High speed wind tunnels 2.0 Definition of high speed. 2.1 Types of high speed wind tunnels

Transcription

1 Module Lectures 6 to 1 High Seed Wind Tunnels Keywords: Blow down wind tunnels, Indraft wind tunnels, suersonic wind tunnels, c-d nozzles, second throat diffuser, shocks, condensation in wind tunnels, and liquefaction in wind tunnels..0 High seed wind tunnels.1 Tyes of high seed tunnels. Suersonic wind tunnels..1 Test section flow arameters Dynamic ressure Mass flow rate Test section velocity Maximum velocity Free stream reynolds number.3 Comonents of suersonic wind tunnels Air storage tanks Settling chamber /wide angle diffusers Convergent-divergent (c-d) nozzle Diffuser.4 Power required for the oeration of suersonic wind tunnels.5 Closed circuit suersonic wind tunnel.6 Actual flow in the suersonic wind tunnel.6.1 Starting the wind tunnel with the model in the test section.6. Sizing the wind tunnel model.6.3 Two roblems in the oeration of the suersonic wind tunnel (i) Condensation (ii) Liquefaction Det. of Aerosace Engg., Indian Institute of Technology, Madras 1

2 High seed wind tunnels.0 Definition of high seed When comressibility effects are re dominant the flow is generally said to be of high seed. A lower limit is aroximately M=0.5. Power requirements vary as cube of velocity in the wind tunnel. This does not hold into the high seed regime exactly. Because of large ower requirements, high seed wind tunnels are of the intermittent tye..1 Tyes of high seed wind tunnels 1. Continuous (for all seed ranges). Intermittent.1 Blowdown (Fig.1). Indraft (Fig.) M > 0.5 < Intermittent ressure vacuum tunnel for M>5 Fig..1 Pressure driven blow down suersonic wind tunnel Det. of Aerosace Engg., Indian Institute of Technology, Madras

3 Fig. Indraft tye wind tunnel Table.1 Comarison between Indraft and Pressure driven wind tunnels Indraft wind tunnels Pressure driven wind tunnels Stagnation temerature at suly condition is constant during a run. Reynolds number can be varied at a So also is total ressure. No fluctuations articular Mach no. as those generated by a ressure regulator. No ossible contamination such as that Cost is much less than of an indraft due to oil. tunnel. Vacuum is safer to handle than ressure. Pressure regulators are not needed. The wind tunnels described above can be converted as continuous tunnels. The comarison between blow down and continuous wind tunnels are as given in Table. Det. of Aerosace Engg., Indian Institute of Technology, Madras 3

4 Table. Comarison between intermittent and continuous wind tunnels Intermittent(blow down) wind tunnels Continuous wind tunnels More in control of conditions and return Simle to design and less costly to a given test condition with more accuracy. A single drive may run several Check oints are easily obtained Tunnels No anic of raid testing Test conditions can be held constant for Model testing is more convenient a longer time. Extra ower is available to start Failure of model will not result in tunnel damage. Suersonic wind tunnels Introduction The nozzle regulates the seed of air entering the test section (T.S) of the wind tunnel so that the desired Mach number is established. Mach number is uniquely determined by the area ratio of the nozzle. A well designed nozzle makes the flow arameters uniform across the cross section. The design of a suitably shaed nozzle contour to obtain the desired uniform flow at the nozzle exit is based on the method of characteristics...1 Test section arameters (i) Dynamic ressure 1 The local dynamic arameter ρv can be related to the local Mach number and static ressure. Det. of Aerosace Engg., Indian Institute of Technology, Madras 4

5 1 1 q= ρ v = v RT 1 1 = v = M RT (ii) Mass flow rate m=ρva = ρ a A reresents choked conditions (M = 1) m ρ A v A = A A A ρ A v A = A A Since, ρ = and v = a = RT RT One has m A = RT A RT A A = R T A Using equation for T T and 0 0 and writing in terms of stagnation conditions, T0-1 = 1 + M T T = 1 + = = T When M = 1, 0 +1 = -1 Det. of Aerosace Engg., Indian Institute of Technology, Madras 5

6 -1 m +1 0 A = 1/ A R T0 A m 0 A = A R T +1 A 0 Mass flow density is exressed as a function of stagnation conditions and the area ratio. For isentroic flow, A is a constant and M A 1 = A M / -1 m -1 A R T = 0 M 1+ M 0 (iii) Test section velocity V = a M RT 0 M = M 1 A A is a unique function of local Mach number. (iv) Maximum velocity v c T + = c T P 0 v is maximum when c T = 0 c - c = R v c / c = V c c - = R Det. of Aerosace Engg., Indian Institute of Technology, Madras 6

7 cp -c P =R c -1 =R R c = -1 v = c T max 0 R v max = T0-1 1 The test section flow velocity v for a given stagnation temerature T 0 aroaches the maximum value v max at relatively low suersonic Mach numbers. For examle, In the case of T 0 = 300K R = 87J/kgK and a test section Mach number of 5.0, the ratio of v/v max can be calculated to see that it is equal to This means at ordinary stagnation temeratures, the velocity in the test section reaches 91% of the maximum ossible velocity corresonding to the total energy of the fluid. The stagnation temerature T 0 rather than the Mach number which is imortant to attain high velocities. (v) Free stream Reynolds Number (Re) ρvl Re = μ Exerimental observation is that μ is indeendent of ressure in the range of to 0 atmosheres. Det. of Aerosace Engg., Indian Institute of Technology, Madras 7

8 0 0 n μ T = for air n = μ T μ T 0 +C T = μ0 T+C T0 C = 130 T = T If this relation is assumed then the free stream Re can be exressed as a function of M 1, the T.S Mach no and of the stagnation arameters. Reynolds no er unit length Re L exressed in stagnation quantities as given below. ρv = ρ,v,μ μ are -1 = 1 + M 0-1 = 1+ M n T 1 μ = μ 0 = μ0 T M v M= a v = Ma = Ma M n Det. of Aerosace Engg., Indian Institute of Technology, Madras 8

9 a a RT = RT 0 0 Re = L M 1 M a n M 1 μ M n= for air Simlifying Re ρ -1 L μ 0 = a0 M 1+ M Both a 0 and μ0 are functions of stagnation temerature. Both increase with temerature. Hence, areciable changes in free stream Re/unit length for a given M can be obtained only by varying stagnation density..3 Comonents of suersonic wind tunnels.3.1 Air storage tanks Size of the storage will be deendent on the mass flows required and the frequency of runs. Pressure storage tanks are available on the shelf basis They are mounted horizontally or vertically. Tanks are ainted black to absorb heat. They are rovided with safety disk or ressure relief valve. As air is drawn from the storage, olytroic exansion takes lace within the tank. This results in dro of reservoir temerature which is very bothersome. Fall of stagnation temerature causes resultant change in the stream temerature for a given Mach Det. of Aerosace Engg., Indian Institute of Technology, Madras 9

10 number. Change in temerature results in the change of viscosity which in turn affects the boundary layer thickness. Changes in Reynolds number and Mach number during a run are thus consequential to the fall in reservoir temerature. To maintain constancy of stagnation temerature, it is a ractice to stack the reservoir volume with emty metallic cans. They serve as heat storing matrix during comression and release heat during the exansion rocess. Another way to maintain the constant stagnation temerature is by roviding heater units in the reservoir..3. Settling chamber /wide angle diffusers Fig..3a, b Wide angle diffuser Wide angle diffusers lead the flow to the settling chamber. Arrangements for leading the flow to the settling chamber may be by one of the methods shown in Figure.3a, b or c. Det. of Aerosace Engg., Indian Institute of Technology, Madras 10

11 Fig..3c Reverse entry into the settling chamber Uniformity of flow in the test section is imroved if a large area ratio contraction is rovided..3.4 Convergent-divergent (c-d) nozzle The c-d nozzle forms the heart of the suersonic wind tunnel.for generating suersonic flow in the test section, it is essential that there is a c-d nozzle in the tunnel circuit before the test section. The area ratio of the c-d nozzle (A exit /A throat ) uniquely decides the Mach number. Det. of Aerosace Engg., Indian Institute of Technology, Madras 11

12 Fig..4 Convergent divergent nozzle and the ressure rofile When the tunnel oeration starts, the flow is initiated in the nozzle as subsonic and reaches the sonic Mach number at the throat when sufficient mass flow is allowed. This is called the choked condition of the nozzle. Under this condition, maximum mass flow rate for the given stagnation conditions takes lace through the nozzle. The ratio between the ustream stagnation ressure (P 0 ) and the downstream back ressure (P b ) corresonding to the first time choking is called the first critical ressure ratio of the nozzle. At this ressure ratio, the flow in the divergent art of the nozzle is subsonic. The exit Mach number will be the subsonic value corresonding to the A/A in the Fig..5. In this context A is the exit area and A the throat area of the choked nozzle. As the value of P 0 /P b is rogressively increased, the flow in the divergent art of the nozzle accelerates to be suersonic but shocks are formed in the divergent art until a ressure ratio corresonding to the suersonic Mach number of the nozzle is reached. The ressure ratio corresonding to this Mach number is the third critical ressure ratio of the nozzle. Between the first and third critical ressure ratios shocks of varying strengths take lace in the nozzle and outside of it as there is no other isentroic solution between the 1 st and 3 rd critical ressure ratios. The ressure ratio corresonding to the occurrence of a shock at the exit lane of the nozzle is the second critical ressure ratio of the nozzle. Det. of Aerosace Engg., Indian Institute of Technology, Madras 1

13 Fig..5 A/A vs. Mach numbers All the shocks generated at the different ressure ratios inside the nozzle will make the ost shock Mach number subsonic and the subsonic nozzle exit ressure will be made equal to the ambient ressure in the remaining art of the diffusing divergent channel. Between the second and third critical ressure ratios, oblique shocks of varying strengths deending on the ressure ratio will be formed emanating from the nozzle li. The hysical urose of these oblique shocks is equalization of ressures between the exit lane and the ambient. If the ressure ratio is increased beyond that corresonding to the third critical ressure ratio, exansion fans will be formed at the li of the nozzle. Det. of Aerosace Engg., Indian Institute of Technology, Madras 13

14 .3.5 Diffuser- the necessity of roviding a diffuser Fig..6 a Nozzle of a free jet facility Take the case of a free jet facility as in Fig..6 making use of a c-d nozzle of Mach number 3.0 exiting to the ambient conditions at one atmoshere ressure. In order to avoid shocks and exansion waves at the exit of the nozzle, e must be b. o e M = 3 = 36.7 Pressure ratio required will be o = 36.7 e for a wave free exit flow from the nozzle. Det. of Aerosace Engg., Indian Institute of Technology, Madras 14

15 Fig..6 b Free jet nozzle with a test section In the Figure.6b, a constant area section is added to the nozzle exit. The duct similar to the test section (T.S) of a wind tunnel attached to the nozzle exhausts to atmoshere. corresonds to static ressure at the exit lane of the nozzle before the shock. Static ressure after the shock ( ) is equal to ambient ressure. o o e 1 = = 36.7 = 3.55 e In the equation above, e / reresents the shock ressure ratio at M=3.0. In the third case, as in Figure.8 a divergent channel is rovided after the constant area duct and the shock stands at the end of the constant area duct. e Fig..8 Free jet facility with test section and a diffuser Det. of Aerosace Engg., Indian Institute of Technology, Madras 15

16 When M << 1, = o o 0 e 1 = = = e o M = = 3.04 The three cases described above make it clear that rovision of a diffuser of suitable design is required for reducing the ressure ratio required for the oeration of the wind tunnel. It is shown in section.5 that the ower required to run the wind tunnel increases with the ressure ratio. In suersonic wind tunnels, most commonly used diffuser is of convergent divergent tye (also called the second throat diffuser).. 4 Power required for the oeration of suersonic wind tunnel Fig..9 Free jet tye wind tunnel with an attached test section Refer to figure.7 where a free jet tye wind tunnel is shown. Let the suersonic tunnel is secified by the Mach number (M) in the test section and test section (A) area.the throat area Det. of Aerosace Engg., Indian Institute of Technology, Madras 16

17 is secified as A NT. The flow arameters in the test section are denoted as, T, A etc.. Once M is secified, the area ratio A T /A NT and ratios of ressure and temerature / 01 and T/T 01 are all known from the isentroic equations. If the comressor is idealized (isentroic) the suction and reservoir conditions are related. Where T T S = S / andt S s reresent ressure and temerature at the comressor suction. If the nozzle is choked, the mass flow rate can be written as, m = A NT ( +1)/ R +1 T 0 The ower required to oerate the comressor may be found as follows: If the comressor is isentroic, the work er unit time may be found from the enthaly difference across the comressor. 01 s W = -m h -h R -1 = -m T -T 01 s [ W = work / unit time in W or Nm S ] = m RT s T Ts -1 RT s 01 = -m -1-1 s RTs -1 / W = -m (r ) The ressure ratio is known as the oerating ressure ratio and is denoted by r s Det. of Aerosace Engg., Indian Institute of Technology, Madras 17

18 The very large ower required for the oeration of a suersonic wind tunnel is attributed to the large oerating ressure ratio. If the wind tunnel is equied with a suitably designed diffuser and a closed circuit arrangement as shown in the next section, the stagnation ressure of the diffused high velocity air can be made use of by the comressor and the effective ressure ratio can be reduced..5 Closed circuit suersonic wind tunnel Fig..10 Continuous tye suersonic wind tunnel A convergent-divergent (c-d) diffuser is rovided as shown in Fig..10. Only if the flow is isentroic, the stagnation ressure regained in the receiver following the diffuser ( 0 ) is equal to that of the flow entering the nozzle ( 01 ). In that case, 0 = 01 Then, r = 1, so that comressor does no work. In ractical cases, because of entroy changes 0 < 01 and r > 1. If the entroy change is confined to the region between the two throats, the diffuser throat area A DT must be larger than the nozzle throat area A NT. Diffuser throat area must be large enough to accommodate the stagnation ressure loss of the strongest shock. A cooler is included rior to the comressor because comressor work is roortional to the intake temerature. Det. of Aerosace Engg., Indian Institute of Technology, Madras 18

19 The ractical oeration of the closed circuit wind tunnel may be exlained as follows: As the tunnel is started, flow through it begins as subsonic and as the ressure ratio is increased the nozzle is choked. Further increase in the ressure ratio causes shock to be formed in the divergent section. At a ressure ratio corresonding to second critical ressure ratio, shock is formed at the exit lane of the nozzle which is same as the entry section to the test section. The formation of shocks during the starting rocess gives rise to fall in stagnation ressure. The total ressure after the shock is designated as 0. This necessitates that the diffuser throat is designed larger as decided by the ratio 0 / 01. The ratio of diffuser throat area to the nozzle throat is in the inverse ratio of total ressures given above. A NT = 0 < 1 A DT 01 The ratio of areas for different test section Mach numbers calculated based on normal shock losses is given in Fig..11. This makes sure that the starting shock asses through the diffuser throat. The diffuser throat area calculated as above does not take in to account the nonisentroy of frictional flows and only the shock losses are considered. Fig..11 Ratio of diffuser throat and nozzle throat for different test section Mach numbers Det. of Aerosace Engg., Indian Institute of Technology, Madras 19

20 Assuming a frictionless oeration, the shock may assume any section in the constant area test section. But, the effect of friction is to make the shock unstable in the constant area duct. The shock that is generated during starting of the tunnel does not stay at the nozzle exit (entry to test section) but is moved downstream by the effect of friction. Fig..1 Shock movement from nozzle exit to diffuser The starting ressure ratio minimum required to cater to the shock at the test section Mach number is corresonding to that for locating the shock at the nozzle exit. (worst shock) r s 01 0 worst shock As the starting ressure ratio is maintained, the starting shock which moves down stream can be stable only at an area equal to that of the test section. In the convergent art of the diffuser the Mach number will be less than that in the test section. With the value of starting ressure ratio which roduced the shock at the test section Mach number being maintained, shock losses at that Mach number is being catered to. Hence the starting shock stabilizes only in the diverging art of the diffuser at a section where there is equal area and Mach number as the test section. The starting shock crossing the diffuser throat and remaining in its divergent art is called the swallowing of the starting shock. It has to be remembered that as the diffuser throat is larger than the nozzle throat, the Mach number there will be more than one but less than that in the test section. After the brief Det. of Aerosace Engg., Indian Institute of Technology, Madras 0

21 duration of starting, the ressure ratio may be decreased and the shock may be brought to the diffuser throat. Therefore the higher ressure ratio is required only during the starting when a shock at the test section Mach number is necessarily to be catered to and thereafter the ressure ratio can be that corresonding to shock at the diffuser throat. The smallest ressure ratio at which the tunnel may be continuously oerated (r Po ) after its starting is that corresonding to the stagnation ressure loss of the weakest starting shock which can be made to occur at the diffuser throat. 01 r PO = 0 Shock at M In summary, the ressure ratio for starting the wind tunnel is corresonding to the normal shock losses at the test section Mach number and that for oeration is that corresonding to normal shock losses at the diffuser throat. Hence the ower required can be considerably reduced by incororating the well designed diffuser and by judicious control of the two ressure ratios during starting and oerating of the wind tunnel. DT Fig..11 Pressure ratios for starting and oerating the wind tunnel of different Mach numbers Det. of Aerosace Engg., Indian Institute of Technology, Madras 1

22 .6 Actual flow in the suersonic wind tunnel The boundary layer (B.L) thickness and the total loss of momentum increase with increasing distance from the 1 st throat. The growth of boundary layer thickness with distance from first throat is redictable and can be accounted for in the nozzle design. In the steady state oeration, viscous effects between the throat and test section are not of much imortance. During the transient rocess in which tunnel is started, viscous effects are much imortant. So, imortant are these effects that ressure ratios required to start high Mach number tunnels are atleast 100% greater than the normal shock ressure ratio 01 equal to normal shock losses. 0 i.e. viscous losses are almost B.L. is stable when the ressure is decreasing in the direction of its growth. When the ressure is increasing in the direction of flow, it has a tendency to searate. As normal shock asses through the nozzle, it imoses a severe unfavorable ressure gradient which can cause searation. If B.L searates, it disturbs the flow over a large ortion of nozzle. If B.L. does not searate the high ressure gain in the downstream of shock will tend to flow to low ressure B.L. and the flow in the duct will be altered over a significant length of the nozzle. In the diffuser viscous effects are redominant during starting and steady state oeration of the wind tunnel. Unfavorable ressure gradient exists always. An oblique shock from the convergence creates additional ressure gradients when they strike the oosite wall..6.1 Starting a tunnel with a model in the test section It is exlained earlier that A DT = A 01 NT 0 Det. of Aerosace Engg., Indian Institute of Technology, Madras

23 which imlies that losses in total head resulting from shocks necessitate a larger diffuser throat. Hence, losses due to shocks on the model must also be rovided for. So, for starting a tunnel with a model, a second throat larger than that for a clear tunnel is needed..6. Sizing the wind tunnel model The theoretical unobstructed cross section area of the test section at the model required for starting is the same as the second throat area. Fig..1 Tyical shock wave attern from a model In choosing the dimensions of the model, reflection of shocks should be also considered. The oblique shocks formed as shown in Figure.1 at the leading edge of the model get reflected from the wind tunnel wall. It has to be remembered that shock reflection is not secular which means that the angle of incidence of the shock at the test section wall is not same as that for reflection. The chord length of the model is so chosen that the reflected shocks do not interfere with the model..6.3 Two roblems in the oeration of suersonic wind tunnels (i) Condensation The amount of moisture that can be held by a unit volume of air increases with increasing temerature. When the air isentroically exands to higher Mach numbers in the test section, the temerature falls. It may become suer cooled. Moisture will then condense. Det. of Aerosace Engg., Indian Institute of Technology, Madras 3

24 Factors affecting condensation a) Amount of moisture in the stream b) Static temerature of the stream c) Static ressure of the stream d) Time during which the stream is at low temerature Effects of condensation Condensation results in changes of local Mach number and other flow roerties due to latent heat addition. The extent of changes deends on how much heat is released through condensation and may be evaluated using the two equations given below: dm 1+ M dq da = - M -M H A d M dq da = M H A The notations used in the equations are: dq = heat added through condensation H = enthaly er unit mass A = duct area When M > 1, Mach no decreases and ressure increases. When M < 1, Mach no increases and ressure decreases. Drying the working fluid is the best way to avoid condensation. Increasing the temerature by roviding stagnation heaters is another solution. Det. of Aerosace Engg., Indian Institute of Technology, Madras 4

25 (ii) Liquefaction In a manner arallel to condensation, the comonents of air liquefy when roer temerature and ressure conditions are met. Liquefaction troubles might start around M=4 if high ressure air is exanded from room temerature. Fig..13 Stagnation temerature to avoid liquefaction at different Mach numbers Fig..13 shows the stagnation temerature required to avoid liquefaction at different Mach numbers. It can be seen that corresonding to a Mach number above 1 the temerature required will be about 000K. Det. of Aerosace Engg., Indian Institute of Technology, Madras 5

26 Exercises Answer the following 1. Comare and contrast ressure storage and indraft wind tunnels. Why are air storage vessels of suersonic wind tunnels stacked with emty metallic cans? 3. How justified are the stagnation ressure measurements being done in the settling chamber of the suersonic wind tunnels? 4. What decides the exit Mach number of a c-d nozzle? 5. What is understood by the term choking in c-d nozzles? 6. How to decide the exit Mach number of a c-d nozzle before it is choked? 7. Is there any change in the flow through the c-d nozzle if the stagnation ressure is increased after the nozzle is choked? 8. Define the three critical ressure ratios of the c-d nozzle. 9. Exlain the flow in the c-d nozzle of the suersonic wind tunnel between the 1 st and nd critical ressure ratios. 10. Justify the rovision of a diffuser for a blow down wind tunnel. 11. Why the diffuser of a suersonic wind tunnel converging-diverging? 1. How to arrive at the dimensions of the second throat diffuser vis-a vis the nozzle dimensions. 13. Derive the exression for the ower required for the oeration of a suersonic wind tunnel in terms of the oerating ressure ratio. 14. Differentiate between the starting and oerating ressure ratios of the suersonic wind tunnel rovided with a second throat diffuser. 15. What factors decide the condensation in suersonic wind tunnels? 16. How can condensation be avoided/reduced in suersonic wind tunnels? 17. What is meant by liquefaction in suersonic wind tunnels? Det. of Aerosace Engg., Indian Institute of Technology, Madras 6

27 Work out the following numerical roblems Problem 1 Part I In a suersonic wind tunnel of the following configuration, it is desired to simulate a flow of Mach number,m = 3.0, = 0.680bar in a cross section of 30cm by taking comressor suly from 1bar and 30 0 C.Determine the resultant test section temerature and the ower required to oerate the wind tunnel. Part For the wind tunnel given in Part I, in order to convert it to a continuous flow facility, a diffuser is rovided so roortional that it will barely swallow the starting shock. For identical flow conditions as in Part I, find the size of the nozzle and diffuser throats and the ower required to (i) start and (ii) oerate the wind tunnel. Problem A two dimensional double wedge airfoil of semi wedge angle is laced at zero angle of attack in a Mach 3.0 suersonic wind tunnel. What should be the minimum height of the wind tunnel test section in terms of the chord so that the reflections of the oblique shock formed at the leading edge of the model does not disturb the model. Det. of Aerosace Engg., Indian Institute of Technology, Madras 7