7.6. Nomenclature
Symbol |
Definition |
Units |
|---|---|---|
\(a\) |
Constant \(\left( 9.325 \times 10^{-2} \right)\) |
|
\(a_{0}, a_{1}, a_{2}, a_{3}\) |
Momentum equation coefficients |
|
\(A\) |
Flow area |
\(m^{2}\) |
\(b\) |
Constant \(\left( 2.356 \times 10^{-4} \right)\) |
|
\(B\) |
Valve damping coefficient |
\(kg - m / s\) |
\(c, c_{p}\) |
Specific heat |
\(J / kg - K\) |
\(c_{b}\) |
Bucket coefficient |
|
\(c_{n}\) |
Nozzle velocity coefficient |
|
\(c_{r}\) |
Reaction coefficient |
|
\(C\) |
Valve calibration constant |
\(m^{2}\) |
\(CF\) |
Calibration factor |
|
\(CV\) |
Elevation of heater center |
\(m\) |
\(C_{1},\ C_{2},\ C_{3},\ C_{4}\) |
Coefficients in the expression for the Moody friction factor (\(C_{1}=0.0055\), \(C_{2}=20000\), \(C_{3}=106\), and \(C_{4}=1/3\)) |
|
\(D_{h},\ D_{H}\) |
Hydraulic diameter |
\(m\) |
\(\widehat{E}\) |
Total energy |
\(J / kg\) |
\(f_{l}\) |
Liquid friction factor |
|
\(f_{tp}\) |
Two-phase friction factor |
|
\(F\) |
Force |
\(N\) |
\(F\) |
Heat flux |
\(W / m^{2}\) |
\(F\) |
Pressure loss coefficient |
|
\(FL\) |
Fouling resistance |
\(m^{2} - K / W\) |
\(FR\) |
Friction calibration coefficient |
|
\(F_{1}\) |
Valve driving function |
\(kg - m / s^{2}\) |
\(g\) |
Gravitational constant |
\(m / s^{2}\) |
\(G\) |
Mass flux |
\(kg / m^{2} - s\) |
\(G_{2}\) |
Orifice coefficient |
|
\(h\) |
Specific enthalpy |
\(J / kg\) |
\(hp\) |
Primary side heat transfer coefficient in the simple heater model |
\(W / m^{2} - K\) |
\(h_{tot}, H\) |
Total heat transfer coefficient |
\(W / m^{2} - K\) |
\(H\) |
Height |
\(m\) |
\(H\) |
Work |
\(W\) |
\(I\) |
Moment of inertia |
\(kg - m^{2}\) |
\(j\) |
Lowermost node in a region |
|
\(k\) |
Thermal conductivity |
\(W / m - K\) |
\(k\) |
Valve spring constant |
\(kg / s^{2}\) |
\(k_{p}\) |
Thermal conductivity of the primary side in the simple heater model |
\(W / m - K\) |
\(K\) |
Loss constant |
|
\(L\) |
Element length, or distance |
\(m\) |
\(L_{B} / D_{B}\) |
Effective length-to-diameter ratio per bend |
|
\(m, M\) |
Mass |
\(kg\) |
\(n\) |
Index on the discretized time variable |
|
\(n\) |
Number of nodes in a region |
|
\(N_{B}\) |
Number of bends along a flow path |
|
\(Nu\) |
Nusselt number |
|
\(P,\ P^{*}\) |
Pressure |
\(Pa\) |
\(POD\) |
Pitch-to-diameter ratio |
|
\(Pr\) |
Prandtl number |
|
\(q\) |
Heat flux |
\(J / s - m^{2}\) |
\(Q\) |
Heat source |
\(J / s\) |
\(Q\) |
Volumetric heat source |
\(W / m^{3}\) |
\(Q\) |
Energy transfer rate |
\(W\) |
\(r\) |
Radius |
\(m\) |
\(r_{5}\) |
Two-phase multiplier |
|
\(R\) |
Thermal resistance |
\(K / W\) |
\(R\) |
Loss factor |
|
\(Re\) |
Reynolds number |
|
\(s\) |
Distance |
\(m\) |
\(s\) |
Specific entropy |
\(J / kg - K\) |
\(sgn \left( j, l \right)\) |
+1 if the steady state flow in segment \(j\) is entering volume \(l\) -1 if the steady state flow in segment \(j\) is leaving volume \(l\) |
|
\(t\) |
Time |
\(s\) |
\(T\) |
Temperature |
\(K\) |
\(TP\) |
Elevation of two-phase interface |
\(m\) |
\(u, v\) |
Fluid velocity |
\(m / s\) |
\(U_{pseu}\) |
Pseudo-heat conduction coefficient |
\(W / K\) |
\(v\) |
Specific volume |
\(m^{3} / kg\) |
\(V\) |
Volume |
\(m^{3}\) |
\(V_{a},V_{b}\) |
Steam velocities relative to the blade and parallel to the blade motion at the blade entrance and exit, respectively |
\(m / s\) |
\(V_{1}\) |
Absolute steam velocity at the blade entrance |
\(m / s\) |
\(V_{2}\) |
Steam velocity relative to the blade at the blade entrance |
\(m / s\) |
\(V_{3}\) |
Steam velocity relative to the blade at the blade exit |
\(m / s\) |
\(V_{4}\) |
Absolute steam velocity at the blade exit |
\(m / s\) |
\(w\) |
Mass flow rate |
\(kg / s\) |
\(WR\) |
Wall resistance on water side |
|
\(WRNA\) |
Wall resistance on sodium side |
|
\(x\) |
Quality |
|
\(y\) |
Valve stem position |
\(m\) |
\(z\) |
Spatial variable |
\(m\) |
\(Z\) |
Spatial location, region length, or elevation of pipe center |
\(m\) |
\(\Delta z\) |
\(z_{0} - \ z_{I}\), the elevation difference between the outlet and the inlet of a flow element |
\(m\) |
\(\alpha\) |
Void fraction |
|
\(\alpha\) |
Nozzle exit angle |
\(rad\) |
\(\beta\) |
Volumetric quality |
|
\(\gamma\) |
Blade exit angle |
\(rad\) |
\(\delta\) |
Thickness |
\(m\) |
\(\varepsilon\) |
Element roughness |
\(m\) |
\(\eta\) |
Efficiency |
|
\(\theta\) |
Angle of inclination with respect to the vertical |
|
\(\mu\) |
Dynamic viscosity |
\(Pa - s\) |
\(v\) |
Specific volume |
\(m^{3} / kg\) |
\(\rho\) |
Density |
\(kg / m^{3}\) |
\(\tau\) |
Viscous stress tensor |
\(Pa\) |
\(\tau\) |
Torque |
\(N - m\) |
\(\varphi\) |
Valve characteristic |
|
\(\chi\) |
Quality |
|
\(\omega\) |
Rotor angular velocity |
\(rad / s\) |
Subscripts |
||
\(ACC\) |
Accumulated pressure at which value fully opens |
|
\(b\) |
Bottom |
|
\(B\) |
Blade |
|
\(BLD\) |
Blowdown pressure at which valve closes |
|
\(D\) |
Drain, or DNB |
|
\(E\) |
Exhaust |
|
\(f\) |
Liquid |
|
\(fg\) |
Vapor minus liquid |
|
\(g\) |
Vapor |
|
\(G\) |
Generator |
|
\(hf\) |
Location of hf |
|
\(hg\) |
Location of hg |
|
\(i\) |
Node number, region number, inside |
|
\(I, in\) |
Inlet |
|
\(j\) |
Segment number |
|
\(m\) |
Metal tube, or tube wall |
|
\(misc\) |
Miscellaneous |
|
\(M\) |
Moisture, or mid-wall |
|
\(nz\) |
Nozzle |
|
\(Na\) |
Sodium |
|
\(o\) |
Outside, theoretical |
|
\(O,out\) |
Outlet |
|
\(r\) |
Reference |
|
\(R\) |
Rotation |
|
\(s\) |
Sodium, shell side, steam drum |
|
\(S\) |
Surface |
|
\(sat\) |
Saturation |
|
\(SC\) |
Subcooled zone |
|
\(SG\) |
Steam generator |
|
\(SH\) |
Superheated zone |
|
\(t\) |
Top, tube side, total |
|
\(T\) |
Total, turbine |
|
\(TP\) |
Boiling zone |
|
\(u\) |
Upper |
|
\(w\) |
Water |
|
\(l\) |
Volume number |
|
\(\infty\) |
Ambient |
|
Superscripts |
||
\(k,n\) |
Time step index |
|
\(n\) |
Normalized |
|
\(u\) |
Unnormalized |
|
\(-\) |
Isentropic quantity |