Prediction of transients and control reactions in a transonic wind tunnel

Prediction of Transients and Control Reactions in a Transonic Wind Tunnel

João Batista Pessoa Falcão Filho

CTA/IAE – Aeronautical Systems Division (ASA-L), São José dos Campos, 12228-904, SP, Brazil.

[e-mail]

Marcos Aurélio Ortega

CTA/ITA – Department of Aeronautical Engineering (IEA), São José dos Campos, 12228-900, SP, Brazil.

[e-mail]

Luiz Carlos Sandoval Góes

CTA/ITA – Departament of Mechanical Engineering (IEM), São José dos Campos, 12228-900, SP, Brazil.

[e-mail]

This work describes a lumped parameter mathematical model for the prediction of transients in an aerodynamic circuit of a transonic wind tunnel. Control actions to properly handle those perturbations are also assessed. The tunnel circuit technology is up to date and incorporates a novel feature: high-enthalpy air injection to extend the tunnel’s Reynolds number capability. The model solves the equations of continuity, energy and momentum and defines density, internal energy and mass flow as the basic parameters in the aerodynamic study as well as Mach number, stagnation pressure and stagnation temperature, all referred to test section conditions, as the main control variables. The tunnel circuit response to control actions and the stability of the flow are numerically investigated. Initially, for validation purposes, the code was applied to the AWT ("Altitude Wind Tunnel" of NASA-Lewis). In the sequel, the Brazilian transonic wind tunnel was investigated, with all the main control systems modeled, including injection.

Keywords. Transonic Wind Tunnel, Lumped Parameters, Control Systems, Injection.

Introduction

The design and production of the passenger’s jet EMB-145 by EMBRAER has placed the Brazilian aeronautical industry in the transonic era. Prior to that, since about the mid-eighties, the Air Ministry has started a coordinated effort in order to equip the Aerospace Technical Center ("Centro Técnico Aeroespacial"-CTA) in São José dos Campos, SP, with a modern transonic testing facility. To this end the American firm Sverdrup Technology was contracted, and the conceptual design of both the tunnel circuit and the pilot circuit were completed with success (Sverdrup, 1989).

The construction of the pilot facility, in a 1:8 scale, is a must due to the introduction of mass injection in the TT (Transonic Tunnel) circuit. The idea of injecting a stream of high-enthalpy air in the CTA’s TT circuit, to obtain a low-cost extension of the tunnel’s envelope, was introduced by Nogueira (Nogueira et al, 1988).

The timetable of the project as a whole, which includes the detailed design and construction of both pilot and main tunnel, has been extended several times because due investments have not been allocated in proper time. Albeit this, and after great effort, the TT team has succeeded in designing and building the pilot facility and the first runs will begin soon. Besides the designing and building work, many theoretical studies were also conducted with the basic aim of understanding the many physical phenomena that happen in a transonic wind tunnel run. As an important example, Fico (Fico, 1991, Fico and Ortega, 1993) obtained curves of flap losses, which hitherto did not exist. The present paper reports one more of these theoretical efforts. A numerical technique is proposed for analyzing physical transients and the corresponding response of the involved controllers. The results of a calculation such as this are always very helpful, because it can be used to optimize future tunnel runs. The reader should be aware that a transonic wind tunnel run is in general very expensive.

The mathematical model to be used is the result of the application to the transonic aerodynamic circuit of a technique known as "lumped parameters approach" (Arpaci, 1966). This technique is also sometimes recognized as a zero-dimensional treatment of the problem. Basically, parameters are lumped in successive domains (which together form the gross problem) with a step of parameter values between them. The first application to a wind tunnel circuit is the one of Krosel et al (1986). In this work the authors treated the problem of a subsonic circuit. Our main interests lie in the transients in a transonic tunnel with the ultimate aim of assessing the behavior of the control systems. The point here is that in order to reach and maintain conditions along the tunnel corresponding to a certain point in the operational envelope, one has to make use of automatic control. Therefore, considering the circumstance that, for some reason whatsoever, a transient appears in the flow, one is interested in knowing beforehand, at least approximately, how the control systems will react.

In summary, the contributions of this paper to the literature are twofold. Firstly, the lumped parameters technique is extended to a transonic aerodynamic circuit and, secondly, and by far the most important, an injection section is aggregated to the transonic circuit to be studied, what represents an important novelty in wind tunnel circuitry.

Nomenclature

A -Control volume cross-sectional area, m²

Â-Lumped element cross-sectional area, m²

c_P -Specific heat at constant pressure, J/(kg K)

D - Lumped element diameter, m

e - Specific internal energy, J/kg

E - Internal energy, J

E - Control system error signal, (*)

f - Pressure loss coefficient,(-)

- Resultant of external forces, N

k - Index, (-)

K - Control system proportional gain, (*)

K - Pressure loss coefficient, (-)

l - Tunnel module length, m

L - Lumped element length, m

M - Mach number, (-)

m - Mass, kg

N - Rotation, rps

- Versor normal to control surface, (-)

p - Pressure, N/m²

Q - Heat crossing control surface, J

Re - Reynolds number, (-)

S - Laplace transform variable, 1/s

t – Time, s

T – Temperature, K

T - Control system sample time, s

u - Thermodynamic specific internal energy, J/kg

U - Thermodynamic internal energy, J

V - Volume of a real tunnel segment, m³

V – Velocity, m/s

V - Control volume, m³

W - Work crossing control surface, J

X - Control valve position, m

z - ‘Z’ transform variable,(-)

Greek letters

d - Pressure ratio to atmosphere cond., (-)

l - Pressure ratio (outlet/inlet), (-)

q - Temperature ratio to atmosphere, (-)

- Fluid density, kg/m³

_v - Control valve natural frequency, 1/s

z _v - Control valve damping ratio, 1/s

Subscripts

o - Stagnation condition

amb - ambient

boff - Blow-off

C - Related to the compressor

CO - Compressor outlet

COR - Corrected value

CI - Compressor inlet

CS - Control surface

CV - Control volume

in - Inlet

inj - Injection

out - Outlet

res - Reservoir

S - Quantity crossing control surface

SP - Set point

T - Tunnel segment

TS - Test section

V - Valve

Signals

’ (comma) - Variable perturbation signal

- (dash over a variable) Mean value

. (dot over a variable) - Temporal rate

.. (double dot over a variable) - Temporal rate of rate

(-) - nondimensional

(*) - dependable upon other related variables

The Problem

The aerodynamic circuit of CTA’s transonic wind tunnel includes the main classical solutions of a "typical" closed circuit wind tunnel. Table 1 summarizes the main characteristics of the TT, considered today as ‘the state of the art’. The injection effect is better observed in Fig. 1, which illustrates the gain in the operational envelope, related to test section conditions, when an energized mass flow is injected in the tunnel. ‘Injection’ as the main source of energy to provide flow acceleration is a known practice (Long et al, 1984), but rather, its use as a "boosting" device represents a new technology.

Figure 2 shows the TT’s aerodynamic circuit with its main components labeled as: 1 - main compressor; 2 - heat exchanger; 3 - honeycomb and screens; 4 - first and second (flexible) nozzles; 5 - test section with ventilated walls (allow mass flow out from test section to establish transonic regimes); 6 - plenum chamber (adjusts pressure in the test section); 7 - reentry flaps (return mass to the main circuit); 8 - second throat (forces shock formation to prevent flow disturbances from moving backward into the test section); 9 - injectors (provide extra momentum to the main flow, saving main compressor power requirements); 10 - diffuser (decelerates the flow); 11 - blow-off (exhausts mass flow injected); 12 - plenum extraction and re-admission ports. One of the main features of this transonic wind tunnel circuit is the existence of ventilated walls in the test section. The mass flow extracted through the walls of the test section permits the establishment of transonic regimes; furthermore, the openings in the walls alleviate wall interference, especially shock reflection. In most cases of small tunnel design, this mass flow is readmitted into the circuit through the reentry flaps by the main flow induction effect. For large tunnel installations, which is the case of the present TT, reentry flaps suction is not enough to extract all the necessary mass, making necessary the use of auxiliary compressors (Goethert, 1961).

What basically distinguishes the TT from other transonic wind tunnel circuits is the introduction of mass injection (in Fig. 2, the injection section is shown at the entrance of the high-speed diffuser, its most probable positioning). Suppose now that the compressor is supporting a steady state condition in the tunnel, but at the same time, running at maximum power. If, at this point, a highly energized (supersonic) air stream is injected, the flow total energy is increased, in consequence the test section stagnation pressure is also increased and the operational envelope is extended (see Fig. 1). It is important to mention that this is an intermittent effect, with run time of 30 seconds in the worst operational condition. The mass flow to the injection system comes from pressurized reservoirs that are discharged in a "blow-down" process.

The problem to be addressed in this work can now be established. The tunnel is running in steady state and for some reason whatsoever a disturbance sets in. We want to know how this disturbance will affect the whole circuit behavior, its time evolution and how the tunnel’s control system will handle it. The reader should observe that the intermittent injection itself represents a great disturbance in the circuit and because of its importance, it will be specially focused.

All existing control systems and subsystems act in an integrated manner in order to reach the desired test section conditions in terms of the main parameters of the tunnel, such as: stagnation pressure, stagnation temperature and Mach number, which represent a specific point in its operational envelope (see Fig. 1). Ultimately, one wants to reproduce "on flight" Reynolds and Mach numbers. Considering which parameters to control, the most important one is the test section Mach number. This control can be implemented in several ways and in order to reach larger Mach number ranges, more than one control mode is necessary for each speed range (Davis et al, 1986). The CTA’s TT control capability is quite versatile and incorporates well-known techniques used to reach these ranges today. Combinations of main compressor rotation, inlet guide vanes positioning, first throat contour, flaps opening position, second throat positioning, mass extraction percentage through plenum evacuation system, mass flow in injection system and circuit pressure control may be combined to reach a desired Mach number (Falcão, 1996). However, for simulation purposes, only the main compressor rotation will be considered for Mach number control, because this is the contribution with larger magnitude. An accurate temperature control is also necessary because, besides removing heat from the circuit, one wants to be sure that the test conditions can be repeated whenever needed. A summary of the controlling parameters and respective control actions that have been analyzed in detail, in this work, can be seen in Table 2. These are the most important and representative parameters of the TT control system.

Figure 3, below, shows the tunnel control subsystems with their respective action locations. Pressure control is done through admission and extraction of mass, and are located in the "back leg" duct (6) and stilling chamber (1), respectively. Temperature control is done in the heat exchanger inside the stilling chamber (1) by controlling the water flow through the air-water heat exchanger. In terms of Mach number the main controlling action is on the compressor motor rotation. The rate of mass flow injected or extracted is defined by admission (4) and blow-off (7) valves. More details about each system will be given in section "Control System."

The injection boosting system is a very specific and important feature of the TT circuit. Therefore we believe that an explanatory note about its functioning is appropriate. The system consists basically of highly pressurized reservoirs, a control valve, ducting manifolds, and ten injector nozzles. The nozzles are located at the high speed diffuser inlet, downstream of the second throat, with five of them close to the floor and five close to the ceiling, as can be seen in Fig. 4. The installation of the injector nozzles at the high-speed diffuser inlet, favors the process of mixture of streams; on the other hand, it may affect the diffuser performance. The nozzles installations are such that they can be removed depending on the mass flow range requirement. When removed, the nozzles are substituted by fairing plates and the original geometry of the diffuser’s wall is recovered. The best performance is obtained when the static pressure of the high-speed stream is equal to the local static pressure of the tunnel current. This is the basic condition to be considered in this work.

Mathematical Model

Introduction

Strictly speaking, prediction of physical phenomena that take place inside a wind tunnel should be attempted through the use of a three-dimensional, distributed parameter model. This, of course, is very expensive, and typical results correspond to steady state solutions. Time-accurate, direct numerical simulations of such flows are, as yet, not foreseen for the near future. On the other hand, for control simulations in dynamic response, less accurate but fast solutions are preferred in contrast to solutions of a high degree of accuracy in a steady state condition. So, for the purposes of this work, we have adopted a zero-dimensional lumped parameter model (Kecman, 1988, Arpaci, 1966). Albeit its integral nature, the same idea has been widely used for prediction of transient flow effects in wind tunnels (Muhlstein, 1974, ETW, 1980, NTF, 1982, Long, 1984, Krosel, 1986).

Consider the equations of fluid dynamics in integral form (Zucker, 1977):

(1)

(2)

(3)

where, r is the density, V is the volume of the control volume, is the outward-oriented unit vector normal to the control surface, A is the area along the control surface, is the resultant of the external forces acting on the control volume, t is time, v is the velocity, e is the internal energy, is the time rate of heat flow through the control surface and is the time rate of work flow through the control surface. Furthermore, the fluid (air) is considered as a thermal and perfect gas, the field forces and internal heat generation are neglected and the aerodynamic circuit is taken as adiabatic, except at the heat exchanger and compressor sections. Equations (1), (2) and (3) were discretized in a particular way in order to be applied to new geometric definitions of control volume and lumped element, as defined hereafter, resulting in equations (7), (8) and (9), which have been applied in the mathematical code.

Before proceeding, we ought to introduce the particular concepts of "lumped element" and "lumped control volume" which are useful in the formulations to come. Fundamentally, these concepts are the ones already established in the literature, but here, there are some peculiarities that are worth being discussed.

Imagine a sequence of elements, or modules, by which the tunnel is divided. For example, the contraction, the first throat, the test section and the flap section form a sequence of elements. A "lumped element" is a duct of constant cross section, which, for the sake of building the model, substitutes a sequence of elements. Suppose now that the n-modules that form a particular sequence have lengths and volumes given, respectively, by, l1, l2, ..., ln, and V1, V2, ..., Vn. The total length of the sequence is then Li = l1 + l2 + ... + ln. The cross-sectional area of the lumped element, Â_i, is defined as

(4)

or, considering that A_k = V_k / l_k, (k=1,2,...,n),

(5)

The rationale behind this definition is to obtain the cross-sectional area Â_i closer to the least cross-sectional area of all elements that form the sequence. Why this? Because the lumped element is used exclusively in the application of the momentum equation, where the idea of losses by dissipation is outstanding. It is important to emphasize that, as a consequence of this definition, the volume of the lumped element (Â_i L_i ) is not equal to the total volume of the sequence, i.e., V₁ + V₂ + ¼ + V_n. Inside the lumped element all flow properties are considered uniform (homogeneous flow) for each instant of time. The exception to this is the end section (exit section) where there is a step variation of the properties.

As indicated in Figure 5, the full lines represent the real contour of the tunnel, whereas the dotted lines constitute the frontiers of two consecutive lumped elements, namely, elements (i-1) and (i). The "lumped control volume" is a geometric body such that its lateral surface coincides with the real lateral surface of the tunnel, and with entrance and exit plane surfaces defined in the following manner. Sections a and c are, respectively, entrance and exit sections of lumped element (i-1). Consider now the segment of the real tunnel between planes containing sections a and c. Section b is such that it divides this segment of tunnel in two parts of equal volume. Section b is the entrance section to the control volume (i). By the same token one can define section e as the exit of control volume (i). From these definitions it follows immediately that

(6)

where, V_i is the volume of control volume (i) and V_T,i-1 and V_T,i are the volumes of segments of the real tunnel situated between entrance and exit sections of lumped elements (i-1) and (i), respectively. The consequence of this is that the summation of the volumes of all control volumes is equal to the total volume of the tunnel.

Simplification of the Basic Equations

It is important to emphasize that the present technique is well represented in Fig. 5, because lumped elements and lumped control volumes are used in a coupled fashion. This permits us to exchange, when convenient, values of parameters between both representative geometries. For example, when dealing with control volumes, values at the entrance and exit sections are "borrowed" from the corresponding lumped elements. Equations of mass and energy are worked out with the help of the control volume, whereas the equation of momentum is modeled considering balances in a lumped element. In the latter case one must necessarily account for the momentum carried in by the injection flow due to the high speed of the supersonic stream. After proper simplifications, especially one-dimensionality of the control volumes entering streams, general equations (1), (2) and (3) can be rewritten as (the details can be found in Falcão, 1996):

(7)

(8)

(9)

The subscript "i" identifies one specifically lumped control volume or lumped element among the several that together form the complete tunnel circuit. The number of total modules (element or control volume) by which the tunnel is divided and what particular elements of the tunnel are included in a module are upon the user to define. The dot on a symbol indicates time rate of change of a parameter. The subscript "inj" indicates conditions at the exit of the injector, while subscript "o" stands for local stagnation condition. The symbol f is the friction factor defined commonly, as the ratio between shear wall stress and dynamic pressure (Shapiro, 1953), while L stands for the length of the lumped element and D for its diameter. The symbol V is velocity, p is thermodynamic pressure, and

_s and _s are respectively thermal and mechanical power crossing the control surface.

After updating the three basic variables, r _i, E_i and _i, one is able to update all other variables by simply applying basic relations of gas dynamics. The code written to solve Equations (7), (8) and (9) uses a fourth-order Runge-Kutta integration scheme and is fast enough to allow the simulation of control actions in real time with the use of typical microcomputers.

Values of f_i are taken from theoretical or experimental sources. Sometimes, and for certain specific conditions, one finds data in terms of K instead of f. K is the so called pressure loss coefficient, which for the case of an adiabatic element is the non-dimensionalized stagnation pressure variation, as normally found in wind tunnel literature (Jackson, 1976). Based on the present lumped parameter conception, one can find the relation between f and K as

(10)

where, Â_i is the lumped element cross sectional area and A_i is the inlet control volume area. Pressure losses along the tunnel circuit stems from the transformation of mechanical energy into heat, due to inevitable irreversibilities present in the flow process. The role of the main compressor is simply to supply fresh power to the airflow, recovering in this way the stagnation pressure at the compressor exit. Physically, the compressor "feels" pressure demand and "answers" with mass flow, according to its operational characteristics for a given rotation. The model mimics the compressor behavior by discretizing its operational envelope, a chart that relates corrected rotation and mass flow functions to the pressure ratio and efficiency of the machine (see Fig. 22). The precise operation point is interpolated starting from the global pressure loss for the tunnel circuit and, as a result, we obtain a new value for the mass flow in an iterative process. From compressor ratio and efficiency one can obtain, considering an adiabatic compression, a new stagnation temperature at the compressor exit.

Control Systems

Table 2 lists the main controls of the tunnel, the ones we thought as the most representatives. Among them, two should be granted special attention, the test section Mach number, M_TS, and the injection process. The former because M_TS is the premier parameter in a transonic wind tunnel and the latter because of the novelty. For numerical purposes the transfer functions equations were discretized using a backward difference scheme (Ogata, 1987), with S = (1 – z ^-1)/T (here, S is the Laplace transform variable, z is the ‘z’ transform variable and T is the discretization time). The resulting discretized expressions were solved together with the aerodynamic equations (7), (8) and (9). Control valves were modeled based upon a second order system according to the specialized literature (Ogata, 1970, Buckley, 1964) to better describe their stem mass, viscous friction and spring.

As an example, we shall discuss briefly the injection/blow-off system. The control variable for the injection system is the stream stagnation pressure, which determines the mass flux by aerodynamic choking condition at the injectors. The stagnation pressure signal at the injectors is compared with the set point signal and the difference is processed through a PI (proportional plus integral) controller to obtain the proper adjustment of the control valve (see Fig. 6). The control valve parameters together with reservoir conditions determine the output mass flow and the stagnation pressure perturbation which feedbacks the control plant. Equations (11), (12) and (13) are the backward-difference discretization expressions for the related parameters from the plant.

(11)

(12)

(13)

The quantity of mass that is injected in the main current has to be extracted, otherwise an unbalance would set up. Extraction is performed by a blow-off system, which includes a control valve (see Fig. 7). The injection mass flux is the set point for the blow-off. The signal is compared to the effective flux through the blow-off valve. The error, i.e., the difference of fluxes, is transformed in pressure signal by a PI (proportional plus integral) controller and sent to the blow-off valve. This valve exit signal corresponds to its position and a position-dependent flux component is generated. There happens then a combination of this component with two other components coming from pressure levels upwards and downwards the control valve, blow-off and atmospheric pressures, respectively. Equations (14), (15) and (16) are the backward-difference discretization expressions for the related parameters from the plant.

(14)

(15)

(16)

The symbols used in those equations are standard usage in control theory (Ogata, 1987). Physical limitations on the injection system valves operation were not considered because the purpose was to determine maximum design parameters. Although it has been considered the saturation for other control systems, injection system performance is not impacted by them and vice-versa, once injection operates on a "start and go" mode (see page 334). Pertinent details concerning the other systems can be found in Falcão (1996).

Results And Discussion

The interested reader can find in Falcão (1996) a great amount of data relative to the present work in the form of tables and graphs. For the sake of space restrictions an assortment of these information is presented here, what, anyhow, might very well be biased by our own judgement of what is more important and representative.

Code Validation

For validation purposes, a test case was calculated and results compared with data of Krosel et al (1986). The tunnel is the AWT - Altitude Wind Tunnel, NASA Langley - a subsonic facility up to Mach number 0.8. Figures 8, 9 and 10 show how the control systems of test section stagnation pressure, stagnation temperature and Mach number respond to a top-hat-like perturbation in the test section stagnation pressure. The perturbation is applied at t = 300 s and lasts 400 s; after that the regime is entitled to return to initial conditions. One can observe that both overshoots’ amplitudes and response frequency compare well. Some discrepancies appear though, what we regard as possibly due to differences in the time discretization for each control system - in Krosel et al (1986) one does not find how this time was discretized. The total number of lumped elements for this calculation was 5, the same number used by Krosel et al. Also, the nature and number of the tunnel modules per lumped element were the same ones used by the reference.

Results for the TT

In the following, the code was used in the testing of the CTA’s TT. Control systems with their controllers were set up in a trial-and-error approximation process in order to get the best possible performance. The lumped parameter technique behaved consistently and good results were in general obtained. For all cases involving a total number of four, or less, lumped elements, the code converged and responses were always stable. Nevertheless, when five or more elements were tried, the code diverged, even for small time increments. Anyhow, other calculations reported in the literature were also done with a seemingly small number of elements, namely, five for the AWT (Krosel et al, 1986) and three for the ETW (ETW, 1980). Many numerical experiments were then attempted: (i) Each control system subjected to commands of set point variation with all other systems linked in a sort of main-circuit-closed-loop process. The impact of those command variations upon the other systems parameters were then assessed; (ii) Probing upon the whole control system robustness through variations in the controllers characteristic parameters. Those and other interesting results will be now presented.

Stagnation Pressure Control without Injection

For this case the tunnel circuit was divided into four lumped elements. Figure 11 shows the details of this division. Control volumes associated with this arrangement were determined as described in page 320.

Starting the tunnel simulation at 101.3 kPa stagnation pressure, 313 K stagnation temperature and sonic Mach number in the test section, Figure 12 shows the response to a 10% top-hat command in stagnation pressure during 400 seconds. A rising time of 12 s, signal overshoot of 11% and settling time of 25 s, were observed, what is adequate to the real tunnel behavior. To accomplish this task, the pressure control system (as seen in Fig. 3) acts delivering or extracting air to or from the tunnel circuit through the auxiliary compressors. The evolution of mass flow admission and extraction is shown in Fig. 13. The system modeled has a non-linear operational characteristic, with a maximum mass flow limitation of 67 kg/s through the control valves. Mass admission or extraction to or from the tunnel alters pressure distribution along the circuit, as well as all other flow parameters, causing, ultimately, a disturbance in the main compressor operational point. Therefore, temperature and Mach number control systems move automatically to new positions, performing the system fine tuning. Figures 14 and 15 show the impact caused to the stagnation temperature and Mach number, respectively. Higher pressure levels in the tunnel results in increased pressure losses and, consequently, the stagnation temperature at main compressor exit also increases. The temperature raised from 313 K to 318 K in the test section in 7 s. Thus, the heat exchanger is required to react and water mass flow raises in order to reduce the air temperature in the circuit, and this is done in 60 s. After stabilization of the whole system, when the pressure set point is commanded to return to the original position, we can observe analogous reactions of the temperature control but in a reverse direction (see Fig. 14).

To overcome the higher level of pressure losses, the compressor reacts immediately with a correspondent increase in the pressure ratio. Due to the great inertia of the machine, there happens initially a diminishing of mass flow and this causes a decrease in the test section Mach number, from 1 to 0.95 in 3 s (see Fig. 15). Immediately, the Mach number control system starts to increase the compressor rotation in order to recover the initial Mach number condition (see again Fig. 15). Other numerical experiments, analogous to the one just described, but with perturbations of stagnation temperature and Mach number were done, and the code gave always very consistent results. For these data the reader is referred again to Falcão (1996).

System Sensibility

Variations in the proportional and integral gains of the controllers were tried in order to assess the system sensibility to those kind of stimuli. Figures 16 and 17 illustrate these results. The perturbation is a step of 10% amplitude in stagnation pressure applied at t = 100 s. In Fig. 16 one can see that, an increase in the controller proportional gain causes a less efficient pressure control and an increase in the rise time. Figure 17 shows that an increase in integral gain worsens the overshoot effect. The best proportional and integral gains where chosen based on these analysis.

The use of Injection

For this case the tunnel circuit was also divided into four lumped elements as depicted in Fig. 18. The best choice in this case would be to put the frontier of two lumped elements halfway in the test section. This would lead, necessarily – due to other important links –, to the creation of five elements. Unfortunately, with five elements the code diverged. This forced us to consider the test section parameters as extrapolated values – downwards from the stilling chamber, and upwards the injectors.

Initially, the controls were set up in order to drive the compressor up to its power limit, i.e., 34 MW. Stagnation pressure was set to 185 kPa, stagnation temperature to 313 K and Mach number to 0.96. The injection was turned on and maintained during 100 s. During this period all automatic control was set off. This means that, during injection, main compressor rotation and water flow through heat exchanger were left constant and no mass flow was admitted through the pressure control system. After injection, automatic controls were set on again, and injection and blow-off valves were kept shut off in order to restore conditions in the tunnel as for before injection. For this particular injection condition, the tunnel mass flow was 203 kg/s – three times less than the mass flow for the worst tunnel operational condition. This explains an injection run time of 100 s. Higher tunnel mass flow rates preclude longer injection runs, because this would correspond to a condition beyond the highest mass flow rate that the compressor would be able to handle.

The stagnation pressure at the injectors supply line was set up to 400 kPa in order to guarantee that the static pressure at the injectors exit section would be about the same local static pressure of the main stream. This is the best working condition because it corresponds to the least level of turbulence production. Figure 19 shows the adjustment of Mach number. The high frequency oscillations, gradually decreasing in amplitude, were observed during injection - and only during injection. As yet, we’re not able to say if oscillations are numerical or physical. Future experiments will certainly settle this point. As can be seen, the stabilizing time is 25 s and Mach number is stable during an interval of 75 s. With the help of modern measuring technology this amount of time is perfectly sufficient for data collecting. On the other hand, a stabilization time of 25 s is too high. Both injection and exhaustion valves act in about 5 s and the result reflects the tunnel circuit inertia. In practice, this performance can be improved by acting on the inlet guide vanes at the main compressor inlet. This factor is not simulated in the present work, and then the model does not profit from it.

In Figs. 20 and 21 one can observe the final impact on stagnation temperature and pressure, caused by injection. Indeed, the momentum of the main flow steps to a higher plateau following the stagnation pressure trend (see Fig. 21). At this point an analysis of the main compressor behavior is appropriate. The main compressor operational envelope is depicted in Fig. 22. Observe firstly that the impact in its set point due to injection is small. This is so because both injection and exhaustion ("blow-off") are made before the main compressor. Observe secondly that the main compressor set point dislocation occurred along a constant rotation direction. Figure 23 shows a zoom upon the main compressor set point variation. As the amplitudes are small and changes are relatively fast, an adequate mean to improve injection initial steeping response is the use of guide vanes at the main compressor inlet.

One of the most important results of this research is the confirmation that the use of injection with controls activated is improper. As can be seen in Fig. 24, which shows the variation of test section Mach number as a function of time during the process of injection (with controls activated to reach the well known final condition according to Figs. 19, 20 and 21), there is not a reasonable stable plateau during the existence of which one could collect data - the time for stabilization is about 80 s. This shows that phenomena related to the injection process are faster than the tunnel’s overall control response. As it was shown before, some systems spend about 30 s to reach their steady state condition, what represents in some cases the total time of the injection operation mode. The conclusion here is that the tunnel’s modus operandi with injection is one of "start and go". In other words, with everything set, including the presence of the model, the tunnel is run with injection and data collected. No attempt is made of controlling the process (with the exception, evidently, of the injector’s feeding process).

It is important to point out that more realistic data will be available only after the tunnel’s calibration phase, when the configuration parameters may be obtained from experiments, especially friction factors, which for now we are assuming as constants. Figure 25 shows the position of the initial and final injection states - indicated by "start" and "end" - with sufficient accuracy. Nevertheless, the path between these points is simply an illustration, since the temperature changes during the process, but the tunnel’s operational envelope chart corresponds to a fixed test section temperature (in this particular case, 313 K). So, the path plot is approximate.

Conclusions

The computational code proposed in this paper was able to reproduce, confirm and quantify a normal operating condition of the tunnel, i.e., the tunnel running without injection. The control systems are adequate and fast enough to maintain the test section desired conditions. On the other hand, results showed also, decisively, that with injection there is no chance of proper automatic controlling. The time response of the whole controlling system is too high when compared to a necessary stabilized time interval of the injection operation. In this case, the tunnel will have to be operated on a "start and go" basis.

The method developed and here presented turns out to be a very helpful tool for the team in charge of operating the tunnel. When used beforehand, the code will indicate the major limits and possibilities of a tunnel run.

Acknowledgments

The work of M. A. Ortega was supported in part by the Brazilian agency, National Council of Scientific and Technological Development – CNPq, through grant 522413/96-0.

Manuscript received: March 1999. Technical Editor: Paulo Eigi Miyagi.

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Publication Dates

• Publication in this collection
  18 Dec 2000
• Date of issue
  2000

History

• Received
  Mar 1999