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Jet Impinging on an Inclined Plate



Jet impingement on solid structures is a widely used process in technological applications, such as material cutting in the manufacturing industry and energy generation from hydraulic sources. Jet impingement consists of releasing a fluid through a nozzle from a high-pressure region to a low-pressure region and striking or impinging the jet upon a structure. During the process of impingement, forces generated by the interplay between pressure and velocity of the flow field are exerted on the object's surface. For example, in the case of a vertical takeoff and landing or VTOL aircraft, two jets combined produce enough lift to help the aircraft take off vertically without using the runway. Two additional smaller jets issued on each side of the aircraft provides stability. The effects of impingement depend on the jet's dimensions and speed, the characteristics of the impingement surface, and the distance between the nozzle and surface. When the temperatures of the surface and the jet are significantly different, jet impingement would produce high levels of heat transfer. This video will illustrate how to determine the load exerted by a jet on an object and also how to calculate other parameters of interest for flow diagnostics, such as jet velocity and mass flow rate.

Before delving into the experimental protocol, let's study the principles behind jet impingement. For a steady incompressible flow of a fluid with zero viscosity, the kinetic energy and pressure potential energy are free to transform into each other along the streamlines. While the sum of the two forms of energy is always constant, this is Bernoulli's Principle derived from the Principle of Energy Conservation. According to this principle, an increase in speed and in consequence in the kinetic energy of a fluid occurs simultaneous with a decrease in its pressure and potential energy. Such as their sum is always constant. This is Bernoulli's Equation. Expressed in dimensions of pressure, the term associated with kinetic energy is called dynamic pressure. While the term associated with the pressure potential energy, is called static pressure. The addition of these two terms gives the Bernoulli's constant, also known as stagnation pressure. Stagnation pressure is defined as the maximum pressure that the flow would reach if brought to a halt by transforming all of its dynamic pressure into static pressure. Now let's talk about the experimental setup. An air jet exits from a high-pressure plenum through a slit of width W and span L to a lower-pressure receiver where the jet impinges on an inclined plate of angle theta. The intermediate streamline divides the jet in two regions. One deflected upwards and the other one downwards. The dividing streamline stops right at the wall at the stagnation point where the dynamic pressure is converted completely into static pressure. At the stagnation point, the profile of the pressure exerted by the jet on the plate has a maximum value p0. While away from this point, the pressure profile steadily decreases since progressively less dynamic pressure gets converted into static pressure. The pressure profile depends on the impingement angle theta. When theta is 90 degrees, the centerline is also the stagnation line. By decreasing the impingement angle, the stagnation streamline moves away from the centerline of the jet, and in consequence, the peak of the pressure profile gets smaller and shifts towards regions of the plate closer to the jet exit. The total pressure on the surface of the plate exposed to the jet is the result of the addition between the impingement pressure and the static pressure inside the receiver. Since the pressure inside the receiver is homogeneously distributed, the surrounding pressure exerted on both sides of the plate cancels out. In consequence, the net load on the plate is due to the overpressure and it is calculated by integrating over the impingement pressure distribution across the area of the plate. When a fluid is discharged through a slit from a high-pressure region to a low-pressure region, the jet tends to converge to an area called vena contracta. This is the first location after the jet leaves its discharge port in which the streamlines become parallel and consequently the static pressure equals the pressure of the surroundings. Let's apply the Bernoulli's equation between the position where the jet exits from the plenum and the position at the vena contracta. Considering the velocity inside the plenum to be negligible, the velocity at the vena contracta can be calculated using the pressure difference between the plenum and the receiver. Finally, knowing the contraction ratio between the slit width and vena contracta, the mass flow rate can be estimated using the jet velocity and area of the vena contracta. In the following sections, we will measure the resulting pressure distribution on the plate and then calculate the total force by integrating the pressure field over the plate's area.

Before starting the experiment, since opening the door to the receiver while in operation is potentially hazardous and damaging to the facility, make sure that the facility is not in use. If the door to the receiver is open, the facility is not in use. If the door to the receiver is closed, look through the window. If there are no personnel inside, the door is safe to open because the facility can only be started from inside while the door is closed. To begin, set the instruments according to the schematic. Connect the positive port of the pressure transducer to the output of the scanning valve. Make sure the scanning valve is at the home position. Connect the piezometric hoses of the plate to the scanning valve in subsequent order. Remember to start the measurements at the intake next to the output of the scanning valve. First, adjust the plate to the desired angle theta. Second, measure the jet nozzle width. Third, measure the span and height of the plate. Zero the pressure transducer and record the value for the calibration constant. Record all the basic parameters of the experiment in a reference table. First, open the low-pressure port to sense the pressure in the receiver. Then connect the high-pressure point of the transducer marked as positive to the pressure tap of the plenum. Next, start the flow facility. Measure the voltage associated with the pressure difference sensed by the pressure transducer between the plenum and the receiver using the digital multimeter. Calculate this quantity using the calibration constant.

Once the instrument is calibrated and the basic parameters are recorded, you are ready to start data acquisition. First, connect the high-pressure port of the transducer to the common port of the scanning valve. Also hone the scanning valve to start your measurement from the first pressure tap position on the plate. Run Traverse six on your computer, input the conversion factor from volts to pressure, and set the sampling rate to 100 hertz and the total of samples to 500 to get five seconds of data. Next, enter zero in the virtual instrument for the position of first pressure tap and then record the data. The value on the screen is the pressure difference between the pressure tap and the receiver. Step the scanning valve to the next tap position. Introduce the new position in the software knowing that the distance between two consecutive taps is 25.4 millimeters and record the new value of the pressure difference. At the end of the experiment, the software generates a table and a plot of the tap position versus the pressure. Modify the flow rate by changing the position of the flow control plate to close the flow area roughly by half and repeat the pressure measurements. Repeat the measurements for different flow rates and inclination angles and record every time your results in a table. When all of the data has been collected, turn the flow facility off.

Based on the experimental data, several parameters of interest can be obtained. Look at the results table and for each plate angle and flow rate, use the pressure difference between the plenum and receiver to calculate the jet velocity at the vena contracta. From the reference table, take the values for the span L and the slit's width, and use the speed at the vena contracta previously calculated to estimate the mass flow rate. Then look at the position versus pressure plot generated by Traverse six and read the peak value of the pressure. Introduce the value in the results table. This value is a direct estimation of the stagnation pressure. Now, compute the force impinged on the plate by integrating the pressure distribution over the plate area. In order to do this, use the pressue difference versus position plot and calculate the area under the curve with the Trapezoid Rule or Simpson's Rule. Introduce the value in the results table.

Begin by plotting on the same graph four sets of results obtained for the plane jet impingement on a plate at two different angles and two different flow rates. Now, compare the pressure profiles for the two different impingement angles and the same flow rate. The pressure profile at 90 degrees is higher than the one for 70 degrees. While the peak for 90-degree impingement is centered, the peak for 70 degrees is shifted toward a lower x value. These results tell you that for a 90-degree impingement angle, the stagnation streamline corresponds to the flow centerline. The centerline is characterized by the peak velocity and, thus, by the maximum dynamic pressure. As the impingement angle decreases, the stagnation streamline moves away from the peak velocity line and bends away from its original path. Next, compare the pressure profiles for the two different flow rates and the same impingement angle. The maximum pressure decreases with the flow rate because there is a reduction in the kinetic energy and hence in the dynamic energy as the flow rate decreases. Look at the results table and compare the values calculated for the load on the plate. The impingement angle has the effect of reducing the total load because it shifts the stagnation pressure from the one coinciding with the centerline velocity to a streamline carrying lower levels of dynamic pressure.

Impinging jets are widely used in many industrial and engineering applications spanning from hydraulics and aeronautics to electronics. The interplay of pressure and velocity can be used for flow diagnostics. A Prandtl or pitot-static probe is composed of two concentric tubes. The inner tube faces the flow to detect the stagnation pressure. While the outer tube has a set of side ports that sense the static pressure. The difference in pressure is detected with an integrated sensor, and this value is used to estimate the velocity. This device is extensively used in fluid engineering. To determine for example, the velocity of the wind relative to the airplane. Soft materials like plastics and wood can be cut with a thin waterjet at high speed. While metals can be cut with water upon adding abrasive particles to the stream. To generate a high-speed jet for cutting purposes, it is necessary to impose high pressure in the flow to be able to accelerate it through a converging nozzle. The high kinetic energy carried by the jet is then converted into dynamic pressure at the surface of the object being cut, exerting a force strong enough to remove material at the impinging surface.

You've just watched Jove's Introduction to Jet Impingement on an Inclined Plate. You should now understand how the interplay between pressure and velocity generates forces on the structures and be able to calculate the impingement forces, flow velocities and mass flow rates. Thanks for watching.

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