ME331L

Date: May 2nd, 2025

Subject: The tank system stores pressurized air pressure blowdown.

Introduction

The purpose of this experiment was to verify that the air release from a pressurized tank through different sized holes can be modeled as a first-order differential system. It can be modeled because the early stages of the blowdown process have a predictable exponential pressure drop, which is characteristic of a first-order system. To support this, data on pressure and temperature were collected using two different sensing methods: a thermocouple and a pressure transducer. Both sensors were calibrated and used to capture the response of a pressurized air tank during blowdown through different sized orifices. The pressure and temperature data were recorded at a rate of 10 Hz using an Arduino and MATLAB. This data was then processed and fitted to a first-order model to analyze the blowdown behavior. and calculate the discharge coefficient. The memo compared the model’s predictions to the experimental data to verify the accuracy of the isothermal assumption and the system’s behavior. with different orifice sizes.

Experimental Methods

To support this experiment, a pressurized air tank was set up to study the blowdown process through three different size orifices: small, median and large. The tank was setup with two sensors: a thermocouple to measure the temperature inside the tank and a pressure transducer to measure the dynamic pressure during blowdown. The thermocouple was calibrated by comparing its output to known temperature values using the EGT-K amplifier, and the pressure transducer was calibrated by matching its output to the Bourdon pressure gauge readings from 80 psig to 0 psig to ensure accurate measurements. The output from each sensor was processed using a custom function for MATLAB. Pressure and temperature data were recorded at a rate of 10 Hz, with approximately 4200 samples collected for each orifice size tested. After calibration, the tank was pressurized, and blowdown was initiated through small, medium, and large orifices. Pressure and temperature data were recorded simultaneously throughout the experiments. This data was then analyzed and compared to theoretical models to assess the system’s behavior. and validate the assumption that the blowdown process is isothermal, meaning the temperature inside the tank remains constant throughout the release of air. This assumption is made to simplify the model, as it allows the system’s behavior. to be modeled using a first-order differential system, making the calculations more manageable and theoretically predictable.

Results and analysis:

Figure 1. Calibration of pressure transducer

Figure 1 shows the pressure transducer has a strong linear relationship between the raw counts and pressure. The raw pressure data from the sensor matches closely with the counts from the Arduino. The uncertainty interval and Scheffe Band cover a consistent range across the data points, suggesting that the uncertainty in the measurements is relatively uniform. across the full range of counts. This indicates that the deviation observed in Fig.1 is likely due to minor measurement error that affects the entire range of pressure readings.

Figure 2. Discharge Coefficient vs. Orifice Diameter with Uncertainty Intervals.

Figure 2 that the discharge coefficient appears to remain relatively consistent across the range of orifice diameters tested, with values slightly varying between 0.7 and 0.9. With the diameter increases, the discharge coefficient decreases, meaning that the flow of the air through the orifices may be decreasing, which might be caused by measurement error or nonideal orifice edges. Still the trend indicates that, for the given experimental setup, changes in the orifice diameter have effect on the discharge coefficient.

Figure 3. Pressure decay over time for 3 different orifices: large, medium, and small.

The actual data is compared to the theoretical model based on a first-order exponential decay. The pressure decay can be described by the formula for the time constant (τ):

where volume of the tank is V , the discharge coefficient is C , and the initial temperature is T0. The small orifice shows the best match between the actual data and the theoretical model, meaning the model works well because the flow is slower, and the pressure drop follows the expected pattern. The small orifice likely has a smaller C since the flow through smaller openings is less influenced by factors like turbulence and friction, making the pressure decay match the theoretical curve more accurately. For the medium and large orifices, the deviation between actual and theoretical data increases, which can be explained by the fact that frictional losses and compressibility effects become more significant in larger orifices where the flow rate is higher. As these factors are not included in this first-order system model, the pressure drop behavior. is less predictable for median and larger orifices.

Figure 4. Comparison of experimental temperature data with isothermal and adiabatic models for different orifice sizes

In Fig 4, the isothermal model remains nearly constant because it assumes that the temperature stays the same during the blowdown process. On the other hand, the adiabatic model describes a system where no heat is exchanged with the environment. The formula for adiabatic temperature variation is:

Where T is the temperature at any time, T0 is the initial temperature, γ is the specific heat ratio, t is the time, τ is the time constant. For the small orifice, the flow rate is slower, leading to a larger τ, meaning the pressure and temperature decay more slowly over time. This slower decay means it takes longer for the pressure and temperature to reach the same level as the large orifice. For the large orifice, where the air flow is faster, the temperature drop is more significant, and the adiabatic model becomes more relevant. The medium orifice shows a temperature drop somewhere between. Hence, smaller orifices align closer with the isothermal assumption due to slower changes in pressure and better heat exchange with the environment.

Conclusion

This experiment evaluated the pressure blowdown behavior. of a pressurized air tank through different sized orifices, comparing the experimental data with isothermal and adiabatic models. The results showed that the isothermal model worked well for smaller orifices, where the flow was slower and the temperature stayed almost constant. However, the adiabatic model explained the behavior. better for larger orifices, where the faster flow caused the temperature to drop more. The analysis showed that the first-order model works well for smaller orifices, but for larger ones, we need to consider factors like friction and compressibility to improve accuracy. In conclusion, the experiment confirmed that while simple models can provide good insights, more complex models are needed for larger orifices, and reliable data is essential to check the assumptions and predictions of these models.