Superficial velocity (or superficial flow velocity), in engineering of multiphase flows and flows in porous media, is a hypothetical (artificial) flow velocity calculated as if the given phase or fluid were the only one flowing or present in a given cross sectional area. Other phases, particles, the skeleton of the porous medium, etc. present in the channel are disregarded.
In fluid mechanics, multiphase flow is simultaneous flow of (a) materials with different states or phases, or (b) materials with different chemical properties but in the same state or phase.
In continuum mechanics the macroscopic velocity, also flow velocity in fluid dynamics or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar. It is also called velocity field; when evaluated along a line, it is called a velocity profile.
In the physical sciences, a phase is a region of space, throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase.
Superficial velocity is used in many engineering equations because it is the value which is usually readily known and unambiguous, whereas real velocity is often variable from place to place, its mean not readily available in complex flow systems, and subject to assumptions.
Superficial velocity can be expressed as:
where:
- us - superficial velocity of a given phase, m/s
- Q - volume flow rate of the phase, m3/s
- A - cross sectional area, m2
Using the concept of porosity, the dependence between the advection velocity and the superficial velocity can be expressed as (for one-dimensional flow):
Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure the "accessible void", the total amount of void space accessible from the surface. There are many ways to test porosity in a substance or part, such as industrial CT scanning. The term porosity is used in multiple fields including pharmaceutics, ceramics, metallurgy, materials, manufacturing, hydrology, earth sciences, soil mechanics and engineering.
In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion. The properties of that substance are carried with it. Generally the majority of the advected substance is a fluid. The properties that are carried with the advected substance are conserved properties such as energy. An example of advection is the transport of pollutants or silt in a river by bulk water flow downstream. Another commonly advected quantity is energy or enthalpy. Here the fluid may be any material that contains thermal energy, such as water or air. In general, any substance or conserved, extensive quantity can be advected by a fluid that can hold or contain the quantity or substance.
where:
is porosity, dimensionless- u is the average fluid velocity (excluding the other phase, solids, etc.), m/s.
The local physical velocity can still be different than the average fluid velocity because the vector of the local fluid flow does not have to be parallel to that of average flow. Also, there may be local constriction in the flow channel.
In fluid dynamics, potential flow describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero.
Flow measurement is the quantification of bulk fluid movement. Flow can be measured in a variety of ways. The common types of flowmeters that find industrial application can be listed as below:
a) Obstruction type(differential pressure or variable area)
b) Inferential(turbine type)
c)electromagnetic
d)Positive-displacement flow meters accumulate a fixed volume of fluid and then count the number of times the volume is filled to measure flow.
e)fluid dynamic(vortex shedding)
f)Anemometer
g)Ultrasonic
H)Mass flowmeter(Coriolis).
A shear stress, often denoted by τ, is the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section of the material. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts.
Permeability in fluid mechanics and the earth sciences is a measure of the ability of a porous material to allow fluids to pass through it.
Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences.
In hydrology, discharge is the volumetric flow rate of water that is transported through a given cross-sectional area. It includes any suspended solids (e.g. sediment), dissolved chemicals (e.g. CaCO3(aq)), or biologic material (e.g. diatoms) in addition to the water itself.
In fluid dynamics, the Buckley–Leverett equation is a conservation equation used to model two-phase flow in porous media. The Buckley–Leverett equation or the Buckley–Leverett displacement describes an immiscible displacement process, such as the displacement of oil by water, in a one-dimensional or quasi-one-dimensional reservoir. This equation can be derived from the mass conservation equations of two-phase flow, under the assumptions listed below.
In petroleum engineering, the Leverett J-function is a dimensionless function of water saturation describing the capillary pressure,
In physics and engineering, mass flux is the rate of mass flow per unit area, perfectly overlapping with the momentum density, the momentum per unit volume. The common symbols are j, J, q, Q, φ, or Φ, sometimes with subscript m to indicate mass is the flowing quantity. Its SI units are kg s−1 m−2. Mass flux can also refer to an alternate form of flux in Fick's law that includes the molecular mass, or in Darcy's law that includes the mass density.
HydroGeoSphere (HGS) is a 3D control-volume finite element groundwater model, and is based on a rigorous conceptualization of the hydrologic system consisting of surface and subsurface flow regimes. The model is designed to take into account all key components of the hydrologic cycle. For each time step, the model solves surface and subsurface flow, solute and energy transport equations simultaneously, and provides a complete water and solute balance.
Sonic logging is a well logging tool that provides a formation’s interval transit time, designated as
, which is a measure of a formation’s capacity to transmit seismic waves. Geologically, this capacity varies with lithology and rock textures, most notably decreasing with an increasing effective porosity. This means that a sonic log can be used to calculate the porosity of a formation if the seismic velocity of the rock matrix,
, and pore fluid,
, are known, which is very useful for hydrocarbon exploration.
The Kozeny–Carman equation is a relation used in the field of fluid dynamics to calculate the pressure drop of a fluid flowing through a packed bed of solids. It is named after Josef Kozeny and Philip C. Carman. The equation is only valid for laminar flow. The equation was derived by Kozeny (1927) and Carman from a starting point of (a) modelling fluid flow in a packed bed as laminar fluid flow in a collection of curving passages/tubes crossing the packed bed and (b) Poiseuille's law describing laminar fluid flow in straight, circular section pipes.
In fluid dynamics, aerodynamic potential flow codes or panel codes are used to determine the fluid velocity, and subsequently the pressure distribution, on an object. This may be a simple two-dimensional object, such as a circle or wing, or it may be a three-dimensional vehicle.
The Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow. These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow, and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full size version. The predictions of the onset of turbulence and the ability to calculate scaling effects can be used to help predict fluid behaviour on a larger scale, such as in local or global air or water movement and thereby the associated meteorological and climatological effects.
The multiphase particle-in-cell method (MP-PIC) is a numerical method for modeling particle-fluid and particle-particle interactions in a computational fluid dynamics (CFD) calculation. The MP-PIC method achieves greater stability than its particle-in-cell predecessor by simultaneously treating the solid particles as computational particles and as a continuum. In the MP-PIC approach, the particle properties are mapped from the Lagrangian coordinates to an Eulerian grid through the use of interpolation functions. After evaluation of the continuum derivative terms, the particle properties are mapped back to the individual particles. This method has proven to be stable in dense particle flows, computationally efficient, and physically accurate. This has allowed the MP-PIC method to be used as particle-flow solver for the simulation of industrial-scale chemical processes involving particle-fluid flows.
In fluid mechanics, fluid flow through porous media is the manner in which fluids behave when flowing through a porous medium, for example sponge or wood, or when filtering water using sand or another porous material. As commonly observed, some fluid flows through the media while some mass of the fluid is stored in the pores present in the media.
Phase contrast magnetic resonance imaging (PC-MRI) is a specific type of magnetic resonance imaging used primarily to determine flow velocities. PC-MRI can be considered a method of Magnetic Resonance Velocimetry. It also provides a method of magnetic resonance angiography. Since modern PC-MRI is typically time-resolved, it provides a means of 4D imaging.
The removal of heat from nuclear reactors is an essential step in the generation of energy from nuclear reactions. In nuclear engineering there are a number of empirical or semi-empirical relations used for quantifying the process of removing heat from a nuclear reactor core so that the reactor operates in the projected temperature interval that depends on the materials used in the construction of the reactor. The effectiveness of removal of heat from the reactor core depends on many factors, including the cooling agents used and the type of reactor. Common coolers for nuclear reactors include: heavy water, the first alkaline metals, lead or lead-based alloys, and
.