Leading-edge receptivity of boundary layer to three-dimensional free-stream turbulence

The laminar-turbulent transition has always been a hot topic of fluid mechanics. Receptivity is the initial stage and plays a crucial role in the entire transition process. The previous studies of receptivity focus on external disturbances such as sound waves and vortices in the free stream, whereas those on the leading-edge receptivity to the three-dimensional free-stream turbulence (FST), which is more general in the nature, are rarely reported. In consideration of this, this work is devoted to investigating the receptivity process of three-dimensional Tollmien-Schlichting (T-S) wave packets excited by the three-dimensional FST in a flat-plate boundary layer numerically. The relations between the leading-edge receptivity and the turbulence intensity are established, and the influence of the FST directions on the propagation directions and group velocities of the excited T-S wave packets is studied. Moreover, the leading-edge receptivity to the anisotropic FST is also studied. This parametric investigation can contribute to the prediction of laminar-turbulent transition.

Unsteady three-dimensional boundary layer flow due to a permeable shrinking sheet

The unsteady viscous flow over a continuously permeable shrinking surface is studied. Similarity equations are obtained through the application of similar transformation techniques. Numerical techniques are used to solve the similarity equations for different values of the unsteadiness parameter, the mass suction parameter, the shrinking parameter and the Prandtl number on the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. It is found that, different from an unsteady stretching sheet, dual solutions exist in a certain range of mass suction and unsteadiness parameters.

Mechanism of three-dimensional boundary-layer receptivity

Boundary-layer receptivity is always a hot issue in laminar-turbulent tran- sition. Most actual laminar-turbulent transitions belong to three-dimensional flows. An infinite back-swept fiat-plate boundary layer is a typical three-dimensionalflow. Study of its receptivity is important both in theory and applications. In this paper, a free- stream turbulence model is established. A modified fourth-order Runge-Kutta scheme is used for time marching, and compact finite difference schemes are used for space dis- cretization/ On these bases, whether unsteady cross-flow vortices can be excited in the three-dimensional boundary layer （the infinite back-swept flat-plate boundary layer） by free-stream turbulence is studied numerically. If so, effects of the level and the direc- tion of free-stream turbulence on the three^dimensional boundary-layer receptivity are further studied. Differences of the three-dimensional boundary-layer receptivity are then discussed by considering the non-parallel effect, influence of the leading-edge stagnation point of the flat plate, and variation of the back-swept angle separately. Intensive studies on the ＇three-dimensional boundary-layer receptivity will benefit the development of the hydrodynamic stability theory, and provide a theoretical basis for prediction and control of laminar-turbulent transition.

Mathematical Formulation of Bubble Formation after Compressible Boundary Layer Separation: Preliminary Numerical Results

Laminar boundary layer (BL), under adverse pressure gradient, can separate. The separated shear layer reattaches to form a laminar separation bubble. Such bubbles are usually observed on gas turbine blades, on low Reynolds number wings and close to the leading edges of airfoils. Presence of bubbles has a weakening effect on the performance of a fluid device. The understanding of the prevailing mechanism of the separation bubble and ways to control it are essential for the efficient design of these devices. This is due to the significance of drag reduction in these various aerodynamic devices, such as gas turbines, re-entry space vehicles and airfoils. This study introduces a two-dimensional mathematical formulation of bubble formation after flow separation. The laminar BL equations with appropriate boundary conditions are dimensionalized using the Falkner-Skan transformation. Additionally, using the Keller-box method, the nonlinear system of partial differential equations (PDEs) is numerically solved. This study presents preliminary numerical results of bubble formation in low Mach numbers. These results reveal that after separation, a laminar bubble is formed in all studied cases, for Mach numbers, M = 0.2, 0.33 and 1.0. The flow after separation reverses close to the wall and finally reattaches downstream, in a new location. As the Mach number increases, this effect is more intense. After reattachment, the BL is again established in a lower energy level and the velocity field is substantially reduced, for all cases.

In uence of Endwall Boundary Layer Suction on the Flow Fields of a Critically Loaded Di usion Cascade

Boundary layer suction is an e ective method used to delay separations in axial compressors. Most studies on bound?ary layer suction have focused on improving the performance of compressors,whereas few studies investigated the influence on details of the flow fields,especially vortexes in compressors. CFD method is validated with experi?mental data firstly. Three single?slot and one double?slot endwall boundary layer suction schemes are designed and investigated. In addition to the investigation of aerodynamic performance of the cascades with and without suction,variations in corner open separation,passage vortex,and concentration shedding vortex,which are rarely seen for the flow controlled blades in published literatures,are analyzed. Then,flow models,which are the ultimate aim,of both baseline and aspirated cascades are established. Results show that single?slot endwall suction scheme adjacent to the suction surface can e ectively remove the corner open separation. With suction mass flow rate of 0.85%,the overall loss coe cient and endwall loss coe cient of the cascade are reduced by 25.2% and 48.6%,respectively. Besides,this scheme increases the static pressure rise coe cient of the cascade by 3.2% and the flow turning angle of up to 3.3° at 90% span. The concentration shedding vortex decreases,whereas the passage vortex increases. For single?slot suction schemes near the middle pitchwise of the passage,the concentration shedding vortex increases and the passage vortex is divided into two smaller passage vortexes,which converge into a single?passage vortex near the trailing edge section of the cascade. For the double?slot suction scheme,triple?passage vortexes are presented in the blade passage. Some new vortex structures are discovered,and the novel flow models of aspirated compressor cascade are proposed,which are important to improve the design of multi?stage aspirated compressors.

Linear spatial instability analysis in 3D boundary layers using plane-marching 3D-LPSE

It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional （3D） boundary layers to predict the transition with the e^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation （3D- LPSE） approach, a 3D extension of the two-dimensional LPSE （2D-LPSE）, is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation （DNS） rather than a 2D-eigenvalue problem （EVP） procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.

Numerical Analysis of Electromagnetic Control of the Boundary Layer Flow on a Ship Hull

In this article, electromagnetic control of turbulent boundary layer on a ship hull is numerically investigated. This study is conducted on the geometry of tanker model hull. For this purpose, a combination of electric and magnetic fields is applied to a region of boundary layer on stern so that produce wall parallel Lorentz forces in streamwise direction as body forces in stern flow. The governing equations including RANS equations with SST k-ω?turbulent model coupled with electric potential equation are numerically solved by using Ansys Fluent codes. Accuracy of this turbulent model of Fluent in predicting Turbulent flow around a ship is also tested by comparing with available experimental results that it shows a good agreement with experimental data. The results obtained for ship flow show that by applying streamwise Lorentz forces that are large enough, flow is accelerated. The results are caused to delay or avoid the flow separation in stern, increase the propeller inlet velocity, create uniform flow distribution behind the ship’s hull in order to improve the propeller performance, and finally decrease the pressure resistance and total resistance.

EXPERIMENTAL INVESTIGATION ON THE TURBULENT COHERENT STRUCTURES OF LAMINAR SEPARATION FLOW OVER A BACKWARD FACING STEP

The experimental investigation is conducted with LDV and hydrogen bubble technique in water flow. The shear layer thickness. the vorticity thickness. the maximulll value of turbulence intensities. the turbulent coherent structure. the variations of wall shear stress and the boundary layer shape factor are obtained. In the redevelopment region. the detailed analysis is first made for the streak structures in the near wall region and the turbulent boundary layer is formed at (x-xr) / h = 20.

STUDY OF THREE-DIMENSIONAL SEPARATION OF BOUNDARY LAYER OVER BLUNT BODIES

In the case of three-dimensional flows, the separation can be defined in more than one way. Discussions about three-dimensional boundary layer separation in the literature have found a rational extension of the zero skin friction. Attempts have been made to establish the identity of “separation lines”. Among definitions, these may be found： （1） envelopes of limiting streamlines, （2） lines dividing flow which has come from different regions, （3） lines of singularities （problems of topology）, （4） lines on which some component of the skin friction vanishes. Each of these is valid under certain conditions, but none is universally valid. In the present work, we use the definition （4）, i.e. at low incidence of a blunt body the separation line is identified as the zero of the meridian skin friction component （Wang 1975）. So the separation line on a flattened spheroid （6：3：1） at 6° of incidence is calculated, as well as experimentally determined by using the electrochemical method, which allows to follow the evolution of the parietal velocity gradient.

FAST SOLUTION OF TURBULENT SEPARATION BY STRAWN'S METHOD

A quasi-simultaneous viscous/inviscid interaction model and a new integral method are tried to predict twodimensional incompressible turbulent boundary-layer separating flows. The results are compared with experiments and other prediction.

SEPARATION CONTROL FOR THE OUTWING OF A STRAKE－WING BY ROTATING CONE PLACED NEAR THE LEADING EDGE

Based on the research result on the strake-wing, when the size of a strakeis not large, there is a separation zone near the leading edge of the outwing of thestrake-wing at middle angles of attack. So the idea on separation control by rotating acone placed near the leading edge is presented. The cone surface consists of the part ofthe wing. The effect of rotating the cone on aerodynamic characteristics of thestrake-wing is investigated. The results show that a rotating surface could play an important role in controlling the flow separation for a 3-dimensional wing. For example,the relative increment in maximum lift coefficient attains 30%. The separation zone issuppressed to a certain extent.

Near-wall behaviors of oblique-shock-wave/turbulent-boundary-layer interactions

A direct numerical simulation （DNS） on an oblique shock wave with an incident angle of 33.2° impinging on a Mach 2.25 supersonic turbulent boundary layer is performed. The numerical results are confirmed to be of high accuracy by comparison with the reference data. Particular efforts have been made on the investigation of the near-wall behaviors in the interaction region, where the pressure gradient is so significant that a certain separation zone emerges. It is found that, the traditional linear and loga- rithmic laws, which describe the mean-velocity profiles in the viscous and meso sublayers, respectively, cease to be valid in the neighborhood of the interaction region, and two new laws of the wall are proposed by elevating the pressure gradient to the leading order. The new laws are inspired by the analysis on the incompressible separation flows, while the compressibility is additionally taken into account. It is verified by the DNS results that the new laws are adequate to reproduce the mean-velocity profiles both inside and outside the interaction region. Moreover, the normalization adopted in the new laws is able to regularize the Reynolds stress into an almost universal distribution even with a salient adverse pressure gradient （APG）.

CALCULATION OF THREE DIMENSIONAL BOUNDARY LAYER EQUATIONS USING DIFFERENTIAL QUADRATURE METHOD

An extended differential quadrature method is used to compute nonlinear partial differential equations for tbree-dimensional laminar boundary layer now in this paPer. The key technique to differential quadrature, which is used in determining weighting coefficients for discretization of any order partial derivative, is investigated. The method of computing different weighting coefficients is presented. Three dimensional boundary layer equations are discretized by the differential quadrature method, and relative formula is obtained. The resulting scheme is applied to the computation of examples, which shows that the differential quadrature method can achieve rather high accurate solution using much less grid points than those of other methods, suck as finite difference and finite element methods.

Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory(LST) with the equivalent spanwise wavenumber correction(ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.

Boundary layer separation control on a highly-loaded,low-solidity compressor cascade

Separated flow can be effectively controlled through the management of blade boundary layer development.Numerical simulations on a highly-loaded,low-solidity compressor cascade indicate that combined blowing and suction flow control technique can significantly improve cascade performance,especially in increasing the cascade loading and static pressure ratio as well as decreasing the loss coefficient.Meanwhile,it is more effective to improve cascade performance by blowing near leading edge on suction surface than suction near trailing edge.Both the locations and flow rates of blowing and suction are major impact factors of this method to cascade performance.Comparing to the baseline,the static pressure ratio increases by 15% and loss coefficient decreases by 80%,with a blowing fraction of 1.7% and a suction fraction of 1.38% of the inlet mass flow.

Topological Studies of Three-dimensional Flows in a High Pressure Compressor Stator Blade Row without and with Boundary Layer Aspiration

This paper presents a numerical study of the flow topologies of three-dimensional （3D） flows in a high pressure compressor stator blade row without and with boundary layer aspiration on the hub wall. The stator blade is representative of the first stage operating under transonic inlet conditions and the blade design encourages development of highly complex 3D flows. The blade has a small tip clearance. The computational fluid dynamics （CFD） studies show progressive increase of hub corner stall with the increase in incidence. Aspiration is implemented on the hub wall via a slot in the comer between the hub wall and the suction surface. The CFD studies show aspiration to be sensitive to the suction flow rate; lower rate leads to very complex flow struc- tures and increased level of losses whereas higher rate renders aspiration effective for control of hub comer separation. The flow topologies are studied by trace of skin friction lines on the walls. The nature of flow can be explained by the topological rules of closed separation. Furthermore, a deeper analysis is done for a particular case with advanced criterion to test the non-degeneracy of critical points in the flow field.

Sidewall influence of varying free stream Mach number in ramp induced shock wave boundary layer interactions

This study investigates the three-dimensional(3D)effects introduced by the end walls for an aspect ratio of1 in ramp-induced shock wave boundary layer interactions.The simulations are performed using a symmetry boundary condition in the spanwise direction at free-stream Mach numbers in 3D.The simulations are performed using an in-house compressible supersonic solver“Open SBLIFVM”.Two free stream Mach numbers 2.5,and3 are used in the current work,and the simulated results are compared with the aspect ratio 1 simulations by Mangalagiri and Jammy.The inflow is initialized with a similarity solution;its Reynolds number based on the boundary layer thickness is adjusted such that the Reynolds number at the start of the ramp is kept at 3×10^(5)for all simulations.From the results,it is evident that the introduction of sidewalls resulted in a shorter centerline separation length when compared with the two-dimensional(2D)simulations.This contradicts the results at Mach 2 by Mangalgiri and Jammy where the vortex observed at Mach 2 in the central separation region disappeared with increasing free-stream Mach number.Additionally,the topology of interaction shifted from owl-like separation of the second kind to the first kind when the freestream Mach number increased from2 to 2.5.It can be concluded that the interaction topology is crucial to the increase or decrease of the central separation length when compared to 2D simulations.

TURBULENT SEPARATED REATTACHED FLOW IN A TWO-DIMENSIONAL CURVED-WALL DIFFUSER

A turbulent separation-rcattachment flow in a two-dimensional asymmetrical curved-wall diffuser is studied by a two-dimensional laser doppler velocimeter.The turbulent boundary layer separates on the lower curved wall under strong pressure gradient and then reattaches on a parallel channel.At the inlet of the diffuser,Reynolds number based on the diffuser height is 1.2×10~5 and the velocity is 25.2m/s.The re- sults of experiments are presented and analyzed in new defined streamline-aligned coordinates.The experiment shows that after Transitory Detachment Reynolds shear stress is negative in the near-wall backflow region. Their characteristics are approximately the same as in simple turbulent shear layers near the maximum Reynolds shear stress.A scale is formed using the maximum Reynolds shear stresses.It is found that a Reynolds shear stress similarity exists from separation to reattachment and the Schofield-Perry velocity law ex- ists in the forward shear flow.Both profiles are used in the experimental work that leads to the design of a new eddy-viscosity model.The length scale is taken from that developed by Schofield and Perry.The composite velocity scale is formed by the maximum Reynolds shear stress and the Schofield Perry velocity scale as well as the edge velocity of the boundary layer.The results of these experiments are presented in this paper

NATURE OF THE SURFACE HEAT TRANSFER FLUCTUATION IN A HYPERSONIC SEPARATED TURBULENT FLOW

This paper presents the results of an experimental study of the unsteady nature of a hypersonic sepa- rated turbulent flow.The nominal test conditions were a freestream Mach number of 7.8 and a unit Reynolds number of 3.5x10^7/m.The separated flow was generated using finite span forward facing steps.An array of flush mounted high spatial resolution and fast response platinum film resistance thermometers was used to make mul- ti-channel measurements of the fluctuating surface heat trtansfer within the separated flow.Conditional sampling ana- lysis of the signals shows that the root of separation shock wave consists of a series of compression wave extending over a streamwise length about one half of the incoming boundary layer thickness.The compression waves con- verge into a single leading shock beyond the boundary layer.The shock structure is unsteady and undergoes large-scale motion in the streamwise direction.The length scale of the motion is about 22 percent of the upstream influence length of the separation shock wave.There exists a wide band of frequency of oscillations of the shock system.Most of the frequencies are in the range of 1-3 kHz.The heat transfer fluctuates intermittently between the undisturbed level and the disturbed level within the range of motion of the separation shock wave.This inter mittent phenomenon is considered as the consequence of the large-scale shock system oscillations.Downstream of the range of shock wave motion there is a separated region where the flow experiences continuous compression and no intermittency phenomenon is observed.

激波/湍流边界层干扰中的自适应控制技术

从激波/湍流边界层干扰机理以及流动控制的迫切需求入手,从自适应涡流发生器、自适应鼓包、自适应微射流以及自适应次流循环四个方面对激波/湍流边界层干扰中的自适应控制技术研究进展进行了总结。分析认为,结合AI技术发展自适应流动控制技术,加速控制方式智能化,可作为新一代高超声速飞行器宽速域飞行的重要技术手段。具体来说,就是通过调节外加激励对高超声速飞行器不同区域实现局部流动加/减速、气动热防护、气动控制等功能,根据流场参数建立控制反馈回路,自适应调整局部流场结构,以满足工程实际需求。