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Concept# Velocity

Summary

Velocity is the speed and the direction of motion of an object. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.
Velocity is a physical vector quantity: both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called , being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object is said to be undergoing an acceleration.
Constant velocity vs acceleration
To have a constant velocity, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed.
For example, a car moving at a constant 20 kilome

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Matthias Timothee Stanislas Wojnarowicz

Subsurface geothermal in combination with Ground Heat Exchanger (GHE) and heat pumps systems had proved over the past decade to be an effective way in space heating and cooling. GHE’s embedded in geostructures such as tunnels has become more and more attractive in the current state where we try to mitigate greenhouse gas effects. The scope of this paper is to provide a fully coupled numerical model to assess the different physical aspects of an energy tunnel such as the kinetic and thermal boundaries layers development, thermally induce stress, and the heat generation. To do so, a finite element model is used to assess the heat exchange between, the GHE, the concrete lining, the air within the tunnel, the surrounding ground, and groundwater flow. The numerical model is then confronted with data from real-scale experimentation that was performed in Torino in 2018. The predictions from the numerical model show a quite good match with the data from the experimental prototype. Later on, similar models are generated to assess the effect of the heat exchange on air velocity and temperature within the tunnel as well as the induced thermal stress. The numerical results highlight the formation of both the kinematic and thermal boundary layer and shows that those boundaries are affected by the GHE’s activation. For the kinematic aspect, the lower temperatures observed in the vicinity of the heat exchangers tend to lower the velocity magnitude especially close to the wall surface. This change in velocity may be linked to a buoyancy effect cause by the lower temperature of the air in this regions. Indeed natural convection occurs along the tunnel, cooler fluid is pushed down while the warmer fluid rise; locally a lower temperature tends to decrease the viscosity of the fluid and increase its volumic mass. It was observed that the activation of GHE’s enhances this phenomenon in their vicinity due to the temperature gradient that they produce. Moreover, GHE’s activation tends to increase the overall turbulence of the flow and thus the eddies’ formation. The locations of those disturbance are difficult to predict due to the fact that small disturbance may generate large vorticity within the flow. However, it is shown that after passing the GHE zone, the velocity profile tends to stabilize to the undisturbed case. The kinematic entry length seems to happen further down the stream in the case where GHE’s are activated. This is due to the temperature disturbance generated by GHE’s activation. This phenomenon is increased with respect to the number of GHE loops activated. Furthermore, some probing was performed in the vicinity of the heat exchanger to assess the thermal induce stress due to the heating operation. The recorded stress shows peaks at early stages due to the higher temperature gradient that is generated between the GHE’s and concrete at beginning. Finally, after some time, the temperature reaches a steady state hence the stabilized thermal response recorded.

2020We study the evolution of a system composed of N non-interacting particles of mass m distributed in a cylinder of length L. The cylinder is separated into two parts by an adiabatic piston of a mass M ≫ m. The length of the cylinder is a fix parameter and can be finite or infinite (in this case N is infinite). For the infinite case we carry out a perturbative analysis using Boltzmann's equation based on a development of the velocity distribution of the piston in function of a small dimensionless parameter ε = √(m/M). The non-stationary case is solved up to the order ε ;; our analysis shows that the system tends exponentially fast towards a stationary state where the piston has an average velocity V. The characteristic time scale for this relaxation is proportional to the mass of the piston (τ0 = M/A where A is the cross-section of the piston). We show that for equal pressures the collisions of the particles induce asymmetric fluctuations of the velocity of the piston which leads to a macroscopic movement of the piston in the direction of the higher temperature. In the case of the finite model a perturbative approach based on Liouville's equation (using the parameter α = 2m/(M + m)) shows that the evolution towards thermal equilibrium happens on two well separated time scales. The first relaxation step is a fast, deterministic and adiabatic evolution towards a state of mechanical equilibrium with approximately equal pressures but different temperatures. The movement of the piston is more or less damped. This damping qualitatively depends on whether the ratio R = Mgas/M between the total mass of the gas and the mass of the piston is small (R < 2) or large (R > 4). The second part of the evolution is much slower ; the typical time scales are proportional to the mass of the piston. There is a stochastic evolution including heat transfer leading to thermal equilibrium. A microscopic analysis yields the relation XM(t) = L(1/2 - ξ(at)) where the function ξ is independent of M. Using the hypothesis of homogeneity (i.e. the values of the densities, pressures and temperatures at the surface of the piston can be replaced by their respective average values) introduced in the previous analysis the observed damping does not show up. This can be explained by shock waves propagating between the piston and the walls at the extremities of the cylinder. In order to study the behaviour of the system there is hence a need to adequately describe the non-equilibrium fluids around the piston. We carry out an analysis of the infinite case, based on the perturbative approach introduced earlier. In this case the initial conditions are chosen in such a manner that the piston on average stays at the origin. It is shown that it is possible to describe the evolution of the fluids in such a way that it is coherent with the two laws of thermodynamics and the phenomenological relationships. Finally we study the case of a constant velocity of the piston in a finite cylinder. Such a condition and elastic collisions allow us to derive an explicit expression for the distribution of the fluids and hence for the hydrodynamics fields. This expression reveals the presence of shock waves between the piston and the extremities of the cylinder.