Draught tower driver for infra-turbulence aerodynamics.

Chiciudean, T.G. ; Rugescu, R.D. ; Tache, F. 等

Abstract: Design principles, prediction means and preliminary experiments on a draught accelerator (DA) for infra-turbulence aerodynamics are addressed. Performing with no mechanical moving parts, the DA is recommended as an almost perfect tool for very low turbulence studies. The key part of the proposed facility is its thermal driving system, which avoids mechanical components for blowing the air and thus eliminates the sources of vibrations. Up to the present, an opposite concept was proposed to extract energy from Sun-warmed air to generate electricity (Solar Tower project in Australia). In contrast, in the draught driver the cold air speedy sweeps a contracted test chamber, eventually being flawlessly sucked by heating into the draught tower. All existing aerodynamic tunnels use fan-type drivers only, but undesirably the fans are always sources of turbulence. Here they are removed and the pure aerodynamic pressure fluctuations remain under investigation. Under these circumstances the turbulence phenomena and its generation could be ideally studied. The scale transition and protrusion of microscopic processes into macroscopic properties becomes accessible. Measurements in a small-scale demonstrator were performed to assess the acceleration of the air and its numerical prediction.

Key words: Draught tower, Infra-turbulence wind tunnel

1. INTRODUCTION

The well-known principle of thermal up-draft in exhaust chimneys is currently used to enhance combustion in domestic or industrial heating installations (Raiss, 1970). The thermal convection was also imagined for driving a wind turbine to produce electricity, first in Germany (Gunter, 1931). Recently, a German team, now Schlaich-Bergermann-und-Partners Stuttgart, had tested this principle in a Spanish demonstrator facility with a height of 194 m (Haaf, 1983; Schlaich et al. 1990) and is currently involved in the construction of a 1-km tall Solar Tower for electric power production in Australia (Schlaich et al. 2004). The potential of this propelling mechanism for boosting the air from low to compressible speeds has not yet been applied and is here proposed as a solution for innovative infra-turbulence wind tunnels. In theory, the draught depends on the chimney height. For negligible cooling, the higher the chimney, the greater the air velocity is, but gradual cooling of the ascending gases ends in a different behavior. Along the global estimates, numerical simulations and experiments, as seen below, reinforce the WINNDER idea, showing that considerable air speeds are available in the contracted test chamber of a thermal tower.

2. CONVECTION THEORY

The up-draught force of a chimney results from a decreased weight of the worm gases in respect to the surrounding air, the Archimedes' effect, and acts under gravity only. Reducing the ascending force to the unit area and regarding a mean density, the ascending pressure [DELTA]p appears (Raiss, 1970),

[DELTA]p = l x g x ([[rho].sub.a] - [[rho].sub.i]) [mm [H.sub.2]O] (1)

where l is given in meters and the density [rho] in kg/[m.sup.3]. While in fact the inner density varies, the draught is given by

[DELTA]p = g/10 x [[integral].sup.l.sub.0] ([[rho].sub.a] - [[rho].sub.i])dx. (2)

The outside and inside densities are related to the local temperature through the equation of state, where the gas constant is usually set to R=287 for the air and R=280 for the exhaust gases. When a given cooling law is considered, e.g. a linear one, a medium temperature [T.sub.med] is associated with the chimney and from (Raiss, 1970) the draught in Table 1 results.

Table 1 shows that under a constant 0.8[degrees]/m cooling a maximal global draught appears in a 300-m tall chimney. Extra height is not profitable. Usual power plant stacks do not exceed 350 m. Examples in (Raiss, 1970) show that in a non-isolated 30-m tall chimney 0.6 m in diameter the temperature gradient is 2.0[degrees]/m. Tall, concrete or composite towers manifest higher insulation, however. The effect of possible cooling gradient is given in Table 2 for very tall towers.

When intense cooling manifests, its simple consideration ends in an upper limit for the height of the tower. The drag works in the same direction. That the draught continuously increases with height may be cautiously assumed (Schlaich et al. 2004), unless cooling stands below 0.4[degrees]/m, which seems to be the case for concrete or composite towers. Into an aerodynamic accelerator a large amount of heat is to be introduced and the cooling conditions are aggravating. Preliminary estimates show that a 300-m high tower suffices.

The loss of draught by drag E (Raiss 1970) is given by

E [equivalent to] ([lambda] x l/S + [summation][zeta]) x [w.sup.2]/2 x [[rho].sub.i] [mm [H.sub.2]O] (4)

with [lambda]=0.085/0.6 the drag coefficient, S the cross area, [summation][zeta] [equivalent to] 3/4 for local losses, w, [rho] the mean velocity and density of the air.

A formula (Weinrebe, 2004) estimates the air velocity at,

[w.sub.max] = [square root of 2 x g x l x [DELTA]T/[T.sub.a], (5)

where [DELTA]T is the heating of the air in the stack over the ambient temperature [T.sub.a]. Published data (Grober, 1943) show that the eigen-loss E is roughly 25% of the theoretical draught. A similar quota must seemingly lower data in tables 1 and 2. Starting with these valuable estimates, advanced numerical simulations are yet required to validate the flow capability.

3. EXPERIMENTS AND COMPUTATIONS

Problem-oriented codes were announced (Schlaich et al. 2004) and general codes are also available. A 1D-wave front code was also adapted for this problem (Rugescu, 2004). Simulation for the scale stack model in Fig. 1 were performed by the authors. Geometry is given in mm. An electrical resistor of 2/3 Kw heats the air to create the required draught. Through the large inlet the air enters a nozzle (linear contraction 1/4) that forms the test chamber, made from transparent materials to allow visualization. The visualization is enhanced with a white smoke (Fig. 5). Photo recording and movies were used to measure the mean velocity of the air. A convenient grid was structured at nozzle and corner zones, set to 17025 cells, 34756 faces and 17732 nodes (Fig. 2).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

An inlet temperature of 300K, exit pressure of 101000 Pa and an exit total temperature of 300K were used, besides a transfer coefficient of 50 w/[m.sup.2]/K and an eigen-temperature of 1400 K for the heater. No heat transfer outside was considered as confirmed by direct measurements. While the standard g=9.80665 m/[s.sup.2] was used, the air was considered as incompressible at those very low speeds and manifesting the following standard properties: [c.sub.p] = 1006.43 j/kg/K, [lambda] =0.0242 w/m/K, [eta] =1.7894 x [10.sup.5] kg/m/s, [mu] =28.966 g/mole. A thermal accommodation coefficient of 0.9137 and an equal momentum accommodation coefficient were also introduced, as required by the numerical solver.

4. RESULTS AND CONCLUSIONS

Laminar and turbulent simulations were compared. The actual situation in the stack is however laminar. A temperature increase of 13[degrees]C was computed for the radiator after some 10000 iterations, producing a small but sensible acceleration of the air. In the figures below the velocity field and vectors at nozzle and corner zones are suggestively drafted.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Either measurements and computations confirm that velocities of more than 20 m/s are deliverable in the contracted test chamber of the small-scale stack experimented, and considerably higher velocities can be achieved with taller towers of 70 m or 200 m as propose in the WINNDER project.

Acknowledgement: the research was sponsored by grant CNCSIS nr. 27692/14.03.2005, theme 44 code 308

5. REFERENCES

Gunter, H. (1931), In hundert Jahren--Die kunftige Energieversorgung der Welt, Kosmos, Gesellschaft der Naturfreunde, Franckh'sche Verlagshandlung, Stuttgart.

Haaf, W. (1983), Solar towers, Preliminary Test Results from the Manzanares Pilot Plant, Solar Energy, 2, 141-161.

Raiss, W. (1970) Heiz- und Klimatechnik, Springer, Berlin, vol. 1, pp. 180-188.

Rugescu, R. D. (2004), Wave front code for transients in solid rocket motors, 1st IC-EpsMsO, Athens, Greece.

Schlaich, J., Schiel, W., Friedrich, K., Schwarz, G., Wehowsky, P., Meinecke, W. & Kiera, M. (1990), Abschlussbericht Aufwindkraftwerk, Ubertragbarkeit der Ergebnisse von Manzanares auf grossere Anlagen, BMFT Forderkennzeichen 0324249D, Stuttgart.

Schlaich, J., Bergermann, R., Schiel, W., Weinrebe, G. (2004), Design of Commercial Solar Updraft Tower Systems--Utilization of Solar Induced Convective Flows for Power Generation, Commercial Solar Towers JSEE Rev.C2.

Unger, J. (1988), Konvektionsstromungen, Teubner, Stuttgart.

Weinrebe, G. (2004), Das Aufwindkraftwerk-Wasserkraftwerk der Wuste, Nova Acta Leopoldina NF91, Nr.339, 117-141.

Table 1. Draught vs. height l with 0.8[degrees]/m cooling

 l [t.sub.med] [[rho].sub.a] [[rho].sub.I]
 m [degrees]C kg/[m.sup.3] kg/[m.sup.3]

 10 300 1.2 0.652
100 255 1.2 0.705
200 205 1.2 0.741
300 155 1.2 0.801
400 105 1.2 0.873

 [P.sub.a]-
 l [[rho].sub.I] [DELTA]p
 m kg/[m.sup.3] bar

 10 0.548 5.5
100 0.495 49.5
200 0.425 85.1
300 0.340 102.1
400 0.234 93.7

Table 2. Draught vs. height for different cooling gradients.

 l [DELTA]p, bar [DELTA]p, bar [DELTA]p, bar
 m 0.2[degrees]/m 0.4[degrees]/m 0.6[degrees]/m

 10 5.5 5.5 5.5
 100 52.8 52.8 51.7
 200 105.4 100.8 95.9
 300 154.5 143.5 131.3
 400 201.1 180.3 156.1
 500 245.1 210.4 168.3
 600 286.2 233.1 165.2
 700 324.4 247.4 143.3
 800 359.4 252.1 98.0
 900 391.1 245.8 22.9
1000 419.3 227.0 -

 l [DELTA]p, bar [DELTA]p, bar
 m 0.8[degrees]/m 1.0[degrees]/m

 10 5.5 5.5
 100 50.6 49.5
 200 90.7 85.1
 300 117.6 102.1
 400 127.6 93.7
 500 115.9 49.1
 600 75.3 -
 700 - -
 800 - -
 900 - -
1000 - -