Experimental investigation on aero-heating of rudder shaft within laminar/turbulent hypersonic boundary layers

Qing LI ,Ling NIE ,Kouli ZHANG ,Yu LI ,Suyu CHEN ,Gungsheng ZHU ,*

a Hypervelocity Aerodynamics Institute,China Aerodynamics Research and Development Center,Mianyang 621000,China

b Science and Technology on Space Physics Laboratory,China Academy of Launch Vehicle Technology,Beijing 100076,China

KEYWORDS Heat flux;Hypersonic boundary layer;Rudder;Shock tunnel;Transition;Vortex generator

Abstract The aero-heating of the rudder shaft region of a hypersonic vehicle is very harsh,as the peak heat flux in this region can be even higher than that at the stagnation point.Therefore,studying the aero-heating of the rudder shaft is of great significance for designing the thermal protection system of the hypersonic vehicle.In the wind tunnel test of the aero-heating effect,we find that with the increase of the angle of attack of the lifting body model,the increasement of the heat flux of the rudder shaft is larger under laminar flow conditions than that under turbulent flow conditions.To understand this,we design a wind tunnel experiment to study the effect of laminar/turbulent hypersonic boundary layers on the heat flux of the rudder shaft under the same wind tunnel freestream conditions.The experiment is carried out in the ?2 m shock tunnel(FD-14A)affiliated to the China Aerodynamics Research and Development Center(CARDC).The laminar boundary layer on the model is triggered to a turbulent one by using vortex generators,which are 2 mm-high diamonds.The aero-heating of the rudder shaft(with the rudder)and the protuberance(without the rudder)are studied in both hypersonic laminar and turbulent boundary layers under the same freestream condition.The nominal Mach numbers are 10 and 12,and the unit Reynolds numbers are 2.4×106 m-1 and 2.1×106 m-1.The angle of attack of the model is 20°,and the deflection angle of the rudder and the protuberance is 10°.The heat flux on the model surface is measured by thin film heat flux sensors,and the heat flux distribution along the center line of the lifting body model suggests that forced transition is achieved in the upstream of the rudder.The test results of the rudder shaft and the protuberance show that the heat flux of the rudder shaft is lower in the turbulent flow than that in the laminar flow,but the heat flux of the protuberance is the other way around,i.e.,lower in the laminar flow than in the turbulent flow.The wind tunnel test results is also validated by numerical simulations.Our analysis suggests that this phenomenon is due to the difference of boundary layer velocities caused by different thickness of boundary layer between laminar and turbulent flows,as well as the restricted flow within the rudder gap.When the turbulent boundary layer is more than three times thicker than that of the laminar boundary layer,the heat flux of the rudder shaft under the laminar flow condition is higher than that under the turbulent flow condition.Discovery of this phenomenon has great importance for guiding the design of the thermal protection system for the rudder shaft of hypersonic vehicles.

1.Introduction

Lifting body aircrafts1-6are controlled and stabilized by the elevator and rudder,but the local structure of the air rudder is relatively simple,which consists of a local plate and a rudder structure.The gap7-8between the air rudder and the body surface makes the aero-heating of the rudder shaft very harsh and leads to complicated flow structures in the near-wall region.Therefore,wind tunnel tests and numerical calculations are necessary to be carried out to understand the thermal environment in the rudder gap.

There are very few works9-11at home and abroad studying the thermal environment of the rudder gap and the rudder shaft due to the following reasons.First,there is a rectifier cap in the front of the air rudder for the re-entry warhead,which can improve the aero-heating of rudder shaft and thus reduces the necessity for respective research.Second,the flow within the rudder gap and on the surface of the rudder shaft is very complicated,but previous numerical computation of the aerothermal characteristics is not very reliable due to limited simulation capability.Third,due to the limitations of wind tunnel size and sensor technology,the diameter of the scale model of the rudder shaft is too small to mount any sensor for heat flux measurement.

However,in the hypersonic lifting body aircraft,the rectifier cap upstream of the air rudder is dropped,thus the heat flux of the rudder shaft rises sharply,which calls for relevant research urgently. In the meantime, advancement in both numerical modelling and wind tunnel test for aerodynamic thermal problems have enabled high reliability research in this regard.In the ?2 m shock tunnel(FD-14A)in the Hypervelocity Aerodynamics Institute(HAI),CARDC,the heat flux of the rudder shaft of the lifting body model,as shown in Fig.1,is measured.It is found that under the Ma=10 turbulent flow condition,when the angle of attack is increased from 10°to 20°,the heat flux of the rudder shaft is increased by about one time;under the Ma=12 laminar flow condition,the rudder shaft heat flux is increased by about four times.We conjecture that this is the result of different boundary layer flow regimes.In the test,the flow parameters of the two flows are quite different,and the influence of the inflow parameters on the test results cannot be excluded.In order to study the thermal environment of the rudder gap and rudder shaft,we intend to carry out experimental research on the influence of both laminar and turbulent boundary layers on the rudder shaft aero-heating under the same freestream conditions,and investigate the effects of flow regimes on the rudder shaft aero-heating.

Therefore,we design a test scheme as follows.First,we choose the appropriate shock tunnel flow conditions to ensure that the boundary layer upstream of the air rudder of the lifting body model(Fig.1)is laminar flow.Second,vortex generators that can trigger the laminar boundary layer into a turbulent one are mounted in the front part of the model,so as to reach different flow regimes upstream of the air rudder under the given freestream conditions.Finally,the influence of flow regimes on the rudder shaft aero-heating is investigated.For the first and second steps,previous research12has obtained satisfactory results.In addition,Ref.12shows that the aero-heating of the forced turbulent boundary layer on the wall was only affected by the incoming flow parameters,and no obvious difference in aero-heating was observed by the use of different vortex generators.

2.Experimental and simulation details

The experiment is conducted in the ?2 m shock tunnel(FD-14A),which is composed of a shock tube and a nozzle,a test section,and a vacuum chamber.The inner diameter of the shock tube is 150 mm,and the length of the high pressure tube and low pressure tube is 9 m and 18 m,respectively.

The wind tunnel test gas is nitrogen,which is driven by hydrogen or a mixture of hydrogen and nitrogen.The driving pressure can reach as high as 50 MPa.Different flow Mach numbers can be obtained by changing the throat or nozzle,and different flow unit Reynolds Numbers can be obtained by adjusting the pressure ratio of the high and low pressure segments,thus various test environments can be achieved.Currently, the wind tunnel can reach Mach number in the range of 6-16,and Reynolds number in the range of 2.1×105-6.7×107m-1.The nozzle exit diameter is 1.2 m,while the cross-sectional area of the test section is 2.6 m×2.6 m.The effective duration time of the test is 4-18 ms.

Two types of sensors,13,14i.e.,cylindrical heat flux sensors and contoured heat flux sensors,are used in the experimental measurement,as shown in Fig.2.The contoured sensor with glass as the substrate has been abraded to match the shape of the leading edge of the rudder shaft.A platinum thin film is coated on the polished surface with the vacuum magnetron sputtering method,and the surface heat flux is measured by the platinum film.

A series of cylindrical heat flux sensors are distributed along the center line upstream of the air rudder to measure the heat flux,so that the flow regime of the boundary layer can be determined.The cylindrical sensor(Fig.2)is fabricated in batches,and the same glass substrate is used to make a glass rod with a diameter of 2 mm and a length of 20 mm.The polished round-end platinized platinum film is connected to the test lead to construct a sensor.Three cylindrical sensors are installed on the front surface of the rudder shaft to measure the effect of boundary layer regimes on the surface aeroheating upstream of the rudder shaft.The transverse coordinates of the test holes are the same,and the perpendicular distance between the center of the test hole and the front of the rudder shaft is 6.125 mm.

Due to the limitation of the size of the shock tunnel nozzle,the test model is a scale lifting model.The air rudder and the rudder shaft are shown in Fig.3.The rudder gap is 5 mm high.In order to separate the rudder shaft,a 5 mm height protuberance model(Fig.4)is designed with the same shape as the rudder shaft.By measuring the heat flux on the protuberance surface at the same position under the same flow condition,the effects of the flow regimes on the aero-heating on the surface of the rudder shaft with the rudder attached can be compared.

In order to make comparison of the heat flux between the rudder shaft and the protuberance in both laminar and turbulent flows, we must first ensure that the boundary layer upstream of the rudder is laminar.According to the experience of shock tunnel tests,the surface transition location of the lifting body model can be estimated in the first place.A condition with high Mach number and low Reynolds number in the shock tunnel is selected.The freestream parameters are shown in Table 1,P0∞is the freestream total pressure,T0∞is the freestream total temperature,Ma∞is the actual freestream mach number in the shock tunnel, the unit Reynolds numbers(Re∞/L)for Ma=10 and Ma=12 are 2.4×106m-1and 2.1×106m-1,respectively,δ is the boundary layer thickness at the center location of the vortex generator,k is the height of the vortex generator,δLand δTare the laminar and turbulent boundary layer thickness before the rudder,respectively.The angle of attack of the lifting body model is 20°.The height of the rudder gap is 5 mm,the deflection angle of the rudder is 10°.The height of the protuberance is 5 mm,the deflection angle of the protuberance is also 10°(note that in Fig.3 the air rudder tip is deflected to the left by 10°).

Fig.2 Cylindrical and contoured heat flux sensors.

Fig.3 Model of rudder and rudder shaft.

Fig.4 Protuberance model(height:5 mm).

Numerical simulations of the aero-heating on the surface of the rudder shaft and the protuberance are performed using the finite volume method,which solves the integral form of the three-dimensional compressible Navier-Stokes equations.The governing equations are as follows:

3.Boundary layer forced transition

Under the flow conditions of the shock tunnel in Table 1,tests are carried out to verify that the boundary layer upstream ofthe air rudder is laminar,and then vortex generators are installed to enforce the boundary layer into turbulence.

Table 1 Test flow conditions and calculated boundary layer thickness.

According to the previous work,a series of 2 mm high diamond vortex generators,as shown in Fig.5,is installed on the surface of the lifting body model at x/L=0.32 from the head,where x is the streamwise coordinate and L the length of the lifting body.As shown in Table 1,the boundary layer thickness(δ)at the center location of the vortex generator is 1.4 mm and 1.7 mm for Ma=10 and Ma=12,respectively,and the corresponding k/δ values are 1.4 and 1.2. The thickness of the laminar(δL)and turbulent(δT)boundary layers at the front location of the air rudder is 3.9 mm and 10.6 mm,4.6 mm and 11.3 mm,respectively,and the corresponding thickness ratio of turbulent to laminar boundary layers is 2.7 and 2.5,respectively.Based on various tests in Refs.15-22and our previous work experience,the current vortex generators with a height of 2 mm can effectively enforce the laminar boundary layer into turbulence without bringing in too much disturbance,which might affect the rudder shaft aero-heating measurement under turbulence conditions.

The flow regime of the boundary layer is determined by measuring the heat flux along the center line upstream of the air rudder.Fig.6 shows the measured and calculated distribution of the heat flux along the center line for both laminar and forced turbulent flows at Ma=10 and Ma=12(q is the measured heat flux result,qtis corresponding stagnation point heat flux).It can be seen that when there are no vortex generators,the measured heat flux distribution along the center line monotonously decreases,which suggests that the boundary layer upstream of the air rudder is laminar,consistent with the simulation results.After installing the vortex generators,the heat flux along the center line downstream of the vortex generators first rises and then stabilizes,which is almost in line with the simulation result for the turbulent flow.This suggests that the boundary layer upstream of the air rudder has become turbulence.Therefore,under the same shock tunnel flow conditions,two different boundary layer regimes are reached.

In Fig.6,for the test results,it can be seen that regardless of laminar or turbulent flow regimes,the non-dimensional heat flux along the center line at Ma=12 is slightly higher than that at Ma=10.The reasons for this difference are relatively complex,related to the Mach number,the Reynolds number,the ratio of the outer edge pressure to total pressure of the local boundary layer,the temperature and velocity of the outer edge of boundary layer, and the viscosity coefficient. At x/L=0.67,the heat flux sharply decreases,which is due to the small expansion angle of the model surface.

Fig.5 Diamond type vortex generators.

Fig.6 Distribution of heat flux along center line.

4.Results

The heat flux measurement results for the rudder shaft and the protuberance are shown in Fig.7(the horizontal coordinate N is the measurement point number).A comparison of the heat flux on the windward side of the rudder shaft and the protuberance under two different flow regimes at Ma=10 is shown in Fig.7(a).Similar results at Ma=12 are shown in Fig.7(b).The two figures indicate that the heat flux on the rudder shaft is higher in the laminar flow than that in the forced turbulent flow.However,the heat flux on the protuberance is higher under the turbulent flow condition,as predicted by the conventional law.Fig.7(c)shows the heat flux for the rudder shaft with different flow regimes and different Mach numbers.Within the same flow regime,the heat flux of the rudder shaft at Ma=12 is higher than that at Ma=10.The heat flux of the rudder shaft monotonously increases from left to right due to the influence of the rudder deflection angle(from Point 1 to Point 5).The peak-valley ratio for the heat flux reaches 3.7.The same comparison but for the protuberances is shown in Fig.7(d).Within the same flow regime,the relation in the heat flux between Ma=12 and Ma=10 is unclear.Affected by the deflection angle of the protuberance,the heat flux on the right for Point 3-Point 5 is only slightly higher than that on the left side.Table 2 compares the averaged ratio of the heat flux under the turbulent and laminar flow conditions in different regions.It can be seen that the heat flux for the last six points along the center line and for the protuberance region(including the protuberance surface and upstream protuberance,as shown in Fig.4)at both Ma=10 and Ma=12 are about 2.5-4.2 times larger under the turbulent flow condition than that under the laminar flow condition,which is consistent with the conventional viewpoint.However,on the rudder shaft area(including the rudder shaft surface and upstream rudder shaft),the heat flux under the turbulent flow condition is only 0.6-0.7 times that under the laminar flow condition.This is contrary to the conventional understanding on how the boundary layer flow regime affects the heat flux on the model surface.

Fig.7 Comparison of heat flux distribution of rudder shaft and protuberance.

Table 2 Averaged ratio of turbulent heat flux to laminar heat flux in each region.

The test data of the aero-heating flux is averaged for better quality,and the repeatability error is within±15%.During the test,the whole batch of the heat flux sensors is replaced in each round.According to the shock tunnel calibration data,if we repeat the same test without replacing the heat flux sensors,the repeatability error under the laminar flow condition is within±5%,and under the turbulent flow condition is within±10%(in this case,the error is mainly due to the uncertainty in the shock tunnel operation).

5.Discussion

To get a deep understanding of the flow physics,we have conducted numerical simulations of the heat flux distribution on the rudder shaft and on the protuberance under the laminar and turbulent flow conditions.The flow conditions in the simulation setup,such as freestream condition,model scale ratio,angle of attack,air rudder angle,rudder gap height,etc.,remain the same as the experimental configuration.The distribution of rudder shaft heat flux at Ma=10 and Ma=12 is shown in Fig.8.It can be seen that the heat flux on the rudder shaft is higher under the laminar condition than that under the turbulent one,which agrees with the wind tunnel test result.

Fig.8 Numerical simulation results of rudder shaft heat flux distribution.

Further analysis suggests that the surprising result observed in both the experiment and the simulation is mainly caused by the difference in the boundary layer velocities within the rudder gap for the two flow regimes.This is due to the difference of thickness of turbulent/laminar boundary layers and the‘‘restricted flow”in the rudder gap.Taking the Ma=10 case as an example,as shown in Fig.9(h is the wall outside normal height,T0is the local total temperature,u is the local flow velocity),upstream of the air rudder(x/L=0.87),we define the line where the total temperature in the flow field is equal to 99%of the total temperature in the freestream as the outer edge of the boundary layer,and this defined thickness is much larger(2.5 times)for the turbulent boundary layer than that for the laminar one.At the gap entrance,the velocity of the laminar flow is significantly greater than that of the turbulent flow,which makes the energy of the fluid entering the gap under the laminar flow condition greater than that under the turbulent flow condition.Within the gap,the laminar flow is more likely to generate the separation vortex,and the restriction of the separation vortex and the upper and lower walls of the gap have narrowed the mainstream flow path that can act as an energy concentrator.The accumulated energy bumps on the rudder shaft to produce high heat flux bands(as shown in Fig.10).

Fig.10 Comparison of flow situations in gap of rudder.

Fig.11 Comparison of flow conditions near protuberance.

From the above numerical and experimental results,it can be seen that in the absence of the air rudder,heat flux on the protuberance in the laminar flow is significantly smaller than in the turbulent case.The Ma=10 state is also taken as an example for illustration.As shown in Fig.11,the laminar flow state is more likely to separate.At the same time,since there is no constraint on the air rudder gap,the separation vortex is fully developed,and the separation vortex lifts the low energy fluid at the bottom of the boundary layer.The larger the laminar-flow separation vortex is,the higher the low-energy fluid is lifted.Consequently,the fluid energy that hits the protuberance is lower than that in the turbulent flow,thus the heat flux is smaller than that in the turbulent flow.

Fig.9 Temperature and velocity profiles for boundary layers upstream of rudder(x/L=0.87,Ma=10).

6.Conclusions

In this paper,vortex generators mounted on a lifting body model in the shock tunnel are used to enforce boundary layer transition.Under the same wind tunnel flow conditions,different flow regimes,i.e.,laminar and turbulent boundary layers,are realized.Under the two flow conditions,i.e.,Ma=10,Re∞/L=2.4×106m-1and Ma=12,Re∞=2.1×106m-1,the difference of thickness of the forced turbulent flow and the laminar one is large.In these conditions,experiments on the effect of the boundary layer flow regime on the aero-heating of the rudder shaft are carried out.The aero-heating of the protuberance,which is the same as that of the rudder shaft in the absence of the rudder,is measured for a comparison under the same conditions.The experimental results show that the heat flux on the rudder shaft in the laminar flow is higher than that in the turbulent flow,but the corresponding heat flux on the protuberance follows the conventional law,i.e.,higher in the turbulent flow than that in the laminar flow.Numerical simulations of the heat flux distribution on the rudder shaft and on the protuberance are performed as well,and the results are in agreement with the wind tunnel test results.Finally,we briefly analyze the causes for the difference in the aero-heating of the air rudder,and find that these are mainly due to the difference in the boundary layer velocities in turbulent/laminar boundary layers and the‘‘restricted flow”within the rudder gap.Of course,the reasons for this situation are complicated,and the study of other possible factors,including shock wave boundary layer interaction,boundary layer separation and reattachment,requires more in-depth numerical simulation research in the future.

We have conducted the shock tunnel test to verify that the heat flux of the rudder shaft under the laminar condition is higher than that under the turbulent condition.The discovery of this phenomenon suggests that when the thickness of the turbulent boundary layer reaches three or more times larger than that of the laminar one,the thermal protection system of the rudder shaft on the hypersonic vehicle must be designed according to the laminar boundary layer condition,rather than the turbulent one.This is especially the case for the aircraft flying at the critical height,or the boundary layer flow regime cannot be accurately predicated due to the complexity of transition.

Acknowledgement

This study was supported by the National Key Research and Development Program of China(No.2016YFA0401201).