Core variable

Pressure and body force adjustment Varying pressure and G (centrifuge) simultaneously allows consideration of all core variables except blackbody radiation. 

Adjustment of composition and temperature of ambient atmosphere Varying pressure and temperature could permit scaling of all core variables except absorptive radiation. 

Adjust pressure, temperature and body force All core variables satisfied, but maximum LSR variation probably limited to about 10. The conclusion must be that satisfactory physical model scaling of all aspects of mass fires is not likely. 

In terms of the boundary-layer variable Y, the outer edge of the boundary-layer corresponds to a very large value of Y, but, as we can see from (4-167), this corresponds to an arbitrarily small value of the core variable y. The symbolic representation for matching is the double-ended arrow <=>. This is intended to distinguish it from a numerical equal sign. 

In considering the matching condition (5-211) it is necessary to either express the core solution in terms of the boundary-layer variables or else express the boundary-layer solution in terms of the core variables. Because both approximations to the solution are valid in the region of overlap where the matching condition applies, either choice is acceptable. However, for present purposes, it is more convenient to introduce the boundary-layer variables into the core solution. 

By the Buckingham theorem, there will be three dimensionless groups. With DAB, L, and p as the core variables, the three pi groups to be formed are... 

L, of the tube. Use the Buckingham method to determine the dimensionless groups to be formed from the variables significant to this problem. Choose Dab, d, and p as core variables. 

We will select D, v, and p to be the core variables common to all three groups. Then the three dimensionless groups are... 

For each O group one must choose a core variable. ... 

A core variable is a parameter that appears in only one U group. It forms the core of a dimensionless group. Because our goal is to find a function in terms of dimensionless groups, such as... 

We now derive the two U groups, which we will designate Hi and 02. Hi will have velocity as its core variable and 02 will have stride length as its core variable. 

We have six unknowns (a to /) and three equations. We thus have 6 — 3 = 3H groups. To solve Eqs. (5.47)-(5.49) we must fix three of the unknowns, which we do by selecting three core variables. What do the guidelines suggest for core variables ... 

The traditional core variables for the terminal velocity of a sphere are (psph—Pfluid), g, and p.. We now use these to derive the If groups. 

Before proceeding, let s consider the effect of choosing different core variables. What would be the result of choosing the obvious candidates for core variables (Psph — Pfluid) and /X If we use an exponent of 1 for each core variable one obtains, for 111,... 

Step 5. Choose three core variables, one for each fl group ... 

As foretold earlier in this chapter, there are rules for a valid set of core variables. 

Rule 1, All dimensions of the system must be represented in the core variables. 

Rule 2. The core variables must not form a dimensionless group. 

There are many valid choices for the three core variables. However, the standard dimensionless groups used to describe a gas are... 

Three dimensionless groups were derived to describe fluid flow through a pipe. Core variables AP, /, and /x were chosen and we obtained the Euler number, the reduced length, and the Reynolds number. 

A) Derive the dimensionless groups that correspond to the core variables v, p, and /. 

D) Derive an expression for the Lewis number using k as the core variable. 

Upon arranging the exponents of the three key dimensions (mass, time, length) into algebraic equations and choosing the height h and 2out as core variables we derive two dimensionless groups ... 

The effluent has the same composition and temperature as the vessel s contents. Although more accurately called a continuous flow stirred-tank reactor, this terminology is less common, core variable a variable that appears in exactly one dimensionless group describing some phenomenon, derived unit a unit created by the product of the base units. The joule, a unit of energy in the mks SI system, is the product of kg, m, and s 1 joule = 1 kg-m /s. ... 

Nevertheless, preliminary studies show there are no major limitations on the RBEC-M reactor operation in any closed fuel cycle, including the on-site fuel cycle. Reactor parameters necessary for safety and other aspects can be provided by a sufficiently flexible set of reactor core variables. 

An integral primary system layout is employed (Fig. 12.4), ie, reactor core, variable frequency submersible coolant pumps, intermediate heat exchanges, safety system heat exchangers, and cold trap filters. The reactor vessel is enclosed in a guard vessel. There are no auxiliary sodium systems in the primary circuit. The reactor core consists of fuel assemblies, boron shield assemblies, and absorber rods. The central part of the core consists of wrap-spaced hexagonal fuel assemblies and cells with absorber rods. The spent fuel is stored in the reactor vessel for up to 2 years, which facilitates spent fuel cooling and eliminates the need for spent fuel storage casks. Assemblies with boron carbide are placed behind the spent fuel to protect the reactor vessel. 

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