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Grout pressures around a tunnel lining
Published in T. Adachi, K. Tateyama, M. Kimura, Modern Tunneling Science and Technology, 2020
A.M. Talmon, L. Aanen, A. Bezuijen, W.H. van der Zon
The flow-field is calculated in a computational domain moving with the TBM. The flow velocity components with respect to the moving frame of reference are: Vs and Vn . The s-co-ordinate is parallel with the tunnel axis. The n-co-ordinate is directed tangential to the circumference of the tunnel lining. The origin of the coordinate system is at the rear of the TBM at the crest. These orthogonal velocity components satisfy continuity. Friction between the grout and the tunnel lining and the undisturbed soil is responsible for pressure losses in the tail void. In order to calculate wall friction, the flow velocity (Us, Un) with respect to these boundaries is considered: Us=Vs−vt?,Un=Vn
Fluid Flow and Its Modeling Using Computational Fluid Dynamics
Published in Shyam S. Sablani, M. Shafiur Rahman, Ashim K. Datta, Arun S. Mujumdar, Handbook of Food and Bioprocess Modeling Techniques, 2006
In most physical phenomena, the familiar reference frame (or the coordinate axes) is fixed in space (stationary). This type of reference frame is called Eulerian frame. In this reference frame, the fluid would flow through a stationary coordinate system. However, in fluid mechanics, there are cases where it is desirable to have the reference frame move either with the fluid body or with a particle moving inside the fluid. This moving frame of reference is called Lagrangian frame. Because fluid dynamics involves fluid in motion, many equations have additional terms that arise from the moving frame of reference. For simplicity, sometimes these terms are grouped with the temporal derivative. This combined derivative term is defined as the operator
Avionic Systems
Published in Mike Tooley, Aircraft Digital Electronic and Computer Systems, 2023
Strap-down systems are fixed to the aircraft structure; the gyros detect changes in angular rate and the accelerometers detect changes in linear rate, both with respect to the fixed axes. These three axes are a moving frame of reference as opposed to the constant inertial frame of reference in the gimballed system. The system computer uses this data to calculate the motion with respect to an inertial frame of reference in three dimensions.
Drying of lithium-ion battery negative electrode coating: Estimation of transport parameters
Published in Drying Technology, 2022
Sindhuja Renganathan, Nizay Ahamed Khan, Ramanuja Srinivasan
Though Equation (6) looks like Fick’s law, the X here denotes the total solvent content, both in liquid and vapor phases taken together, and Deff is actually the effective capillary diffusivity.[23] The coating shrinks in thickness as the solvent evaporates. Hence, we have a moving boundary problem to solve. There are many different approaches available to solve such a problem.[37] In this work, a moving frame of reference approach suggested by Crank is used to calculate the diffusivity.[38] We refer this diffusivity as D* in this study. Solution to Equation (6), subject to all assumptions stated above, has been presented by Crank[38]:
Analysis and mitigation of hydroplaning risk considering spatial-temporal water condition on the pavement surface
Published in International Journal of Pavement Engineering, 2022
In this study, an automobile car tire P205/45R16 with four 9.9-mm wide longitudinal grooves was considered for hydroplaning analysis, as shown in Figure 8(b). The car tire has a constant inflation pressure of 187 kPa and a vertical load of 3767 N. The tire model parameters were first calibrated with the measurements of tire deflection from the static loading test. The hydroplaning analysis was conducted in a moving frame of reference, in which water and road surface were moving toward the tire at a given speed, and the tire rolled at a fixed location with angular velocity. The hydroplaning speed was determined in the following steps. In the initial stage, water and road surface were given the same initial speed, and the simulation run was executed. Then, the process was repeated with 2 m/s speed increments until the fluid uplift force equals or exceeds the tire vertical load, which will give an initial estimation of hydroplaning speed range. Finally, starting from the first estimation of hydroplaning speed, the speeds of water and pavement surface increased at the same small speed increment, such as 0.2 m/s to determine the final hydroplaning speed. The predicted hydroplaning speeds have been validated with field measurements (Ding and Wang 2018).
A new methodology to study the pantograph–catenary dynamics in curved railway tracks
Published in Vehicle System Dynamics, 2020
Pedro Antunes, Jorge Ambrósio, João Pombo, Alan Facchinetti
The track centreline spatial curve is obtained by performing the geometric reconstruction of the track geometry using the curvature and elevation data of the selected track [39], which is the same data that is used by the rail industry to represent the track design. With the track centreline curve and the track cross-level and corresponding cant angle, ϕ, a local moving frame of reference is built along the track using a methodology based on the evaluation and rotation of Frenet-Serret frame, [34,40]. For the purpose of computational applications, the track centreline curve and the moving frame unit vectors, , and , are discretized in particular locations, such way that, by interpolation, the complete track geometry can be used.