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Wind tunnels are experimental setups producing an air or gas stream for investigation of flow around models representing, for instance, vehicles or buildings. Wind tunnels are used to determine aerodynamic resistance forces of bodies, to investigate their stability and controllability, and to determine vehicle and building dynamic loads due to explosion waves and gusts. A special class of wind tunnels with heaters is used for estimating heat loads applied to the surface of the body in the flow and in developing heat protection techniques.

Experiments in wind tunnels are based on the principle of motion reciprocity according to which displacement of a body relative to gas or liquid can be replaced by gas or liquid flow around the body at rest (see Aerodynamics). In mechanics, this is known as the Galileo principle and is applicable, strictly speaking, only to the case of a uniform rectilinear motion. Under these conditions the stream force and heat effect on a body are identical in both direct and reverse motion.

Simulation of body motion in a quiescent medium requires establishing in a wind tunnel a uniform gas or liquid flow with equal and parallel velocity vectors at all points of the working space and with identical values of gas temperature and density. This problem is solved using quite a number of structural components some of which are depicted in Figures 1, 2, and 3. The wind tunnels designed as far back as the early 20th century incorporated a prechamber 1, a nozzle 2, a working section 3, a diffuser 4, and a drive 5.

Recirculating (closed circuit) wind tunnel.

Figure 1. Recirculating (closed circuit) wind tunnel.

Wind tunnel with compressed gas storage.

Figure 2. Wind tunnel with compressed gas storage.

Working section arrangements in wind tunnels.

Figure 3. Working section arrangements in wind tunnels.

The prechamber is a source of a high-pressure gas that is speeded up via a nozzle to a specified and uniform velocity V∞ before the inlet to the working section, the gas pressure and density being much less than in the prechamber. The diffuser zone of the nozzle converts the kinetic energy of the stream to the potential energy of pressure. The wind tunnel drive unit (a fan, a compressor) makes up for energy losses for friction, nonisentropic stagnation in shock waves, etc. For wind tunnels running off compressed gas bottles (Figure 2), reciprocating compressors raising the gas pressure in the cylinders serve as a drive.

These components are all inherent in various types of wind tunnels, both subsonic and supersonic, although they may vary in design, size, and layout (Figure 2). The working section may be closed (Figure 3b) or open (Figure 3a). The jet in an open working section with the static pressure being unequal to atmospheric is separated from atmosphere by a special altitude chamber known as an Eiffel chamber (Figure 3c). Each design has advantages and disadvantages, but open working sections gained wide application owing to ease of observation and recording of optical measurements.

The working section is, as a rule, shaped as cylinder with the circular or rectangular (sometimes, elliptic or polygonal) cross section. The cross section shape of the working section depends on the type of body to be investigated in a wind tunnel. For instance, oval, round, and rectangular shapes are most fitting for aircraft, rockets, and optical observations, respectively.

In addition to the five basic components, wind tunnels may have a number of more specific components. Among them is a gas heater (Figure 2) arranged before the prechamber and various straightener vanes and lattices regulating gas flow before the inlet to the nozzle (a honeycomb or deturbulizing screen) breaking down large vortices, reducing stream turbulence, and eliminating skewness of velocity fields (Figure 1). The return duct in closed-circuit wind tunnels makes it possible to save a considerable portion of kinetic energy in gas stream behind the diffuser.

In closed-circuit wind tunnels, it is advisable to provide a drier (Figure 1) to remove excessive moisture from air which can distort the flow pattern in the working section. In continuous-action wind tunnels, the gas is heated due to stream friction against the walls and the drive operation, therefore, gas-cooling heat exchangers need to be incorporated in such tunnels (Figure 1).

Most importantly for wind tunnel operation is the flow velocity, particularly, its relation to sound velocity. As is known, under adiabatic flow conditions the sound velocity is . The criterion of similarity characterizing the velocity regime of the gas flow is the Mach number Ma = V/a. The schematic of wind tunnel structures presented in Figures 1, 2, and 3 gives only a general idea of the variety of operational regimes of wind tunnels. Thus, bottles, exhaust fans, and vacuum vessels are used, as a rule, in open-circuit wind tunnels designed for gas ejection and single gas utilization in the working section (Figure 2). Compressors and fans built in gas dynamic contour make possible steady state wind tunnel operation, although in this case gas heating generally is not allowed, and the small pressure differential limits the velocity range to subsonic. Filling up a vacuum vessel in the course of an experiment (see Figure 2) is used in the pulsed wind tunnel which operates with variation of basic parameters during the pulse cycle.

Gas storage vessels (bottles) can provide a high-pressure gas supply both directly to the prechamber or alternatively to multistage ejectors at the outlet of the diffuser behind the working section (Figure 2). In these cases, the operation time depends on the gas content of the bottles. This system of gas supply has several advantages over continuous gas supply systems. First, it makes it possible to produce streams with higher Mach numbers at relatively low power consumption of the drive. Second, it enables the achievement of an extremely high Reynolds number which otherwise can only be achieved by simultaneously establishing a high-velocity flow in the working section and, hence, a higher vacuum as the outlet.

An exhauster is a fan creating vacuum. It can diminish pressure at the outlet by nearly two orders of magnitude in relation to that at the inlet with the flow rate of hundreds of cubic meters per second. The most powerful exhausters have 50,000 kW and higher power.

Transonic wind tunnels are distinguished from other wind tunnels by the structure of working section. Their walls are perforated and slotted (Figure 4). The narrowest section in the wind tunnel has a flow velocity equal to the sound velocity. Therefore, in wind tunnels with close to sonic flow, the effect of the model blocking up the cross section of the working section gives rise to local supersonic flows. This is called choking of the wind tunnel. Increasing the pressure in the prechamber, we raise the flow rate, but do not change position of the sonic velocity section, and the wind tunnel becomes inoperable. These tests are not reliable because the model is in the lower velocity flow.

Transonic wind tunnel.

Figure 4. Transonic wind tunnel.

The critical Mach number corresponding to the beginning of choking depends on "obstruction", i.e., the cross section of model and its suspension (SM) relative to the cross-section area of the working section (S*). The graph in Figure 4 allows us to estimate an admissible value of this blockage. For instance, corresponds to the model cross-section area ratio (Sm/S*) of 0.02. Therefore, experiments can only be conducted with a solid blockage lower than 2 per cent. We obtain the same result for a supersonic velocity when .

Variation of with blockage ratio.

Figure 5. Variation of Variation of with blockage ratio. with blockage ratio.

The cross-section area of the model must be zero if sonic velocity is required in the wind tunnel.

Choking of the wind tunnel can be virtually prevented if the working section has perforated walls and is enclosed in an air-tight chamber preventing excessive gas leakage. This produces the effect of flow metering nozzle, i.e., establishing a supersonic flow in the nozzle with a constant cross section area.

In currently used transonic wind tunnels the number of holes drilled at an angle of 60° to the wall surface amounts to 10,000. This is a labor-consuming job, therefore, holes were replaced by slots which, however, are less effective than perforations in minimizing disturbances in the wind tunnel.

The boundary layer (see Boundary Layer) growing on the nozzle and working section walls produces its own effect on the stream. To diminish this effect the working section in closed-circuit wind tunnels has the conicity of the order of 0.5° depending on the Reynolds number. Boundary layer bleed through special slots on the walls is used in some wind tunnels. In others the design nozzle dimensions are increased by the value equal to displacement thickness.

The nozzle portion from throat to outlet section is of most importance for making corrections for the boundary layer displacement thickness. Speeding up the flow from low to sonic velocity in the nozzle throat rapidly thins the boundary layer, but as the velocity grows and the gas density sharply drops in the supersonic portion of the nozzle, it enhances again. This effect is most significant in high-vacuum wind tunnels.

A wind tunnel as a test complex must meet the conditions required to provide correlation of experimental data with the flight and bench test results obtained under similar conditions on other setups. Besides the operating conditions indicating the extent over which the flows may be studied and the degree of stability of controlling and measuring systems, we discuss here only the requirements imposed on gas parameters in the working section. These are velocity field uniformity, the level of longitudinal pressure gradient, and the intensity of turbulence of the free stream. To meet these requirements, it is necessary first and foremost to manufacture carefully the gas dynamic contour of the wind tunnel (prechamber, nozzle, diffuser, working section, and return duct) and also, all the devices arranged inside the tunnel such as straightener vanes, deturbulizing screens, sensors, and sings, and gas supply systems (pipelines, valves, etc.). These must be designed to avoid any disturbances (vortices, boundary layer separation, etc.) in the gas stream.

Disturbances may propagate far downstream distorting the stream. Therefore, the inner surfaces of the tunnel must be thoroughly finished and have faired bend turns and changes in cross section. To prevent separation of the boundary layer, much attention should be given to shaping the regions with stream stagnation. The diffuser angles are confined to 6–8°. In some cases the boundary layer is drawn off or cryogenic systems of surface cooling are used.

The uniformity of velocity field is characterized by an absolute value and an angle of slant. An admissible absolute value is , where V and are respectively the local and the mean flow velocity for a given cross section of the wind tunnel.

The. angle of flow slant Δθ regarding the wind tunnel axis is measured in two projections on a horizontal and a vertical symmetry plane. In currently used wind tunnels, the angles of slant Δθ are less than half a degree. This is achieved by mounting a honeycomb—that is a honeycombed framework—made of thin metal plates. The choice of contraction ratio n (i.e., the ratio of the cross section of a prechamber to the throat of the nozzle) is of great significance. For the best wind tunnels n = 20 – 25.

Longitudinal pressure gradient (dp/dx) arise n in the working section is due to solid blockage of model, inaccurate wall configuration, and the boundary layer buildup in the flow section.

The pressure gradient produces an effect of buoyant force acting on the model in the direction of decreasing pressure p. As a result, the longitudinal force acting on the model is determined with an error that can be approximately calculated by the formula ΔF = VM(dP/dx), where VM is the model volume. This error must be minimized and taken into account in the total experimental error.

An important characteristic of the wind tunnel is the turbulence intensity of the stream. The effect of this parameter is appreciable in the transition Reynolds number region, e.g., in transition from laminar flow in the boundary layer to turbulent flow. The turbulence intensity or the initial turbulence of the free stream is determined by

Here is the averaged flow velocity, , , and are the mean values of squared turbulent fluctuations of the velocity components along the x-, y-, and z-axes. An isotropic turbulence, when is common for wind tunnels. In this case the turbulence intensity is determined as

and it is expressed, as a rule, a percentage. The mean velocity for a definite period of time is calculated via the fluctuation velocity , while the mean value of squared turbulent fluctuations is determined as

Turbulence in the atmosphere is generally estimated as Tu = 0.02 per cent, while in the working section of the wind tunnel it may be three orders of magnitude higher and amount to 1.7 per cent. This is due to the fan operation, breakdown of flow behind the edge of guide vanes, flow straighteners and every kind of projection, and due to the poor finish of inner walls of the wind tunnel duct. Elimination of these drawbacks as well as increasing the contraction ratio in the nozzle and installation of deturbulizing screens make it possible to bring the initial turbulence of the flow to 0.1 per cent. This is of particular importance for low-velocity wind tunnels, where the model resistance is governed mainly by the friction resistance.

The flow turbulence has a strong impact on the results of testing various models, particularly under conditions where separation of the boundary layer and a drastic change of resistance occurs. Taking flow over a sphere as an example, it is found that separation of a laminar boundary layer occurs far further upstream than for a turbulent layer (the laminar layer is less resistant, to a back-pressure). The more downstream the separation occurs, the closer the pressure distribution is to that corresponding to a sphere in an ideal inviscid flow. Although the viscous shear is higher in the turbulent than in laminar flow, the total resistance and, hence, the drag coefficient Cx of the sphere drops more than fourfold (Figure 6). The Cx versus Tu curve is plotted based on tests measuring drag coefficient of the same sphere in different wind tunnels with a variable turbulence Tu. This curve can be used to determine the relationship between turbulence intensity Tu and the critical Reynolds number Re* for transition from laminar to turbulent flow in the boundary layer, results are illustrated in Figure 7.

Effect of Tu∞ on drag coefficient for flow around a sphere.

Figure 6. Effect of Tu on drag coefficient for flow around a sphere.

Variation of Re* with Tu∞ for laminar/turbulent transition in the boundary layer formed in flow round a sphere.

Figure 7. Variation of Re* with Tu for laminar/turbulent transition in the boundary layer formed in flow round a sphere.

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