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.

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.

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.

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.

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.

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.

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.

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.

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.

Effect of expansion waves on cowl shock wave and boundary layer interaction in hypersonic inlet

The interaction of cowl shock wave and boundary layer has a crucial effect on the stability,operability and performance of hypersonic inlets.Many studies on inhibiting the sep-aration and managing the strength of the interaction of the shock wave and boundary layer with expansion corner have been conducted.However,the expansion waves near the circular arc shoulder to effectively control the interaction and cowl shock arrangement is little investigated.Therefore,the interaction of the cowl shock wave and boundary layer under thefluence of the expansion waves is studied by inviscid and viscous numerical simulations.The results reveal that the expansion waves have an important impact on the interaction between the cowl shock wave and boundary layer and the strength of shock wave,and that there are four types of inter-action processes with the change of the relative impingement positions of cowl shock wave.The expansion waves have a different influence on the shock wave and boundary layer inter-action at different incident points.When the incident point of the cowl shock wave goes far downstream from the end of the circular arc shoulder,the influence of expansion waves is weakened,and the magnitude of separation zone increases.However,when the expansion waves are applied to the interaction of the cowl shock wave and boundary layer on the circular arc shoulder,the separation can be effectively controlled.In particular,while the expansion waves interact with the shock wave and boundary layer in the back half of the circular arc shoulder,the separation is best inhibited.Compared with the upstream and downstream inci-dent points,the scale of separation area in the optimal control region is reduced by 65.3%at most.Furthermore,the total pressure recovery coefficientfirst increases and then decreases when the cowl moves from upstream to downstream,and the total pressure recovery coefficient reaches the maximum value of 68.36%at the incident position of cowl shock wave d Z 8.09d0.

An algorithm to separate wind tunnel background noise from turbulent boundary layer excitation

Wall pressure fluctuations generated by Turbulent Boundary Layers(TBL) provide a significant contribution in reducing the structural vibration and the aircraft cabin noise. However,it is difficult to evaluate these fluctuations accurately through a wind tunnel test because of the pollution caused by the background noise generated by the jet or the valve of the wind tunnel. In this study, a new technology named Subsection Approaching Method(SAM) is proposed to separate the wall pressure fluctuations from the background noise induced by the jet or the valve for a transonic wind tunnel test. The SAM demonstrates good performance on separating the background noise from the total pressure compared to the other method in this study. The investigation considers the effects of the sound intensity and the decay factor on the sound-source separation. The results show that the SAM can derive wall pressure fluctuations effectively even when the level of background noise is considerably higher than the level of the wall pressure fluctuations caused by the TBL. In addition, the computational precision is also analyzed based on the broad band noise tested in the wind tunnel. Two methods to improve the precision of the computation with the SAM are also suggested: decreasing the loop gain and increasing the sensors for the signal analysis.

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.

Influence of coupled boundary layer suction and bowed blade on flow field and performance of a diffusion cascade

Based on the investigation of mid-span local boundary layer suction and positive bowed cascade, a coupled local tailored boundary layer suction and positive bowed blade method is developed to improve the performance of a highly loaded diffusion cascade with less suction slot. The effectiveness of the coupled method under different inlet boundary layers is also investigated.Results show that mid-span local boundary layer suction can effectively remove trailing edge separation, but deteriorate the flow fields near the endwall. The positive bowed cascade is beneficial for reducing open corner separation, but is detrimental to mid-span flow fields. The coupled method can further improve the performance and flow field of the cascade. The mid-span trailing edge separation and open corner separation are eliminated. Compared with linear cascade with suction, the coupled method reduces overall loss of the cascade by 31.4% at most. The mid-span loss of the cascade decreases as the suction coefficient increases, but increases as bow angle increases. The endwall loss increases as the suction coefficient increases. By contrast, the endwall loss decreases significantly as the bow angle increases. The endwall loss of coupled controlled cascade is higher than that of bowed cascade with the same bow angle because of the spanwise inverse ‘‘C＂ shaped static pressure distribution. Under different inlet boundary layer conditions, the coupled method can also improve the cascade effectively.

Shock wave-boundary layer interactions control by plasma aerodynamic actuation

This study demonstrates the potential for shock wave-boundary layer interaction control in air by plasma aerodynamic actuation.Experimental investigations on shock wave-boundary layer interactions control by plasma aerodynamic actuation are conducted in a Mach 3 in-draft air tunnel.Schlieren imaging shows that the discharges cause the oblique shock to move forward.Schlieren imaging and static pressure probes also show that separation phenomenon shifts backward and the size of separation is enlarged when plasma aerodynamic actuation is applied.The intensity of shock wave is weakened through wall pressure probe.Furthermore,numerical investigations on shock wave-boundary layer interactions control are conducted with plasma aerodynamic actuation.The discharge is modeled as a steady volumetric heat source which is integrated into the energy equation.The input energy level is about 7 kW through discharge process.Results show that the separation phenomenon shifts backward and the intensity of shock is reduced with plasma actuation.These numerical results are consistent with the experimental results.

Scaling of interaction lengths for hypersonic shock wave/turbulent boundary layer interactions

The interaction length induced by Shock Wave/Turbulent Boundary-Layer Interactions(SWTBLIs)in the hypersonic flow was investigated using a scaling analysis,in which the interaction length normalized by the displacement thickness of boundary layer was correlated with a corrected non-dimensional separation criterion across the interaction after accounting for the wall temperature effects.A large number of hypersonic SWTBLIs were compiled to examine the scaling analysis over a wide range of Mach numbers,Reynolds numbers,and wall temperatures.The results indicate that the hypersonic SWTBLIs with low Reynolds numbers collapse on the supersonic SWTBLIs,while the hypersonic cases with high Reynolds numbers show a more rapid growth of the interaction length than that with low Reynolds numbers.Thus,two scaling relationships are identified according to different Reynolds numbers for the hypersonic SWTBLIs.The scaling analysis provides valuable guidelines for engineering prediction of the interaction length,and thus,enriches the knowledge of hypersonic SWTBLIs.

Passage shock wave/boundary layer interaction control for transonic compressors using bumps

Flow separation due to shock wave/boundary layer interaction is dominated in blade passage with supersonic relative incoming flow,which always accompanies aerodynamic performance penalties.A loss reduction method for smearing the passage shock foot via Shock Control Bump(SCB)located on transonic compressor rotor blade suction side is implemented to shrink the region of boundary layer separation.The curved windward section of SCB with constant adverse pressure gradient is constructed ahead of passage shock-impingement point at design rotor speed of Rotor 37 to get the improved model.Numerical investigations on both two models have been conducted employing Reynolds-Averaged Navier-Stokes(RANS)method to reveal flow physics of SCB.Comparisons and analyses on simulation results have also been carried out,showing that passage shock foot of baseline is replaced with a family of compression waves and a weaker shock foot for moderate adverse pressure gradient as well as suppression of boundary layer separations and secondary flow of low-momentum fluid within boundary layer.It is found that adiabatic efficiency and total pressure ratio of improved blade exceeds those of baseline at 95%-100%design rotor speed,and then slightly worsens with decrease of rotatory speed till both equal below 60%rated speed.The investigated conclusion implies a potential promise for future practical applications of SCB in both transonic and supersonic compressors.

The Boundary Layer Interaction with Shock Wave and Expansion Fan

The results of experimental investigation of a turbulent boundary layer on compression and expansion surfaces are presented. They include the study of the shock wave and/or expansion fan action upon the boundary layer, boundary layer separation and its relaxation. Complex events of paired interactions and the flow on compression convex-concave surfaces were studied. The possibility and conditions of the boundary layer relaminarization behind the expansion fan and its effect on the relaxation length are presented. Different model configurations for wide range conditions were investigated. Comparison of results for different interactions was carried out.