Mathematics

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Research from the Department of Mathematics. The department website may be found at https://www.ndsu.edu/math/

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Browsing Mathematics by browse.metadata.department "Mechanical Engineering"

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    Application of image based finite element analysis for mechanical characterization of materials processed by direct energy deposition technology
    (North Dakota State University, 2024) Smith, David
    The main focus of this study is to analyze the elastic properties of two different additively manufactured materials. To this end, a cobalt chromium (CoCr) metal alloy sample and a tungsten carbide-17% cobalt (WC-17Co) cermet specimen were both fabricated by the direct energy deposition (DED) process and were examined in this study. A comparative study between the results obtained from the application of numerical and analytical techniques versus the experimental results could show the accuracy of these techniques for estimation of elastic properties of the samples. A conventionally manufactured CoCr alloy and WC-17Co samples with similar composition was subjected to the same analysis for the purpose of validation of the results. The object oriented finite element analysis (OOF) technique provided acceptable results for the DED processed CoCr sample, but was unsuccessful in the estimation of the elastic behavior of WC-Co DED sample due to its inhomogeneous microstructure.
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    Experimental investigation of novel designs for aerodynamic flow control over airfoils
    (North Dakota State University, 2024) Refling, William
    In this study, an experimental investigation was performed to characterize and validate three novel flow control strategies for unsteady aerodynamics. These three strategies are based on active and passive flow control designs. The two active control strategies make use of smart material alloy’s (SMA) located on the leading and trailing edge of a Boeing-Vertol VR-12 airfoil used in rotorcraft wings. The SMA used were macro fiber composites (MFC) a piezo-electric actuator. These actuators were located at the 25% and 85% of the chord length. Two different implementation strategies are used: one as an active morphing of the leading and trailing edge, second as acoustic resonators on the leading edge. The third strategy was of a passive flow control structure located on the pressure side of the leading edge of a NACA 0012 airfoil. This strategy makes use a microcavity to mitigate the transient separation and dynamic stall. In addition to the three novel strategies, traditional approaches such as drooping of the leading and trailing edge were studies. All systems were tested in both a static condition where the airfoil is held stationary as a freestream velocity is applied to the airfoil. As well as testing with a dynamic motion of the airfoil simulating a sinusoidal pitching motion. All of these tests were performed in the open loop wind tunnel located in the advanced flow diagnostics lab. The details of the wings design, manufacturing, actuation, programing, control, and test implementation is reported herein. The flow fields were measured through use of 2-D particle image velocimetry (PIV) an optical diagnostic flow methodology used for characterization and validation of the designs. To capture more detail of the unsteady and unpredictable nature of the flow, time resolved 2-D PIV, is implemented to provide full details of the flow while each strategy undergoes multiple pitching cycles. All three flow control strategies showed positive improvements to the airfoil performance. The active morphing provided the largest performance boost as the flow remained attached throughout the pitching experimentation. Showcasing the improvement that active morphing has over traditional methods of droop. The acoustic resonance was a close follow-up showing improvement in both pitching and static conditions, however for the case of pitching the system was inconsistent. This has been attributed to the need to adjust the frequency generated while the angle of attack changes. Lastly the passive cavity structure showed limited improvement during light dynamic stall, improving the flow when compared to the baseline. However, the flow conditions needed to concisely prove the control strategy were not possible with the current equipment.
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    Fluid-structure interaction of steady and pulsating flow through a collapsible thin-walled vessel
    (North Dakota State University, 2024) Chowdhury, Sifat Karim
    An experimental study has been conducted to investigate complex fluid-structure interactions in collapsible tubes under steady and pulsatile flow conditions, which holds significant implications for many physiological fluid transport phenomena. Quantitative analysis of structural deformation and flow field analysis were conducted utilizing Particle Image Velocimetry (PIV) and optical image analysis. The results suggest that the tube wall deformation followed Shapiro’s tube law under static and low-Re steady flow conditions. An increase in flow magnitude triggered self-excited oscillation under a critical range of negative transmural pressure. PIV results revealed periodic asymmetric jet downstream alongside velocity fluctuations during self-excited oscillation. Pulsatile flow induced cyclic symmetrical buckling under positive and neutral transmural pressures, while created traveling wave patterns under negative transmural pressures. Under highly negative transmural pressures, tube collapsed during diastole, limiting the mean flow rate. Brief self-excited oscillation was observed under such conditions, amplifying the peak flow rate within a pulsatile cycle.