A Primary Agent Due to Engineering Creation… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Force System Generated/Needed by Viscous Fluid Flows

Conservation Momentum for A CV

The Body Forces on A Fluid Flow The body forces refer to long-ranged forces such as gravity or that arising from an electromagnetic field, and so on. Such forces, as the name implies, vary slowly with the distance between interacting elements. For instance, the gravitational force per unit mass acting on any object is very well represented by the constant vector g (|g| = 9.8m/s 2 ) for distances from the earth’s surface that are less than the order of the earth’s radius ( 6.4 ×10 6 m). A consequence of this slow variation is that such forces act equally on all the matter within an infinitesimal element of fluid continuum. Thus, long-ranged forces manifest as body forces.

Extensive Nature of Body Forces Assuming the body force per unit mass at a point x in the fluid, and at time t, to be F(x, t). The total force on an infinitesimal element around this point with volume dV is given by ρF(x, t)dV. ρF is now the force per unit volume. For gravity, this force is simply the weight of the element, ρgdV. For a conducting fluid in an magnetic field (B), the Lorentz force: F L  i×B i is the current density.

The System of Body Forces in Fluid Flows Gravitational Forces Magnetic Forces (Magneto Hydrodynamic) –Lorentz force Electrical forces. –Coulomb force –Dielectric force –Electrostriction

Ideal Flows Driven by Gravitational Force

Magneto Hydrodynamics Magneto-fluid dynamics Fluid Dynamics of electrically-conducting fluids and their interactions with magnetic fields. Interaction Magnetic field, Electric field and Plasma flow Magnetic Field flow produce Electric field. Interacting Magnetic& Electrical fields produce Flow Lorentz Force

Important aspects of MDH 1. Accelerate fluids through Lorentz force, which refers to MHD accelerators. 2. Convert the kinetic energy of a fluid and its enthalpy into electric energy. 3. This refers to MHD generators.

Turbo Generator Vs MHD Generator

Principle of Operation The underlying principle of MHD power generation is elegantly simple. An electrically conducting fluid is driven by a primary energy source (e.g., combustion of coal or a gas) through a magnetic field. This results in the establishment of an electromotive force within the conductor in accordance with the principle established by Faraday. If the conductor is an electrically conducting gas, it will expand, and so the MHD system constitutes a heat engine involving an expansion from high to low pressure in a manner similar to that of a gas turbine.

The gas turbine operates through the gas interaction with the surfaces of a rotating blade system. The MHD system, however, involves a volume interaction between a gas and the magnetic field through which it is passing. It is a system that depends on volume rather than surface interaction.

General Characteristics The MHD generator can properly be viewed as an electromagnetic turbine. Output is obtained from the conducting gas-magnetic field interaction directly in electrical form rather than in mechanical form. Electrical conduction in gases occurs when electrons are available to be organized into an electric current in response to an applied or induced electric field. The electrons may be either injected or generated internally, and, because of the electrostatic forces involved, they require the presence of corresponding positive charge from ions to maintain electrical neutrality.

An electrically conducting gas consists in general of electrons, ions to balance the electric charge, and neutral atoms or molecules. Such a gas is termed a plasma.

Principle of MHD Generator

Principle of MHD Accelerator

Development of Micro Pumps

Superiority of The Lorenz Force Simple Structure Only MHD channel (electrodes, insulator) and Magnet High Power density ---- high electric field, current density Compact machine Small output applications High temperature operation ---- looking for suitable material No turbine, and no rotating machine Ceramic material can be used No moving parts No turbine and no rotating generator Good for space applications

Electro Static Forces Principles of Electrostatic Precipitator Supplying high voltage between the Collecting Electrode and Discharge Electrode generates a Corona Discharge that produces minus ions.

The electrically charged dusts are attracted towards the Collecting Electrodes by an electrostatic force

The accumulated dusts, due to the impact strength of hammer rapping to the Collecting Electrodes, are dropped and collected in the hopper.

Electro Static Forces

The Surface Forces on A Fluid Flow The Surface forces are characterized by length scales relevant to the microscopic dynamics. This would mean that such forces decay extremely rapidly with distance on the macroscopic scale. The short-ranged forces will decay on distances of the order of a mean free path. Any infinitesimal element in a continuum description is, by definition, must be much larger than all microscopic scales. The effect of such forces would be negligible unless two interacting elements are directly in contact. These forces are expected to act across the contact surface. In other words, the short-ranged forces manifest as surface forces, in a continuum description.

Flux Nature of Surface Forces The surface forces act to transport momentum across the boundaries of an infinitesimal element. In dilute gases, the momentum transport occurs due to molecules randomly crossing the boundary. Carry momentum across in the appropriate direction. Often referred to as the kinetic contribution to the stress. In liquids, the transport of momentum can occur without physical translation of molecules via short-ranged forces acting between pairs of molecules on either side of the boundary. Separated by a distance comparable to the range of the inter- molecular potential. Considered as the potential contribution to the stress. Clearly, the total effect of short-ranged forces acting on a differential element is decided by its surface area rather than the volume.

A surface force acting on a surface element,  is the force per unit area.

The System of Surface Forces in Fluid Flows Mechanical forces. Electro-kinetic forces. Electroosomosic Forces Electrophoresic Forces

Surface Forces The Second term on the right-hand side of above equation represents the resultant surface force acting on the entire control surface. It can be written as the integral of a scalar product of the normal unit vector with the total stress tensor acting on the surface element ds: The product of the normal vector and the stress tensor gives a stress vector which can be decomposed into a normal and a shear stress force.

Components of Forces n is the normal unit vector that points away from the surface. t is the tangential unit vector. The negative signs of n and t have been chosen to indicate that the pressure p and the shear stress  are exerted by the surroundings on the surface S. Thus, the surface force acting on a differential surface is:

Dealing with Surface Forces In above equation, the integration must be carried out over the entire control surface. Fora control surface consisting of inlet, exit, and wall surfaces, the second integral on the left-hand side gives: