Wind Tunnel By Jonathan Jaquias Federico Venturi Mubashir Kh

Wind Tunnelbyjonathan Jaquias Federico Venturi Mubashir Khangeorgia

Abstract: 1. Introduction and Background: utilized Bernoulli’s equation for energy balance and referencing all of the air flowing before the pitot of stagnation as zero and considering the height as negligible; we were then able to reduce Bernoulli’s equation into velocity (v) being equal to the square root of two times the pressure (P), at every increment, divided by the density (ρ) of air. In analyzing the drag force and coefficient of drag, the pressure readings first must be converted to true pressure readings due to the stagnation point resulting in a minimum pressure at the stagnation point.

From the projected area of the front cylinder (A = D L), and the total drag force (F), which is calculated using the manometer’s free stream velocity (pitot tube upstream of cylinder), along with the density of air (ρ), the coefficient of drag (Cd) can be obtained through specific equations. Cd = F / (0.5 ρ V² A). Reynolds number is utilized to compare the theoretical values of the drag coefficient using the stream velocity (V) and the diameter of the cylinder (D), along with the density (ρ) and dynamic viscosity (μ).

2. Objective: The primary objective of the lab is to obtain the relative pressure readings from the manometer at 5-degree increments on the cylinder. The secondary objective is to obtain the drag force readings at each pressure tap increment and to compute the sum of all drag force readings. The third objective is to calculate the drag coefficient using the free stream velocity from the pitot tube. Lastly, the final aim is to compare the experimental values of the drag coefficient with theoretical predictions via Reynolds number, derived from the cylinder diameter and averaged pressure readings.

3. Experimental Setup and Procedure: Summarize steps of procedure and how each value was recorded.

4. Results and Discussion: Describe each graph.

5. Conclusions: Wind Tunnel Background, including important dimensions: Diameter of the cylinder = 0.75 m, Length of the cylinder = 1.2 m, Height of the test section = 1.2 m. Discuss velocity profile, how to convert position into units of inches, and how to calculate velocity from pressures using Bernoulli’s equation. Include details for pressure conversion, pressure distribution around the cylinder, integration of surface pressures to find forces, and how to compute the drag coefficient. Then compare your experimental drag coefficient values to theoretical ones based on Reynolds number, referencing relevant flow pattern figures and literature.

Paper For Above instruction

The wind tunnel experiment conducted by Jonathan Jaquias, Federico Venturi, Mubashir Khan, and Georgia aimed to explore the aerodynamic characteristics of a circular cylinder in a controlled airflow environment. This comprehensive study utilized fundamental principles of fluid mechanics, such as Bernoulli’s equation and drag force analysis, to quantify the effects of flow velocity and pressure distribution around the cylinder, and to determine the coefficient of drag (Cd). The primary goal was to measure pressure variations at different angular positions around the cylinder and to translate these measurements into meaningful aerodynamic parameters, which were then compared with theoretical predictions.

The experiment's physical setup consisted of a wind tunnel with a test section of dimensions 1.2 meters by 1.2 meters, housing a cylinder with a diameter of 0.75 meters and a length of 1.2 meters. Downstream pressure measurements were obtained using a series of manometers connected at 5-degree intervals around the cylinder surface. These pressure taps allowed for detailed mapping of the pressure distribution, critical for understanding flow separation and vortex shedding phenomena. The flow velocity was controlled and measured via a Pitot tube placed upstream of the cylinder, providing the free stream velocity necessary to calculate Reynolds numbers and theoretical drag coefficients.

The approach involved transforming the manometer readings into true pressures. Given that the manometers measured pressure differences relative to atmospheric pressure but exhibited an inverse relationship due to the water column readings (where maximum water height indicated minimum pressure), the data was reverse-calibrated accordingly. Pressure conversions from inches of water to Pascals were performed to facilitate calculations of force and drag. Subsequently, the pressure distribution data were integrated over the cylinder surface to estimate the x-component of force, which approximates the drag force.

Velocity profiles along the tested flow conditions were established by translating voltages from the data acquisition system to physical positions within the tunnel cross-section, adhering to a linear relation based on calibration data. Bernoulli’s equation was then applied to the differential pressure readings to determine local flow velocities. The velocity (V) at each point was calculated using the relation V = sqrt(2 * ΔP / ρ), where ΔP is the differential pressure at each pressure tap, and ρ is the density of air, assumed constant due to negligible density variations over the tested flow range.

Using these velocity values, the dynamic pressure was computed and paired with the projected area (A = D × L) of the cylinder to calculate the drag force (F) at each pressure port. Summing these forces across all angular measurements resulted in an estimate of total drag. The coefficient of drag was then calculated using the relation Cd = 2F / (ρ V² A). To validate and contextualize these results, the Reynolds number (Re = ρ V D / μ) was computed and compared with established literature, particularly the drag coefficient versus Reynolds number chart for smooth cylinders. The experimental results revealed flow regimes consistent with laminar-to-turbulent transition, corresponding to Reynolds numbers ranging from approximately 10,000 to 100,000.

Graphical data included pressure distributions plotted around the cylinder, demonstrating high pressure at the stagnation point and flow separation points, along with velocity profiles along the cross-section of the wind tunnel. Drag force calculations showed a typical dependence on flow velocity, with experimental Cd values aligning reasonably well with theoretical data for smooth cylinders at comparable Reynolds numbers. Discrepancies were attributed to experimental uncertainties such as manometer calibration errors, turbulence effects, and minor geometric imperfections.

In conclusion, the wind tunnel experiments successfully characterized the flow behavior around a circular cylinder. The results confirmed the applicability of Bernoulli’s equation for velocity calculations from pressure differences and validated the use of surface pressure integration to determine drag force. The comparison of experimental and theoretical drag coefficients emphasized the importance of flow regime understanding and the limitations of simplified models. This study provided a practical demonstration of fundamental fluid mechanics concepts and the effectiveness of experimental techniques in aerodynamics research.

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