Study of boundary layer and vortex shedding at natural frequency
A classic textbook example of failure of large engineering structure is the Tacoma Narrows bridge disaster of 1940. An ultimate failure was related to self-excitation and resonance. The accident led researchers to rethink about the design approach. Although the present project has wide scope in mechanical engineering, the proposed research focuses on hydraulic turbines. Need for energy flexibility and interconnection with wind/solar energy have pushed hydro turbomachines to the limit. Turbines are subject to heavy resonance and forced excitation, which often results in ultimate (premature) failure. Then, the question is how to minimize the damage. Insofar, damping is determined a generic approach, engineering linear relation, based on damped natural frequency. However, boundary layer has essential role to create damping effect. For instance, when a structure reverberates, it dissipates kinetic energy to the fluid through boundary layer, i.e., fluid structure interface, and vice versa. This project aims to determine the damping effect that accounts boundary layer complexities. The project will carry out experimental and numerical investigations of boundary layer at a level of multi physics. Pressure, strain and velocity (PIV) measurements will be conducted on a turbine blade. The project aims to quantify the flow instability, mainly kinetic energy fluctuations, inside the boundary layer, and the role of fluid added damping. Three different test cases will be investigated: (1) radial blade cascade, (2) rotating disc and (3) planar flow on reverberating longitudinal plate.
Project overview
Project: Study of boundary layer on reverberating hydrofoil at natural frequency
Type: Internally finance project
Finance: NTNU (EPT)
TRL: 3 - 5
Duration: 01 January 2021 - 31 December 2025
Project cost: 1.3 Million Euro
Coordinator: Chirag Trivedi
Email: chirag.trivedi@ntnu.no
Hydrofoil cascade
The research project aims to investigate the boundary layer on the vibrating surface thorough experimental and numerical methods. As investigated in the work from Bergan (2019) and Tengs (2019), the fluid-hydrofoil coupled system can be assumed as a one degree of freedom system (SDOF system). This means that the system is governed by Newton’s second law of motion and is therefore f(mass, damping, stiffness, force). Among these parameters the damping factor has not been much addressed in the literature despite being critical when runner vibration is around resonance frequency (Monette et al., 2014). The theory behind this phenomena has been studied in the paper from Monette et al. (2014). Hydrodynamic damping investigation in singular hydrofoil configuration with different shapes has been carried out by both Bergan (2019) and Coutu et al. (2012). Bergan (2019) have also investigated a linear blade cascade of 3 double-fixed hydrofoils in a cavitation free test rig. The single hydrofoil research has found a linear relationship between damping ratio and water velocity, and a different gradient of this relationship depending if water velocity is below or above the lock in region. When water velocity is below lock-in the linear relationship gradient is slightly positive and almost constant, while above lock in the gradient is largely positive. Moreover the almost linear relationship in the area of velocity below the lock-in is maintained also for the structural natural frequency while is somehow disrupted above lock-in region where no further trends could be founded. Regarding the linear blade cascade work Bergan (2019) has stated that three blade system behaves as a one bladed system while doubts have been raised on the behaviour of a circular cascade configuration. The interaction between fluid and the structure takes place at the interface/boundary layer, moreover a strong interaction between blades and the surrounding water, which led to change of damping characteristics (Trivedi & Cervantes, 2017) has been demonstrated. Further investigations were performed using different trailing edge profiles and their interaction with the vortex shedding (Sagmo, 2021). Flow characteristics were studied in detail including the turbulent properties for different Reynolds numbers. The research clearly indicated a radial arrangement of the hydrofoil is essential to mimic the the turbine blade effect (Pirocca, 2020). The radial cascade, aim of this PhD, will help to understand how blades react to forced excitation and the interaction between neighbouring blades, with a focus on the hydrodynamic damping effect for a circular configuration.
The experiments will be conducted in a blade cascade, an improved version of previous work in the Waterpower Laboratory. The original work (2016 - 2019) focused on a single hydrofoil test case, studying hydrodynamic damping with respect to the flow Reynolds number. Later, the research extended to three hydrofoils arranged in parallel to examine the impact of nearby structures on hydrodynamic damping. This study observed a moderate impact on the added mass. However, in the linear arrangement, the acoustic waves are normal to the blade surface. In hydraulic turbines, the blades are arranged in a radial pattern, which differs from the linear arrangement of the hydrofoil. This work further extends to a radial arrangement of the hydrofoils to study the impact of the radial pattern during resonance conditions.
Eight hydrofoils arranged radially.
Rotating disc
Our prior studies in the Waterpower Laboratory clearly indicated that a nearby wall significantly impacts the added mass of neighboring structures. Hydraulic turbines consist of several components, each playing a critical role in altering the added mass and eigenfrequencies. Additionally, the rotating turbine runner adds a new dimension to the complexity of the current fluid-structure interaction. Available knowledge is limited, particularly regarding vibration-induced fatigue. We need a robust mechanism to predict blade resonance. This research gap is addressed in the article by C. Trivedi (Engineering Failure Analysis, 77, 2017, pp. 1–22). To tackle these challenges, we have developed a simplified test rig with a rotating disc that allows us to study various influencing parameters. The test rig enables us to change the distance of the nearby wall, angular speed, and submergence level.
Determine the impact of nearby wall on the natural frequency of the blade type structure.
Primary objective
To understand the physics of how the surrounding bulk flow reacts to the resonating plate and how wall proximity affects the natural frequency (added mass). This understanding will help us develop a mathematical relationship between natural frequency and nearby structures. This mathematical relationship will be further refined for more complex situations, such as turbine blades.
Secondary objectives
- Investigate the change of natural frequency of a plate with respect to the proximity of the rigid wall.
- Investigate the flow physics around the resonating plate, focus on possible source and sink pattern.
- Interpret the flow pattern, wall proximity and the change of natural frequency (added mass).
- Develop correlation of point 3 and check Kwak’s theory holds true (or method presented by Askari et al.) and can be extended to the turbine blades.
Experimental setup for rotating disc with an option to adjust the vertical distance.
Hydrodynamic tunnel
Damping is divided into three categories: (1) fluid added (hydrodynamic) damping, (2) structural (friction) damping, and (3) material damping. Hydrodynamic damping depends on changes in mode shape due to fluid pressure, convection through vortex shedding, viscous effects within the boundary layer, flow velocity, surface roughness, proximity of nearby structures, and submergence level. When a structure is subjected to a specific mode shape, it deforms, affecting the flow field, particularly near the antinode boundary of the vibrating structure. This results in rapid changes in pressure and velocity. It is crucial to understand what happens in the boundary layer when a structure vibrates at resonant frequency and undergoes different mode shapes, such as changes in viscosity, inertia, and shear stress within the boundary layer. During resonance, amplitudes near the vibrating wall follow a sinusoidal pattern, with small amplitudes at the node point and high amplitudes at the antinode point. Consequently, the pressure gradient constantly shifts from favorable to adverse, along with changes in Reynolds stresses and viscous effects. In the boundary layer, a three-dimensional fluid element travels upstream and downstream as the flow accelerates and decelerates depending on the mode shape. Reverse flow occurs in regions of low kinetic energy (near the vibrating node point), and large eddies bring outer-region momentum towards the wall, supplying some downstream flow. Generally, three regions are created when backflow occurs.
Investigate the effect of wall vibration on the instability of boundary layer with the variation of, velocity, and static pressure of flow, and study the relation of instability in boundary layer and hydro dynamic damping to establish an empirical relationship between them.
Hydrodynamic tunnel for the study on fluid structure interactions.
We aim to close the knowledge gap on the behavior of hydrodynamic damping, focusing mainly on changes in the boundary layer during resonance and its effect on damping. Boundary layer flow instability, primarily caused by kinetic energy functions resulting from high-frequency vibration of the blade structure, will be studied to understand the relationship between the boundary layer and the damping effect. To achieve this, coupled fluid-structure interaction simulations using ANSYS will be conducted to understand the flow physics around the vibrating body. Then, a small test rig with simple geometry will be built in the laboratory, where PIV measurements will be implemented for flow characteristics. Excitation will be provided by piezoelectric patches, and the response will be registered with the help of strain gauges. Later, the experiments will be scaled to a hydrofoil-type structure to study the impact of the pressure gradient. Stepped sine frequency excitation will be used to avoid transients. For numerical investigation, high-quality simulations will be used. Initially, the simulation will be carried out using a relatively simple model, and complexity will gradually be increased to achieve the desired results.
The boundary layer plays an essential role in creating the damping effect. We have developed a dedicated benchmark test rig in the Waterpower Laboratory to study flow phenomena in an isolated environment. The test rig is highly versatile, allowing us to conduct numerous experiments addressing the fundamentals of fluid dynamics and fluid-structure interactions. We plan to use this test rig with a rectangular cross-section and aim to integrate a reverberating longitudinal plate into the test section to investigate the boundary layer at different Reynolds numbers.
Progress
Experiments on a rectangular thin plate are undeway to investigate the added mass and mode shapes at different frequencies. This reference measurements in air and steady water will serve bases for the future measuremetns with different Reynolds number flow over the plate. The future measurements will be carried out in hydrodynamic tunnel where PIV will be incorporated to study velocity profile.
