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Fundamentals of Computational Fluid Dynamics Modeling and Its Applications in Food Processing
Published in C. Anandharamakrishnan, S. Padma Ishwarya, Essentials and Applications of Food Engineering, 2019
C. Anandharamakrishnan, S. Padma Ishwarya
The prerequisite for the modeling of the interaction between two phases (gas-droplet) involves defining the modeling frames, also known as the reference frames. Reference frames are important in determining how the particles or droplets interact with the surrounding gas medium in the computational domain. For instance, the reference frames for modeling a spray-drying operation deals with two phases, namely, the dispersed and continuous phases constituted by the droplets and gas medium, respectively. As already known, the designation of phases depends on the volume of the component, the one in larger volume is the continuous phase, and that in smaller volume is the dispersed phase. Reference frames differ in the manner how they consider the interaction between the abovementioned two phases (Anandharamakrishnan and Ishwarya, 2015). Accordingly, there are three different types of reference frames, which are discussed subsequently.
Testing Guidance Laws Performance
Published in Rafael T. Yanushevsky, Modern Missile Guidance, 2019
A reference frame (coordinate axes) determines the origin and direction of measurement of the motion states of a dynamic model. The origin is the point from which the states are measured. The axes of the reference frame define the directions of measurement. Common reference frames in simulation are body frames, navigation frames, and inertial frames. The inertial frame is the non-accelerating reference frame used for calculating the Newtonian equations of motion. The navigation frame is generally located at a convenient position in space; for simulation of missiles, the navigation frame may be located on the Earth’s surface at a given latitude and longitude. The navigation frame may be fixed, rotating, accelerating, or moving with respect to the inertial frame. In practice, it is difficult to define a reference frame that is not accelerating with respect to inertial space; e.g., an Earth-fixed reference frame is suitable for some low-fidelity situations. However, in high-fidelity situations, the rotation and movement of the Earth needs to be accounted for in the definition of the inertial frame. The body-fixed frame has its position and orientation fixed to the vehicle body. The body-carried frame has its position fixed to the vehicle body and its orientation fixed to the navigation frame. Different simulations (or phases of a single simulation) may require different inertial reference frames for the fidelity requirements. The choice of reference frames affects the numerical error incurred in the simulation. This suggests that the reference frames used by dynamic models could be chosen to reduce numerical errors.
Measurement for deriving kinematic parameters: numerical methods
Published in Youlian Hong, Roger Bartlett, Routledge Handbook of Biomechanics and Human Movement Science, 2008
A reference frame is a particular perspective from which the motion of a body or system is described or observed. A reference frame fixed to the laboratory is inertial while those fixed to the body segments are non-inertial. The laboratory reference frame is also global (common) since this frame can be used in describing the motion of any body segments. A reference frame fixed to a segment is local and is meaningful only in that particular segment. The object space coordinates of the markers obtained through reconstruction are ‘global’ since they are described in the laboratory reference frame. The acceleration measured by a tri-axial accelerometer attached to tibia is ‘local’ since it is based on the accelerometer reference frame. Local data may be globalized only when the relative orientation and position of the local frame to the global frame is known.
A nonlinear optimal control approach for underactuated offshore cranes
Published in Ships and Offshore Structures, 2022
The diagram of the offshore boom crane is shown in Figure 1. There are two reference frames, namely the inertial frame OXY and the body-fixed frame . The body-fixed frame is aligned with the inertial reference frame after rotation by an angle α. This angle appears because of the roll motion of the vessel which is induced by the waves' motion. The turn angle of the boom crane with respect to the horizontal axis of the body-fixed reference frame is denoted by ϕ. The moment of inertia of the boom is denoted as J. The mass of the boom crane is m and its length is . The payload (e.g. lifted container) has mass and is moved by a string of variable length L. The angle that is formed between the string and the vertical axis of the body-fixed reference frame of the vessel is denoted by θ. The state variables of this model are ϕ, L and θ. The state-space model of the boom crane is obtained through Euler–Lagrange analysis and after computing the potential and kinematic energy of the boom and the load. This model is given by Lu et al. (2018) The inertial matrix of the boom crane's model is given by Lu et al. (2018) where , , , , and .
Verification and Validation of Transient Body Force in GOTHIC for Spent Fuel Pool Response to Seismic Events and Other Applications
Published in Nuclear Technology, 2022
P. C. Skelton, J. W. Lane, T. L. George, S. W. Claybrook
The momentum equations in GOTHIC are written and solved assuming that the frame of reference is an “inertial frame,” i.e., nonaccelerating. In an accelerating reference frame bodies moving experience an inertial “body” force that is opposite in sign to the frame acceleration and is given by the product of the reference frame acceleration and the accelerated mass. Momentum conservation equations in GOTHIC are solved for three “phases” (liquid, vapor, and drop/aerosols) and the body force term is applied to each phase in every computational cell as
BEM applied to the cup effect on the partially submerged propeller performance prediction and ventilation pattern
Published in Journal of Marine Engineering & Technology, 2022
Ehsan Yari, Ali Barati Moghadam
The boundary of the flow region includes the surface of the body , the surface of the wake , and the outer surface that surrounds the surfaces of the body and the trailing vortex surface. Two reference frames are considered: a Cartesian inertial reference frame (X, Y, Z) fixed in space; and a body-attached reference frame described by local Cartesian coordinates (x, y, z). Assuming the flow to be effectively inviscid, incompressible and irrotational. The disturbance velocity is irrotational with the exception of the surfaces of discontinuity of the velocity field in which the wakes of lifting surfaces are replaced. Therefore, the disturbance velocity, being irrotational, may be written as the gradient of the disturbance potential , . For an incompressible flow field, the continuity equation equals . The total velocity at any point of the flow domain, , is the sum of the undisturbed velocity and the disturbance velocity: For an incompressible, inviscid and irrotational flow, the Navier–Stokes momentum equations reduce to the Bernoulli equation. In the body-attached reference system, the unsteady Bernoulli equation reads: In Equation (3), p, ρ and are pressure, fluid density and reference pressure of the fluid, respectively. For a propeller, is the pressure far upstream and it obeys to the hydrostatic law, being the atmospheric pressure at the depth of free surface. Reference () speeds are usually considered as the resultant vector of inlet velocity and rotational speed (nD). D is the propeller diameter and n is the rotational speed (revolution per second) for the propeller, is defined as The unsteady Bernoulli Equation (3) can be rewritten as follows.