Evolution of wall flow structure and measurement of shear stress issuing from supersonic jet with extended shelf

Yun JIAO ,Chengpeng WANG,* ,Jiaqi XIE ,Kang LI ,Keming CHENG

a College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

b Key Laboratory of Unsteady Aerodynamics and Flow Control,Ministry of Industry and Information Technology,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

KEYWORDS Evolution of shock structure;Flow visualization;Quantitative measurement;Shear stress;Supersonic jet

Abstract This paper reports an experimental study on the supersonic jet surface flow structure visualization and shear stress field measurement issuing from a rectangular nozzle with extended shelf.The evolution of the near-field surface flow structures with an increased Nozzle Pressure Ratio (NPR) is successfully captured by the surface oil flow,infrared detection technology,and the Shear-Sensitive Liquid Crystal Coating (SSLCC) technique.Results reveal that under smaller NPR,the wall flow structure is similar to that of a jet without the extended shelf i.e.,clean jets,and this is caused by insufficient effect on the boundary layer.However,at higher amplitudes of NPR,there exists a significant effect of the boundary layer,as a near triangular separation forms on the trailing edge of the Mach stem due to the adverse pressure gradient,which is visualized for the very first time in this paper.Furthermore,the vector field of shear stress is measured quantitatively by SSLCC technique.Results shows that the magnitude of shear stress heightened with NPR increasing,and the directions of shear stress changes across the shock wave and expansion fans.In addition,surface streamlines measured by SSLCC is significantly consistent with the streamlines visualized using the oil flow technique.

1.Introduction

Although supersonic jets have been the subject of numerous theoretical,numerical,and experimental studies,it appears there is little or no empirical studies investigating the wall flow structure of supersonic jets with extended shelf.The motivation for this study comes from the application of propulsion nozzles in military supersonic jets,where a single extended shelf may be present and used to avoid the hot plume from view.In addition,the presence of the extended shelf can restrict entrainment into the jet plume and enhance its twodimensional characteristics,1which may be beneficial in some applications.

The internal structure of supersonic jets is complex,in particular the flow with the extended shelf is usually characterized by a quasi-periodic shock wave structure.About half a century ago,the experimental and theoretical studies on supersonic jets was carried out by Love et al.2They focused on the structure of supersonic jets issuing from a ‘‘clean”nozzle and reported the effects of the Mach number,nozzle configuration,and Nozzle Pressure Ratio (NPR) which is defined as the ratio of upstream stagnation pressure to ambient pressure on the jet’s structure,wavelength,and the shape of the jet’s boundary.Their investigation provided strong evidence that NPR is the main factor affecting the structure of the supersonic jet flow.Subsequently,more detailed investigations on various fluid dynamic parameters,such as velocity,pressure,density and temperature,were also performed.Currently,the development of numerical simulation has provided a powerful means of exploring the structure of supersonic jet.3,4

However,the reports on the wall flow structure with extended shelf are limited.Alnahhal and Panidis1measured the streamwise and lateral velocity of jets with anx-sensor hot wire anemometer and proved that the sidewall can restrict entrainment into the jet and enhance the two-dimensional characteristics of the jet.Also,a research by Deo et al.5suggested that the core region of a jet without side wall is shorter than that with side wall,however,the focus of the experiments performed by Alnahhal and Panidis and Deo et al.was on low speed jets.

Lamb et al.6studied the supersonic jet with extended shelf at different NPR and observed the quasi-periodic structure on the extended shelf using oil flow.Whereas,the motivation behind their work was to examine the effects of different extended shelf configurations on thrust and internal performance of the nozzle.Behrouzi and Mcguirk7captured the near field flow development with NPR using schlieren visualization,Pitot probe,and Laser Doppler Anemometry measurements.The experimental data for the clean nozzle and with the extended shelf proved that the presence of extended shelf has a significant effect on flow development,particularly at high NPR.In addition,for sufficiently high NPR and a sufficiently long extended shelf,separation and reattachment was observed from schlieren results.But the shape of separation bubble over the wall was still uncertain.Zare-Behtash et al.8,9succeeded in obtaining the wall pressure field using Pressure-Sensitive Paint(PSP) technology.

Although various fluid dynamic parameters were measured and spatial flow structures were visualized,the previous studies did little to provide any understanding of the evolution of supersonic jets issuing from a nozzle with extended shelf.Furthermore,in the published literature,there is few researches on the global wall shear stress vector field.Shear stress is an important parameter that must be considered.For the supersonic jet with extended shelf,the shear stress over the extended shelf can significantly influence the performance of nozzle,such as the thrust of propulsion nozzles.However,wall shear stress measurements remain very challenging.Many traditional mechanical or optical measurement methods still have various defects.Therefore,it is very necessary to develop an effective global surface shear stress vector measurement method.

The Shear-Sensitive Liquid Crystal Coating (SSLCC) technique,as a direct measurement technique of global surface shear stress,10has the characteristics of fast response,high resolution,and temperature insensitivity.The SSLCC can be applied to the test surface as a film with a thickness of micron scale,which can detect different levels of surface shear stress by showing different colors.Thus,the change in shear stress can be directly reflected in the observed changes in the color of the film.The SSLCC technology is not only an effective flow visualization technology,but also a quantitative measurement technology of the shear stress vector field.

The development of the SSLCC technique has lasted for approximately 60 years,and it has been successfully applied to visualization and measurement of shear stress.Klein and Margozzi11first attempted to calibrate the relationship between the color response and the shear stress.Subsequently,Reda et al.10,12systematically studied the sensitivity (i.e.,the relationship between color response and shear stress,illumination angle and observation angle)of the SSLCC.Their studies showed that the color response was not only related to the direction and magnitude of the shear stress,but also to the angle of illumination and the viewing angle.After years of development,the measurement object of the SSLCC technique has gradually expanded to curved surfaces13and even airfoil.14,15The application range has also expanded to supersonic.16–19Moreover,the many applications of the SSLCC technique proved that the SSLCC technique is an effective shear stress detection technique.

Currently,researches on the flow structure over the extended shelf of supersonic jets are still limited.This is quite surprising because a correct understanding of this is important in avoiding separation at high NPR.Moreover,no experimental investigations on the shear stress field over the extended shelf have been reported.Therefore,the purpose of the present work is to explain the evolution of wall flow structures in supersonic jets with increasing NPR associating oil flow,infrared detection technology and SSLCC technology,which has quantitatively measured the shear stress vector field in this paper.

2.Experimental setup

2.1.Facility description and test conditions

The experiments were performed in a blowdown-type supersonic wind tunnel in the High-speed Wind-Tunnel Laboratory20,21at Nanjing University of Aeronautics and Astronautics as shown in Fig.1.The dry filtered air supplied by a pressurized gas tank was injected into the atmosphere at room temperature.The stagnation pressure upstream continuously changed from atmospheric pressure to 800 kPa,which was controlled by the upstream pressure regulating valve.

Fig.1 Sketch of test facility.

2.2.Description of test model

The test model consisted of a rectangular nozzle and a flat plate.The supersonic rectangular nozzle had a working section with 40 mm in width and 20.6 mm in height.The flat plate with a size of 250 mm in length and 200 mm in width was mounted at the nozzle’s exit as the extended shelf.The test surface was defined as the upper surface of the flat plate.To improve the quality of the color response,one black anodized aluminum plate was used here.As shown in Fig.2,the region with 100 mm×200 mm was used as the test region.But in order to avoid shielding of the nozzle’s wall,only the region with 130 mm×80 mm was used as the SSLCC’s test area.

Fig.2 Schematics of test model.

2.3.Experimental techniques

The SSLCC technique was used for non-intrusive visualization and measurement of the surface shear stress.The measuring system of SSLCC consisted of a white light source and six synchronous cameras.The light source was required to be vertically illuminated to generate white parallel light.A small halogen tungsten light bulb(20 W)located right above the center of the plate at a distance of 1200 mm was adopted as the illumination source.The difference in the angle of the incident light between the center and boundary of the SSLCC test region was about 3.37°.Six synchronous Canon EOS80D cameras were used to record SSLCC color response,which were set in 0.2 s exposure time.Therefore,the flow field measured in this paper was considered to be a constant.As shown in Fig.3,the six cameras were placed at ±18°,±54° and±85° circumferential angles (φ),respectively,and 28°depression angles.

Fig.3 Sketch of experimental set-up of SSLCC measurement system.

The shear-sensitive liquid crystal selected in this paper was the CN/R2 mixture.The viscosity of CN/R2 was 4950 mPa∙s and the clearing point is 337.6–338 K.The mixture of liquid crystal and acetone was uniformly sprayed on the test surface.A micron-level red thin coating was left after the evaporation of the acetone.The spraying device was a U-STAR U-602G air compressor,and a S130 spray gun.To ensure uniformity while spraying the liquid crystal,a water–oil separator was used to filter the compressed air.

The oil flow technique was a convenient method of visualizing the surface streamline.A mixture of titanium dioxide and silicone oil was applied to the test surface.The silica was used as the tracer particle and 2000 cs (1 cs=1 mm2/s) silicone oil was used as the oil.In addition,when the SSLCC underwent blowing for a long time,the SSLCC would be blown into stripes,forming an SSLCC pattern which was similar to the oil flow pattern.This SSLCC pattern can also accurately record the friction line formed on the wall surface.Due to the high viscosity of the liquid crystal,the friction line structure of the SSLCC pattern in the blowing state would retain after the wind tunnel closed.

The infrared detection technology was conducted on the flat plate.The FLIR T650sc fitted with a frame rate of 30 Hz and a resolution of 640 pixel×480 pixel sensitivity was used to measure the wall temperature.The temperature measurement range was from 233 K to 2273 K.The magnitude of the error in measuring the temperature for the infrared imager was estimated at ±1%.

The Preston tube was used to measure the shear stress.The device is shown in Fig.4.The Preston tube was a Pitot tube appressed with the wall.The Pitot tube with a diameter (D)of 1.2 mm was used to measure the total pressure,whose leading edge was 100 mm away from the nozzle’s outlet.A singledegree-of-freedom coordinate frame was used to control the Pitot tube to move up and down to measure the velocity profile,with each movement step of 0.2 mm.It is worth noting that the tube was in constant contact with the wall while using the Preston tube’s technology to measure shear stress.Five static pressure holes with a diameter of 1.2 mm and 2 mm intervals were arranged along the centerline,which was used to monitor the pressure gradient on the surface of the model,and to provide local static pressure data for the Preston tube.The Kulite XTEL-190 M series pressure transducers were used for measurement of pressure whose acquisition frequency were 1000 Hz.In addition,a K-type thermocouple was used to measure the local wall temperature.

Fig.4 Sketch of experimental set-up of Preston tube measurement system.

3.Transformation of color images to shear stress distributions

Three steps were required to transform the color images to shear stress distributions after acquiring the original images at different circumferential angles,as shown in Fig.5.

Fig.5 Sketch of data processing.

3.1.Image calibration system

Due to the perspective effect caused by the observed view,the original images had a certain degree of deformation.A perspective transformation needs to be performed in order to map the pixel coordinates of the SSLCC images to the actual physical coordinates of the test surface.In the current study,a Direct Linear Transformation (DLT) method22was used.The camera parameters were obtained by the DLT method,including the circumferential and depression angles.But only the circumferential angles played a significant role in this paper.After the analyses,the transformed images were used to calculate the distribution of the shear stress vector.

The cameras recorded all colors as a combination of the three primary colors Red,Green and Blue (RGB).However,no matter which primary color was used alone,it cannot represent the exact color of the image.It is necessary to transform RGB to Hue-Saturation-Intensity(HSI).Hue value was one of the main properties of a color,which was closely related to the dominant wavelength.Therefore,only the hue images were used for further analysis.The second trichromic system23was used to calculated the hue value.

wherehis the hue value;R,GandBare the three primary colors recording by cameras.

3.2.Gaussian curve fittings

For each physical point on the test surface,the hue values taken at various circumferential angles conformed to the Gaussian distribution,as verified by Reda et al.10,12,24Reda and Muratore24performed a detailed analysis on the fitting method of liquid crystal coating.Their findings suggested that each value from the hue data sets could be fitted by a Gaussian curve for -90°≤φ ≤90°,or,by a simple second-order polynomial curve over the limited range -60°≤φ ≤60°.However,the error in the Gaussian curve fitting was significantly lesser than that of the simple second-order polynomial.When the observation angle was more than five,the Gaussian curve yielded measured vector orientations within±1°and measured vector magnitudes within ±5%.However,the second-order polynomial curve yielded measured vector orientations that were 2°-3°of the right value,and the measured vector magnitudes were about 10%of the appropriate values.Hence,this study fitted the hue values obtained by SSLCC with the Gaussian curve due to its higher accuracy.Therefore,a Gaussian curve was fitted to the hue versus circumferential angles in this paper.The data can be calculated from,

wherehVNis the hue observed for a circumferential view angle normal to the shear vector,σ is the standard deviation of the Gaussian distribution,φτandh(φτ)are the shear stress vector orientation and the vector-aligned hue,respectively.

Fig.6 shows one example of the hue vs φ data set taken from the locations atx=60 mm,andy=80 mm (The physical coordinate system was defined as shown in Fig.2).The discrete data points represented by symbols‘‘°”were the hue values measured using the six digital cameras,whereas the solid lines reflected Gaussian curve fittings.The peak of the Gaussian curve was denoted by a plus sign(‘‘+”).The angular location of the peak of the Gaussian curve gave the direction of the shear stress vector (φτ=11.3°).The value of the hue at the peak of the Gaussian curve gave the vector-aligned hue(h=224.3°).The vector-aligned hue was then converted to the actual shear stress magnitude via a vector-aligned hue versus shear stress magnitude calibration curve.

Fig.6 Example of hue vs φ datasets at different surface point.

3.3.Calibration of vector-aligned hue to shear stress magnitude

In this work,Preston tube technology and a turbulent frictional relation were used to calibrate the vector-aligned hue versus shear stress magnitude.The direction of the shear stress at the centerline of the model was theoretically along the direction of the airflow due to the symmetrical model and nozzle.Therefore,the calibration curve can be obtained by fitting the measured shear stress and the vector-aligned hue at the same position on the centerline.

Measuring the shear stress by the Preston tube method depended on the assumption of a universal inner law (or law of the wall) common to the boundary layers and fully developed pipe flow,namely,

whereuis the velocity component parallel to the surface at a distancey,is the frictional velocity,ρ is the fluid density,τwis the local skin friction,yis the distance normal to the surface,v is the kinematic viscosity of fluid.

Thus,the non-dimensional relationship25between the measured pressure of the Preston-tube and the shear stress can be presented more conveniently as,

where ΔPis the dynamic pressure of the Preston tube,Dis the diameter of the Preston tube.Therefore,it is a simple method for determining τw,when the functionFis established.

For incompressible flow,the functional relationship calibrated by Patel26was selected.However,for the compressible flow,the heat exchange between the flow field and the wall surface,and the heat transfer between the fluids may change the inner law.

In this paper,the dynamic pressure-wall temperature method27was used to correct the compressible effect.Then the shear stress was calculated by the functional relationship from Patel.27

Several measured velocity profiles at various NPR conditions are shown in Fig.7.It can be seen that the thickness of the boundary layer δ is less than 9 mm.According to the standards proposed by Allen,28the useful range of the Preston size,D/δ,lies within 0.07

Fig.7 Measured velocity profiles at different NPR conditions.

In addition,the turbulent frictional relation29over the flat plate was carried out to calculate the shear stress.The turbulent friction relation is as follows:

whereU∞is the mainstream velocity.

Fig.8 shows the calibration curve of the vector-aligned hue to shear stress magnitude(τ)fitted by the Preston tube method.The relative error between the results from the Preston tube and the turbulent frictional relation is within 8%,which proves that the two calibration methods used in this paper are reliable.Since the CN/R2 liquid crystal used in this article had a high viscosity and was relatively insensitive to small level shear stress,it could easily lead to a large test error.Therefore,the calibration curve in this paper was only for medium and high-level shear stress.

Fig.8 Calibration curve of vector-aligned hue to shear stress magnitude.

4.Results and discussion

4.1.Near-field surface flow structures visualization and measurement

The oil flow patterns of the flow along with the SSLCC patterns,and the infrared detection results corresponding to the same NPR conditions are given in Fig.9 (Tis the temperature).Several typical flow features can be identified immediately from Fig.9,including the shear layer,the expansion fans,the shock wave reflection structure,the Mach stem,and the separation region.The nozzle exit was located at 30–70 mm on thexaxis.Only the wall flow structure was considered in this paper,hence the wall temperature obtained by the infrared detection technology was not extensively discussed in this paper.

The behavior of a supersonic jet was determined by the difference in pressure between the jet’s outlet pressure and the surrounding pressure,which was concerned with NPR.When NPR was at a low level,the jet outlet pressure was lower than the surrounding pressure,the oblique shock waves appeared at the nozzle’s exit,which reduced the velocity and raised the jet’s outlet pressure to the surrounding pressure.A typical state is shown in Fig.9(a) at NPR=3.1 when the flow was in an over-expanded state.The oblique shock waves appearing at the nozzle’s exit turned the flow inwards.Downstream,the expansion fans formed by the reflection of shock waves caused the airflow expansion.Therefore,the core region exhibited a compressed-expanded structure and the width of the core area gradually shortened.Also,there was a gradual widening of the subsonic zone between the inner boundary of the shear layer and the core area,which corresponded to the dark purple area in the infrared detection results.

With an increase in NPR,the jet outlet pressure was larger than the surrounding pressure.The flow gradually transformed from over-expansion to under-expansion,as shown in Figs.9(b)–(d).An expansion fan formed at the nozzle exit,enhancing the velocity and decreasing the outlet pressure of the jet to the surrounding pressure.As a result,the flow turned outwards and the core region of the supersonic jet displayed an expanded trend at the nozzle’s exit.After that,shock waves formed by the reflection of expanded fans caused the airflow to deflect inlet.Therefore,the core region showed an expansion-compression repetition structure.

When the NPR continued to increase,the regular reflection of the first shock changed to Mach reflection,resulting in a normal shock called a Mach disk in space structures.However,the two-dimensional structure of the wall flow is referred to as the ‘‘Mach stem”in this paper.The slip lines then emanated from the triple point.The Mach reflection appeared first at NPR=3.79 as shown in Fig.9(b).The small subsonic zone formed after the Mach stem was caused by a sudden decrease in the flow velocity after passing through a normal shock wave.After going through a short subsonic zone,the airflow after the Mach stem would also underwent a continuous expansioncompression process.

Comparing Fig.9(b) with (c),it can be seen that,at NPR=4.26,the width of the Mach stem became wider,however,it remained straight,and the slip lines became more separated as the width in the Mach stem increases.With an increasing NPR,the smaller subsonic zone between the inner boundary of the shear layer and the core area can be identified clearly,which was caused by the expansive core region.

Fig.9 Surface oil flow and infrared detection visualization of supersonic jet structure((a):Over-expansion jet;(b)-(d):Under-expansion jet).

In fact,the wall flow structures shown in Figs.9(a)–(c)were the results of the interaction between the supersonic jet and the boundary layer of the extended shelf.The effect of the boundary layer was that it generates an additional reflected shock wave in the plane perpendicular to the extended shelf,and changed the length of the shock cell,7but it was not strong enough to change the jet’s shock wave-expansion fans structure.

At NPR=5.28,the Mach stem transformed from a normal shock to an ‘‘arch”shock.An interesting phenomenon was that a near-triangular separation area formed at the trailing edge of the ‘‘arch”shock.Under such a high amplitude of NPR,the effect of boundary layer had to be taken into account.The growing boundary layer of the extended shelf has been unable to sustain forward flow against the adverse pressure gradient region,therefore a closed separation bubble appeared at the trailing edge of the‘‘arch”shock.The separation and reattachment lines were clearly distinguished.Similar separation and reattachment were also observed using schlieren visualization in the investigation by Behrouzi and Mcguirk.7However,they paid no attention to the shape of the boundary layer separation.In this paper,the shape of the boundary layer separation was clearly described for the first time by means of oil flow,infrared detection and SSLCC technology,and the shape of the separation zone was confirmed to be near-triangular.We speculate that the near triangular separation region may be related to the narrow subsonic region behind the Mach stem.For the supersonic jet without the extended shelf at high NPR,a narrow subsonic region which is bounded by a slip stream follows the normal shock.30When the subsonic flow at the narrow subsonic region interacts with the boundary of the extended shelf,a near triangular separation region is formed.

In addition,throughout the process of supersonic jet evolution,it can be found that the length of shock cell increases gradually with an increase in NPR.This characteristic was not obvious in the first shock cell,but a significant increase in length could be observed after the second shock cell.The spreading width of the core region widened with NPR.

Fig.10 shows the SSLCC color responses observed at different circumferential angles (NPR=4.26).Each image underwent a perspective transformation to map the image coordinates to the physical coordinates on the test surface.However,because the camera’s recording was blocked by the nozzle’s wall,the evolution of the flow field at the nozzle’s exit was not captured.The visualization and measurement areas were set as the region corresponding to the area marked with the red boxes in Fig.9.Fig.10 shows that although the SSLCC showed different colors at different circumferential angles,each image was asymmetric relative to the center line.Note that:images taken at symmetrical circumferential angles were essentially mirror images.The shock structure can be visualized clearly from the SSLCC results,particularly in the images recorded at ±85° circumferential angles.As a result,only the images recorded at -85° circumferential angles were used for further analysis.

Fig.10 SSLCC color changes observed at different circumferential angles (NPR=4.26).

The SSLCC results at -85° circumferential angles at various values of NPR are shown in Fig.11.The flow characteristic in the core region can be observed distinctly from SSLCC images,including shear layer,length of the shock cell,shock structure,subsonic area after Mach stem,and the separation bubble.In the core region,the SSLCC color showed blue,indicating a large magnitude of shear in that region.Also,the color in the core region became darker with an increase in NPR,this demonstrated that the shear stress level was enhanced with NPR.Furthermore,in the shear layer,the color of SSLCC gradually changed from blue-green-red away from the core region,indicating that the shear stress gradually decreased.The small red areas immediately downstream of the Mach stem shown in Fig.11(c) indicated that there were low shear magnitudes in that region caused by a sudden drop in velocity across the Mach stem.At NPR=5.28,a triquetrous separation occurred after the Mach stem,with a clearly distinguishable size and boundary.Comparing Fig.11 with Fig.9,it can be seen that the oil flow patterns,infrared detection and the SSLCC results coincide.

Fig.11 Liquid crystal coating color response of supersonic jet structure ((a):Over-expansion jet;(b)-(d):Under-expansion jet).

The SSLCC technique has obvious advantages and disadvantages compared with the oil flow visualization.First,the SSLCC technique can clearly visualize the position of the shock wave and the separation region in a color change manner.Additionally,the SSLCC technique can intuitively display the changes in the magnitude of the shear stress.As shown in Fig.11,the color changes from light blue to dark blue with an increasing value of NPR,representing a gradual increase in the shear stress.However,the advantages of the oil flow technique focus on the visualization of the frictional lines on the wall.

In order to deepen the understanding of supersonic jet with extended shelf and obtain the evolution of wall friction vector field with NPR,the vector distribution of the shear stress and the measured frictional lines in the supersonic jet were measured by SSLCC technique.The results at different NPR values are shown in Fig.12.The direction and the length of the vector represent the direction and magnitude of the shear stress,respectively.The measured frictional lines were represented by the blue thin lines.Compared with the SSLCC images from a single angle which can only qualitatively visualize and analyze the wall flow structure,the vector distribution of the shear stress can be used to obtain more quantitative information.

Fig.12 Measure shear stress vector field and skin friction lines at different NPRs.

As shown in Fig.12,the boundary of the shear layer and the core region can be distinguished via the direction and magnitude of the vectors.In the core region of the supersonic jet,the frictional lines show an obvious compressed-expanded repetition.Under the influence of shock waves and expansion fans,there was a change in the direction of the shear stress.The direction of shear stress across the shock wave deflected inwards and that across the expansion fans deflected outwards,consistent with the results in Fig.9.A comparison Fig.12(a)with others showed that there are more noises in the high(>240 Pa) and low (<50 Pa) shear stress regions.This is due to the SSLCC being less sensitive to these shear stress levels.It can be found that the triquetrous separation was measured successfully.However,since the cameras were arranged downstream in the current work,the adverse shear stress was not measured,but the downstream shear stress can still indicate that there was a distinct reversed flow residing in the separation region.

Fig.13 shows the oil flow pattern,the SSLCC pattern,and skin’s frictional lines computed using the SSLCC method at NPR=4.26.The oil flow pattern and the SSLCC pattern used here were the images in the red box shown in Fig.9(c).It can be found that the frictional lines measured by the SSLCC basically coincided with the oil flow pattern and the SSLCC pattern,which proved the accuracy of the SSLCC technology for visualizing and measuring the shear stress of supersonic jets.In addition,compared with the oil flow technology,the SSLCC technology performed much better in visualizing and measuring the vector field of the shear stress,in which the direction and magnitude information of the shear stress can be obtained quantitatively.

Fig.13 Oil flow pattern,SSLCC pattern and skin friction lines computed using SSLCC method (NPR=4.26).

4.2.Near-field surface flow structures evolution

Based on the analysis above,the evolution of the supersonic jet’s near-field wall flow structure from over-expansion to under-expansion with an increased NPR is expounded in Fig.14.For a fixed nozzle geometry,the wall flow structure over the extended shelf is primarily dependent on the NPR and the boundary layer of the extended shelf.

Fig.14 Sketch of supersonic jet structure.

Under a low NPR,the supersonic jet is at an over-expanded state as shown in Fig.14(a).The structure of the wall shows a compressed-expanded structure.The structure is similar to that of the supersonic jet without an extended shelf,that is,the effect of boundary layer is not enough to change the structure of the shock wave-expansion fan of the jet.Meanwhile,the first waves at the exit of the nozzle are shock waves,which then changes into the expansion fans,forming a quasi-periodic structure.

With an increase in NPR,the jet’s outlet pressure is larger than the surrounding pressure.Therefore,the jet enters the under-expanded state,as shown in Fig.14(b),and the first waves at the exit transform into expansion fans.Then,these expansion fans reflect into shock waves when they attain a constant pressure streamline.The shock waves reflect,forming a regular reflective structure.Meanwhile,the core region shows an expanded-contracted wall structure.

The regular reflection turns to Mach reflection with further increment in NPR,accompanied by the straight Mach stem and two slip lines which emanate from the triple point,as shown in Fig.14(c).The weight of the straight Mach stem gradually increases as a result of the separation of the slip lines,and there is an enlargement in the normal shock at the downstream subsonic region of the Mach stem.

Until the NPR attains a high amplitude,the straight Mach stem turns into an ‘‘arch”structure.Meanwhile,the effect of the boundary layer of the extended shelf plays a prominent part in the flow.The growing boundary layer was unable to sustain the forward flow against the adverse pressure gradient region,hence,a near-triangular separation region appeared at the trailing edge of the ‘‘arch”shock,as shown in Fig.14(d).

5.Conclusions

In this paper,the evolution of the supersonic jet’s surface flow structure issuing from a rectangular nozzle with an extended shelf from over-expansion to under-expansion was investigated by the oil flow,infrared detection technology,and the SSLCC technology.The quantitatively measured result of the global shear stress vector field of the supersonic jet was obtained by SSLCC.The main conclusions are as follows:

(1) The flow structure affected by boundary layer of the extended shelf is different with that of the ‘‘clean”jet,which is highly distinct at higher NPR values.Under smaller NPR conditions,the wall flow structure is basically similar to that without the extended shelf,which develops from over expansion to under expansion,and its basic feature is also the structure of the alternate shock wave-expansion fans.However,in the case of high NPR,the wall flow structure shows significant difference under the influence of the boundary layer.The most prominent manifestation is the separation and reattachment of the boundary layer at the trailing edge of the Mach stem due to the adverse pressure gradient.In this paper,the separation is visualized for the first time,and its shape is determined to be near-triangular.

(2) The vector distribution of the global shear stress over the extended shelf,which is induced by the supersonic jet at various NPR,was measured quantitatively using the SSLCC technique,and the frictional lines calculated by the SSLCC technique are consistent with that of the oil flow and the SSLCC patterns,indicating that the SSLCC technique can be successfully applied in the visualization and measurement of complex flow structure.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was supported by the National Natural Science Foundation of China (Nos.12072157 and 51776096).