10 °C. Fluorescent illumination allows for simultaneous imaging of both the flow tracers and the vapor bubbles in the flow. Flow structure, time-averaged velocities, and turbulence statistics are reported for the liquid regions within the confinement gap for a range of heat inputs at both Reynolds numbers, and the effect of the vapor generation on the flow is discussed. Vapor generation from boiling is found to modify the liquid velocities and turbulence fluctuations in the confinement gap. Flow in the confinement gap is dominated by vapor flow, and the vapor bubbles disrupt both the vertical impinging jet and horizontal wall jet flow. Moreover, vapor bubbles are a significant source of turbulence kinetic energy and dissipation, with the bubbly regions above the heated surface experiencing the most intense turbulence modification. Spectral analysis indicates that a Strouhal number of 0.023 is characteristic of the interaction between bubbles and turbulent liquid jets.     

Nonlinear turbulence models for predicting strong curvature effects

Prediction of the characteristics of turbulent flows with strong streamline curvature, such as flows in turbomachines, curved channel flows, flows around airfoils and buildings, is of great importance in engineering applications and poses a very practical challenge for turbulence modeling. In this paper, we analyze qualitatively the curvature effects on the structure of turbulence and conduct numerical simulations of a turbulent Uduct flow with a number of turbulence models in order to assess their overall performance. The models evaluated in this work are some typical linear eddy viscosity turbulence models, nonlinear eddy viscosity turbulence models （NLEVM） （quadratic and cubic）, a quadratic explicit algebraic stress model （EASM） and a Reynolds stress model （RSM） developed based on the second-moment closure. Our numerical results show that a cubic NLEVM that performs considerably well in other benchmark turbulent flows, such as the Craft, Launder and Suga model and the Huang and Ma model, is able to capture the major features of the highly curved turbulent U-duct flow, including the damping of turbulence near the convex wall, the enhancement of turbulence near the concave wall, and the subsequent turbulent flow separation. The predictions of the cubic models are quite close to that of the RSM, in relatively good agreement with the experimental data, which suggests that these models may be employed to simulate the turbulent curved flows in engineering applications.