Simulation of the Effect of the Freestream Turbulence Parameters on Heat Transfer in an Unsteady Boundary Layer

A variant of the two-parameter turbulence model which makes it possible continuously to calculate a flow region with laminar, transition and turbulent regimes is proposed for investigating the flow under conditions of high freestream turbulence intensity. It is shown that the properties of the thermal transition can be theoretically described using the quasi-steady turbulence model in the case of periodic freestream velocity distribution. The numerical results are compared with theoretical and experimental data. The approach proposed is developed for determining the combined effect of the parameters of harmonic fluctuations of the external velocity and freestream turbulence on the heat transfer characteristics on a flat plate with different boundary conditions for the enthalpy.     

Statistical modeling of the turbulent transition in the boundary layer

A method of statistical modeling the flow in the boundary-layer transition region is proposed on the basis of experimental data on kinematics and dynamics of turbulent spots (Emmons spots) on a flat plate in an incompressible fluid. This method allows one to determine the intermittency with allowance for overlapping of the spots, the forces on the plate surface, and the flow field in the vicinity of the transition region if the field of the streamwise component of the mean velocity in the developed turbulent boundary layer is known as a function of the Reynolds number. In contrast to multi-parameter models of the transition, this approach makes it possible to avoid the use of physically meaningless parameter values.     

Correlation of laminar-turbulent transition data over flat plates in supersonic/hypersonic flow including leading edge bluntness effects

The paper discusses flat plate boundary layer transition in supersonic/hypersonic flow conditions. Examination of experimental infrared thermography data illustrates the importance of the leading edge thickness and (non-) uniformity to the transition process. Such observations have triggered the collection of a wide range of experimental data on supersonic/hypersonic flat plate boundary layer transition, and a number of attempts to correlate this data with characteristic parameters including leading edge thickness. Results indicate a strong dependence of the relevant transition parameters on the pressure field in the transition region, as this is determined by the combined effects of leading edge thickness and boundary layer growth/viscous interaction, and particularly on the relative importance of the two effects. In fact, two distinct correlation zones are established, depending on whether the pressure distribution at the onset of transition is dominated by leading edge bluntness effects or by boundary layer growth and viscous interaction, thus limiting the observed data scatter to reasonable levels.Received: 13 August 2002, Accepted: 7 February 2003, Published online: 28 April 2003     

Simulation of the Effect of the Freestream Turbulence Parameters on the Boundary Layer of a Curvilinear Airfoil

Modified variants of differential turbulence models which make it possible continuously to calculate both the entire flow region with laminar, transition and turbulent regimes and local low Reynolds number zones are proposed for investigating the flow and heat transfer in the boundary layers developing in compressible gas flow past curvilinear airfoils. The effect of the intensity and scale of free-stream turbulence and their variability along the outer boundary layer edge, as well as the combined action of the turbulence intensity and the streamwise pressure gradient in flow past blade profiles, on the heat transfer and near-wall turbulence characteristics is analyzed. The numerical results are compared with experimental and theoretical data.     

Investigation of interaction between a plane transverse gas jet and a supersonic stream

The problem of interaction between a two-dimensional transverse gas jet emerging from a slot on a flat plate and a supersonic stream is considered. Several theoretical methods based on various approaches and physical models have been proposed to determine the characteristics of such a flow. The following fundamental directions can be isolated: a quasi-one-dimensional method [1], use of blast theory [2], and methods based on the equivalence of the effect of the jet and some solid on the external flow [3, 4]. However, the listed computational schemes [1–4] do not permit any clarification of the flow configuration in the jet and in the outer stream (the shock configuration, the jet boundaries, the distribution of the gasdynamic parameters in the flow field, etc.). Extensive experimental investigations of this phenomenon have been carried out simultaneously with the development of the theoretical methods, wherein the flow picture was determined, the pressure distribution was measured in the interaction domain, etc. [5, 6]. A computation method is proposed in this paper which will permit a detailed investigation of the flow structure in the jet and in the outer flow outside the separation region. Underlying the method is a hypothesis verified experimentally: The separating streamline in the mixing layer of the separated boundary layer (the “constant mass∝ line) intersects the jet boundary at the point of maximum jet standoff from the nozzle exit towards the incoming stream.     

Characteristic Regimes of Transitional Separation Bubbles in Unsteady Flow

This experimental investigation deals with transition phenomena of a separated boundary layer under unsteady inlet flow conditions. The main purpose of this investigation is to understand the influence of the rotor-stator interaction in turbomachinery on the subsequent, highly loaded boundary layer. The research project is divided into two phases. In the first phase, which has been completed recently, only the variation of mean velocity caused by upstream blades was simulated in the experiments while the free-stream turbulence intensity was retained at a constant low level. The experiments are carried out in an Eifel-type wind tunnel to investigate the laminar separated boundary layer of a flat plate under oscillating inlet conditions. The adverse pressure gradient, similar to that of turbomachines, is generated by the contoured upper wall. The unsteadiness is produced by a rotating flap located downstream of the test section. The reduced frequency, the amplitude and the mean Reynolds number are varied to simulate the conditions prevailing in turbomachines. In addition to the Kelvin–Helmholtz instability of the separated shear layer, a lower frequency instability was observed. This is frequently referred to as `free shear layer flapping' and results in two distinctly different ways of re-attachment, depending primarily on the Reynolds number. For low momentum thickness Reynolds numbers at the separation point, large-scale vortices locked to the frequency of the unsteady main flow are identified. They originate nearly at the top of the separation bubble and are ejected downstream. A fully turbulent boundary layer develops after these vortices mix out. For higher Reynolds numbers, transition is completed within a short length of the free shear layer and there-attachment region. The characteristic momentum thickness Reynolds number separating these two regimes in unsteady flow is about 125. The Strouhal number (reduced frequency) does not appear to have any significant effect. Based on the experimental results, this behaviour is discussed in some detail. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerical modeling of laminar-turbulent transition in a boundary layer at a high freestream turbulence level

Disturbances generated by external turbulence in the boundary layer on a flat plate set suddenly in motion are determined by numerically solving the Navier-Stokes equations. The results of direct numerical simulation of isotropic homogenous turbulence are taken as initial conditions. The solution obtained models laminar-turbulent transition in the flat-plate boundary layer at a high freestream turbulence level, time measured from the onset of the motion serving as the longitudinal coordinate. The solution makes it possible to estimate the effect of different factors, such as flow unsteadiness and nonlinearity and the characteristics of the freestream velocity fluctuation spectrum, on laminar-turbulent transition in the boundary layer.     

A study of boundary layer–wake interaction in shallow open channel flows

This paper describes an experimental investigation of the interaction between the boundary layer on a horizontal floor of a shallow open channel flow and the wake of a thin flat plate mounted vertically on the floor of the channel. The nominal thickness of the flat plate was limited to 2 mm in order to minimize the effect of the flume side walls on the generated wake. Two flat plate chord to thickness ratios (10 and 25) and two depths of flow (50 and 80 mm) were considered. The boundary layer thickness of the approaching flow was comparable with the depth of flow. The recovery of the boundary layer is then studied by observing the characteristics of the velocity profile downstream of the flat plate along the wake axis. The results indicate that the recovery process is slow, and that it is clearly non-monotonic. When compared with the approaching flow, the streamwise turbulence intensity values increase in the near-wake region followed by a gradual but slow decrease with increasing axial distance. Neither mean nor higher-order moments indicate a complete recovery even at large distances from the wake generator. The present results also indicate that the inner region appears to develop more quickly than the outer flow. Since the development of the quasi-two-dimensional wake is also of interest, velocity measurements are also presented along the wake cross-section. These velocity profiles indicate that the wake effects are still prevalent at 200 plate widths downstream of the wake generator. Through a proper choice of scaling variables, the mean velocity profiles across the wake can be collapsed onto a single curve, indicating a sense of similarity. Received: 23 September 1999/Accepted: 30 August 2000     

A model of the bursting process in non-newtonian fluids

A model for predicting the frequency of occurrence of sublayer bursts in non-Newtonian fluids is developed. The model is based on the similarity between turbulent pipe flow and a flat plate boundary layer at zero incidence. All parameters in the model are determined from hydrodynamic studies. The predicted bursting periods for Newtonian, power-law, and drag-reducing fluids are in reasonable agreement with previously published data and correlations.     

Evolution of jets effusing from inclined holes into crossflow

The turbulent flow structure and vortex dynamics of a jet-in-a-crossflow (JICF) problem, which is related to gas turbine blade film cooling, is investigated using the particle-image velocimetry (PIV) technique. A cooling jet emanating from a pipe interacts with a turbulent flat plate boundary layer at a Reynolds number Re_∞ = 400,000. The streamwise inclination of the coolant jet is 30° and two velocity ratios (VR = 0.28, VR = 0.48) and two mass flux ratios (MR = 0.28, MR = 0.48) are considered. Jets of air and CO₂ are injected separately into a boundary layer to examine the effects of the density ratio between coolant and mainstream on the mixing behavior and consequently, the cooling efficiency. The results show a higher mass flux ratio to enlarge the size of the recirculation region leading to a more pronounced entrainment of hot outer fluid into the wake of the jet. Furthermore, the lateral spreading of the coolant is strongly increased at a higher density ratio. The results of the experimental measurements are used to validate numerical findings. This comparison shows an excellent agreement for mean velocity and higher moment velocity distributions.     

Study of effect of a smooth hump on hypersonic boundary layer instability

Effect of a two-dimensional smooth hump on linear instability of hypersonic boundary layer is studied by using parabolized stability equations. Linear evolution of mode S over a hump is analyzed for Mach 4.5 and 5.92 flat plate and Mach 7.1 sharp cone boundary layers. Mean flow for stability analysis is obtained by solving the parabolized Navier–Stokes equations. Hump with height smaller than local boundary layer thickness is considered. The case of flat plate and sharp cone without the hump are also studied to provide comparable data. For flat plate boundary layers, destabilization and stabilization effect is confirmed for hump located at upstream and downstream of synchronization point, respectively. Results of parametric studies to examine the effect of hump height, location, etc., are also given. For sharp cone boundary layer, stabilization influence of hump is also identified for a specific range of frequency. Stabilization influence of hump on convective instability of mode S is found to be a possible cause of previous experimental observations of delaying transition in hypersonic boundary layers.     

An experimental study of receptivity of acoustic waves in laminar boundary layers

The receptivity of a laminar boundary layer developing on a flat plate was studied with two- and three-dimensional roughness elements. The layer was subjected to acoustic waves from speakers orientated perpendicular to the surface of the plate. Visualization of the transition patterns were obtained by heating temperature sensitive liquid crystals on the plate and observing the cooling patterns associated with the different flow regimes. Hot-wire data showed that the most amplified Tollmien-Schlichting waves dominated the downstream growth when the roughnesses were placed within the linearly unstable regime. The receptivity depended upon the size and aspect ratio of the three-dimensional roughness as predicted by Choudhari and Kerschen 1990. This research was partially funded by the Office of Naval Research under Contract N00014-89-J-1400. Their support is gratefully acknowledged. We also thank one of the reviewers for his helpful comments.     

Nonlinear development of a wave in a boundary layer

In recent years definite progress has been achieved in the construction of theoretical models of nonlinear wave processes which lead to a transition from laminar to turbulent flow [1, 2]. At the same time, there is a shortage of actual experimental material, especially for flows in a boundary layer. Fairly thorough experimental studies have been carried out only on the initial stage of the development of disturbances in a boundary layer, which is satisfactorily describable by the linear theory of hydrodynamic stability. In evaluating the theoretical models of subsequent stages of the transition, investigators have been forced to turn chiefly to much earlier experiments carried out by the United States National Bureau of Standards [3, 4], in which the main attention was concentrated on the three-dimensional structure of the transition region. The present investigation was undertaken for the purpose of obtaining detailed data on the structure of the flow in the transition region when there is disturbance in the laminar boundary layer of a two-dimensional wave. In order to make the two-dimensional nonlinear effects stand out more clearly, the amplitude of the wave was specified to be fairly large from the very outset. In contrast to earlier investigations, the main attention was centered on the study of the spectral composition of the disturbance field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 49–58, May–June, 1977.     

A bypass wake induced laminar/turbulent transition

The process of laminar to turbulent transition induced by a von Karman vortex street wake, was studied for the case of a flat plate boundary layer. The boundary layer developed under zero pressure gradient conditions. The vortex street was generated by a cylinder positioned in the free stream. An X-type hot-wire probe located in the boundary layer, measured the streamwise and normal to the wall velocity components. The measurements covered two areas; the region of transition onset and development and the region where the wake and the boundary layer merged producing a turbulent flow. The evolution of Reynolds stresses and rms-values of velocity fluctuations along the transition region are presented and discussed. From the profiles of the Reynolds stress and the mean velocity profile, a ‘negative' energy production region along the transition region, was identified. A quadrant splitting analysis was applied to the instantaneous Reynolds stress signals. The contributions of the elementary coherent structures to the total Reynolds stress were evaluated, for several x-positions of the near wall region. Distinct regions in the streamwise and normal to the wall directions were identified during the transition.     

A study in transitional flat plate boundary layers: measurement and visualization

 This study is concerned with transition in flat plate boundary layer flow. Sets of results are obtained as follows: (1) Very clear pictures of the formation and the development of the butterfly-like structures rather than ∧-structures in the K-regime of boundary layer transition are obtained. (2) A chain of ring like vortices, which generate the high-frequency spikes on the time traces of velocity and still present periodical behaviour, at the tip of each ∧-vortex, which is the part of the butterfly-like structure, are visualized for the first time. (3) A wave-like structure is observed to occupy the whole boundary layer, extending from the near-wall region to the outer edge of the boundary layer. Received: 24 September 1998/Accepted: 24 April 1999     

Heat transfer enhancement in a turbulent natural convection boundary layer along a vertical flat plate

An experimental study on heat transfer enhancement for a turbulent natural convection boundary layer in air along a vertical flat plate has been performed by inserting a long flat plate in the spanwise direction (simple heat transfer promoter) and short flat plates aligned in the spanwise direction (split heat transfer promoter) with clearances into the near-wall region of the boundary layer. For a simple heat transfer promoter, the heat transfer coefficients increase by a peak value of approximately 37% in the downstream region of the promoter compared with those in the usual turbulent natural convection boundary layer. It is found from flow visualization and simultaneous measurements of the flow and thermal fields with hot- and cold-wires that such increase of heat transfer coefficients is mainly caused by the deflection of flows toward the outer region of the boundary layer and the invasion of low-temperature fluids from the outer region to the near-wall region with large-scale vortex motions riding out the promoter. However, heat transfer coefficients for a split heat transfer promoter exhibit an increase in peak value of approximately 60% in the downstream region of the promoter. Flow visualization and PIV measurements show that such remarkable heat transfer enhancement is attributed to longitudinal vortices generated by flows passing through the clearances of the promoter in addition to large-scale vortex motions riding out the promoter. Consequently, it is concluded that heat transfer enhancement of the turbulent natural convection boundary layer can be substantially achieved in a wide area of the turbulent natural convection boundary layer by employing multiple column split heat transfer promoters. It may be expected that the heat transfer enhancement in excess of approximately 40% can be accomplished by inserting such promoters.     

中等Reynolds数平板绕流的动理论分析

郭永怀先生1953年给出的中等Reynolds数下、不可压缩流体有限长平板绕流的解析解是边界层理论中的经典工作.许多研究者对平板绕流阻力系数的郭永怀公式以及后续工作进行了 评估,评估的依据是Janour与Schaaf和Sherman的实验数据.本文的动理论分析和计算表 明: Schaaf和Sherman在低亚声速条件下(郭永怀先生1953年给出的中等Reynolds数下、不可压缩流体有限长平板绕流的解析解是边 界层理论中的经典工作. 许多研究者对平板绕流阻力系数的郭永怀公式以及后续工作进行了 评估, 评估的依据是Janour与Schaaf和Sherman的实验数据. 本文的动理论分析和计算表 明: Schaaf和Sherman在低亚声速条件下(郭永怀先生1953年给出的中等Reynolds数下、不可压缩流体有限长平板绕流的解析解是边 界层理论中的经典工作. 许多研究者对平板绕流阻力系数的郭永怀公式以及后续工作进行了 评估, 评估的依据是Janour与Schaaf和Sherman的实验数据. 本文的动理论分析和计算表 明: Schaaf和Sherman在低亚声速条件下(郭永怀先生1953年给出的中等Reynolds数下、不可压缩流体有限长平板绕流的解析解是边 界层理论中的经典工作. 许多研究者对平板绕流阻力系数的郭永怀公式以及后续工作进行了 评估, 评估的依据是Janour与Schaaf和Sherman的实验数据. 本文的动理论分析和计算表 明: Schaaf和Sherman在低亚声速条件下(郭永怀先生1953年给出的中等Reynolds数下、不可压缩流体有限长平板绕流的解析解是边界层理论中的经典工作.许多研究者对平板绕流阻力系数的郭水怀公式以及后续工作进行了评估,评估的依据是Janour与Schaaf和Sherman的实验数据.本文的动理论分析和计算表明:Schaaf和Sherman在低亚声速条件下(0.16相似文献   

Boundary layer in the vicinity of the stagnation point of a body of axial symmetry in a turbulent stream

The flow in the boundary layer in the vicinity of the stagnation point of a flat plate is examined. The outer stream consists of turbulent flow of the jet type, directed normally to the plate. Assumptions concerning the connection between the pulsations in velocity and temperature in the boundary layer and the average parameters chosen on the basis of experimental data made it possible to obtain an isomorphic solution of the boundary layer equations. Equations are obtained for the friction and heat transfer at the wall in the region of gradient flow taking into account the effect of the turbulence of the impinging stream. It is shown that the friction at the wall is insensitive to the turbulence of the impinging stream, while the heat transfer is significantly increased with an increase in the pulsations of the outer flow. These properties are confirmed by the results of experimental studies [1–4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 83–87, September–October, 1973.     

Investigation of intermittency measurement methods for transitional boundary layer flows

Three turbulent intermittency methods, namely the , TERA (turbulent energy recognition algorithm), and M-TERA (modified turbulent energy recognition algorithm) methods, for identifying the intermittent flow characteristics associated with boundary layer transition from laminar to turbulent were considered and compared. The data used were obtained from hot-wire measurements in transitional boundary layer flows on a concave surface with a 2-m radius of curvature and on a flat plate. Comparisons show that the and TERA methods are more sensitive to the choice of threshold constants than the M-TERA method. In terms of the intermittency distribution across the boundary layer, the values obtained by the and TERA methods are unrealistically high in the near-wall region, while those obtained by the M-TERA method are more realistic. In the outer boundary layer region and outside the boundary layer, the and M-TERA methods give reasonable intermittency values, whereas the TERA method produces unrealistically high values in the region outside the boundary layer. In addition, the M-TERA method provides a sharper definition of theend of transition.     

Transition to Turbulence in the Boundary Layer on a Plate in the Presence of a Negative Free-Stream Pressure Gradient

Transition to turbulence in the boundary layer on a flat plate is investigated numerically for an incompressible fluid flow with a given negative free-stream pressure gradient. The transition is investigated using the three-parameter turbulence model developed by the authors. The calculation results are compared with the available experimental data.