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Latin Symbols
Latin Symbols
| Symbol | Meaning |
|---|---|
| $A,B,C$ | Coefficients of the Carreau Law |
| $A$ | Overall cross section of the screw channel |
| $A$ | Parameter for the temperature calculation in the melt film |
| $A_{1-4}$ | Area |
| $A_{1-4}$ | Variables for the calculation of the starting temperature profile |
| $A_{\Delta}$ | Area of the triangular gap between kneading discs |
| $A_f$ | Filled cross section within a screw channel |
| $A_{fr}$ | Free cross section |
| $A_{Pr}$ | Cross section of the screw profile |
| $\overline{A_{zw}}$ | Average free surface in the intermeshing region |
| $A_{Zyl}$ | Cross sectional area of the barrel |
| $B$ | Variables for the calculation of the starting temperature profile |
| $C$ | Machine constant |
| $C_{x,z},C_{1,2,3}$ | Parameter for the calculation of the wall shear rate |
| $D$ | Inner barrel diameter |
| $D_F$ | Pressure screen value |
| $D_N$ | Nominal screw diameter |
| $D_S$ | Outer screw diameter |
| $E$ | Extensive material data |
| $F$ | Distribution function |
| $F$ | Factor |
| $F$ | Screen area |
| $\Delta H$ | Difference of enthalpies |
| $K$ | Coefficient of the power law |
| $K_{Spalt}$ | Coefficient of the power law in the clearance |
| $K_{Kanal}$ | Coefficient of the power law in the channel |
| $K_{0T}$ | Consistency |
| $L$ | Axial length, screw length |
| $L_{Ele}$ | Axial length of the pair of screw elements |
| $L_{ei}$ | Axial length of the intermeshing region |
| $L_{fr}$ | Axial length of the free channel section |
| $L_{Kn}$ | Overall axial length of the kneading blocks |
| $L_R$ | Axial backpressure length |
| $L_{Zw}$ | Axial length of the intermeshing area |
| $M_{1,2}$ | Centerpoints |
| $M_D$ | Torque |
| $M_{D\%}$ | Proportional torque |
| $P$ | Power |
| $P_{1-3}$ | Power in the functional sections |
| $P_{1-4}, P_{M1-M4}$ | Points |
| $P_{Ma.,exp.}$ | Experimentally determined machine power |
| $P_{Ve.,ber.}$ | Calculated power of the processing unit |
| $S$ | Specific energy input |
| $S_{Ma}$ | Overall specific energy input of the entire machine |
| $S_{Ve}$ | Specific energy input in the processing unit |
| $T$ | Temperature |
| $T_{A,E}$ | Temperature at the beginning, end |
| $T_B,T_0$ | Reference temperature |
| $T_i$ | Mass temperature at the location i |
| $T_F$ | Solids temperature |
| $T_1$ | Reference temperature |
| $T_{Fl}$ | Flow temperature |
| $T_G$ | Glass transition temperature |
| $T_K$ | Crystalline melt temperature |
| $T_M, \overline{T}, T$ | Mass temperature |
| $T_{M,0-5}$ | Mass temperature at the location 0-5 |
| $T_S$ | Melt temperature |
| $\overline{T_{Start}}$ | Average start temperature |
| $T_Z$ | Barrel temperature |
| $T_{Z,1-5}$ | Barrel temperature at the location 1-5 |
| $U_{max}$ | Maximum wetted circumference ($s_R = 0$) |
| $U_{min}$ | Minimum wetted circumference ($s_R = 0$) |
| $\overline{U}$ | Average wetted circumference ($s_R = 0$) |
| $U(\Theta^*)$ | Wetted circumference dependent on the screw position $\Theta^*$ ($s_R = 0$) |
| $\dot{V}$ | Volumetric flow rate |
| $\dot{V}_{ei}$ | Volumetric flow rate in the intermeshing region |
| $\dot{V}_{fr1,2}$ | Free volume |
| $\dot{V}_{Leck}$ | Volumetric leakage flow rate |
| $\dot{V}_{Kanal}$ | Volumetric flow rate in the screw channel |
| $\dot{V}_p$ | Pressure flow |
| $V_{real}$ | Realistic free volume |
| $V_{theor}$ | theoretical free volume |
| $\dot{V}_S$ | Drag flow rate |
| $\dot{V}_{Steg}$ | Leakage flow rate |
| $\dot{V}_x$ | Volumetric flow rate in x - direction |
| $\dot{V}_z$ | Volumetric flow rate in z – direction |
| $V_{Zw}$ | Average volume of the intermeshing region |
| $X$ | Concentration of the additive |
| $X$ | Width of the solid bed |
| $X$ | Ratio of element length and lead |
| $X_{1,2}$ | Width of the solid bed |
| $Y_1$ | Parameter of the pressure-throughput equation |
| $Y_2$ | Parameter of the pressure-throughput equation |
| $Z$ | Degree of Dispersion |
| $Z_{ei}$ | Unwound length of the intermeshing region |
| $Z_{fr}$ | Unwound length of the channel region |
| $Z,z$ | Cartesian coordinate (channel direction), length |
| $a$ | Centreline distance |
| $a_{1,2}$ | Constants |
| $a_T$ | Temperature shift factor |
| $b$ | Channel width |
| $\overline{b},b(f)$ | Average channel width |
| $b$ | Width of the residence time distribution |
| $b_i$ | Width of the screw channel in the section i |
| $b_{max}$ | Maximum channel width |
| $b_{SF}$ | Width of the melt film |
| $b_{Steg}$ | Length of the flight |
| $b_{SW}$ | Width of the melt pool |
| $\overline{c}$ | Average concentration |
| $c, c'$ | Constant for the melting calculation |
| $\Delta c_0$ | Change in concentration |
| $c_{1-4}$ | Parameters of the Weibull – distribution |
| $c_{1-3}$ | Constants of throughput equation |
| $c_p$ | Specific heat capacity at a constant pressure |
| $c_{p,0}$ | Specific heat capacity at 0°C |
| $c_{p,m}$ | Pitch of the linear regression of the specific heat capacity (melt regime) |
| $e$ | Width of the flights |
| $e_{max}$ | Maximum width of the flights |
| $f$ | Filling degree |
| $\overline{f}$ | Average filling degree of a pair of screw elements |
| $f$ | Probability density function |
| $f_i$ | Filling degree at the location i |
| $f_1$ | Dimensionless value for the throughput model |
| $f_{l,exp.}$ | Local filling degree, of the left screw (downstream view) |
| $f_{r,exp.}$ | Local filling degree, of the right screw (downstream view) |
| $f_{Korr}$ | Volume correction factor |
| $h$ | Channel height |
| $\overline{h},h(f)$ | Average, effective channel height |
| $h_i$ | Channel height at the location i |
| $h_{max}$ | Maximum channel height |
| $h(\Theta)$ | Channel depth in polar coordinates |
| $h(x)$ | Channel depth in Cartesian coordinates |
| $\Delta h_0$ | Difference of enthalpies at reference temperature $T_0$ |
| $\Delta h_l$ | Pitch of the linearised enthalpy difference (melt regime) |
| $\Delta h$ | Difference of enthalpies |
| $\Delta h_A$ | Melting enthalpy |
| $\Delta h_F$ | Solid enthalpy |
| $i$ | Counter variable |
| $i$ | Number of flights |
| $j$ | Counter variable |
| $j_\Delta$ | Number of triangular gaps in a kneading block |
| $j_{Kn,j}$ | Number of kneading discs |
| $k$ | Number of parallel channels in the channel model |
| $k_i$ | Number of parallel channels in the channel model for element i |
| $k_1, k_2$ | Constants |
| $m$ | Average shape factor for the intermeshing region |
| $m$ | Geometric value |
| $\dot{m}$ | Mass throughput |
| $\dot{m}_D$ | Mass throughput in the pressure screen |
| $m$ | Mass in the screw channels |
| $m_A$ | Mass in the screw channels in the melting regime |
| $m_F$ | Mass in the screw channels in the solids conveying regime |
| $m_S$ | Mass in the screw channels in the melt conveying regime |
| $n$ | Power law exponent |
| $n_{Spalt}$ | Power law exponent in the radial clearance |
| $n_{Kanal}$ | Power law exponent in the free channel section |
| $n_0$ | Screw speed |
| $p$ | Pressure |
| $p_D$ | Pressure in front of the screen pack |
| $p_i$ | Pressure at the location i |
| $p_{max}$ | Maximum radial pressure |
| $p_{1-5}$ | Pressure at the location 1-5 |
| $p_0$ | Zero pressure |
| $p_{0-4}$ | Pressure at the location 0-4 |
| $p_W$ | Die back pressure |
| $\Delta p_x$ | Pressure difference in x-direction |
| $p_x$ | Pressure gradient in x-direction |
| $s_F$ | Tip clearance |
| $s_R$ | Radial clearance |
| $s_{RKorr}$ | Corrected radial clearance |
| $s_W$ | Calander gap |
| $t$ | Lead |
| $t,t_M$ | Time, measuring time |
| $\overline{t}$ | Average residence time |
| $t_0$ | Dead time |
| $t_1$ | Minimum residence time |
| $t_{1i}$ | Minimum residence time in the element i |
| $u$ | Counter variable |
| $v$ | Velocity |
| $v$ | Specific volume |
| $v_{rel}$ | Relative velocity |
| $v_y$ | Velocity in y-direction |
| $v_0$ | Circumferential velocity of the screws |
| $v_{0x}$ | Circumferential velocity of the screws in x-direction |
| $v_{0z}$ | Circumferential velocity of the screws in z-direction |
| $v_{Fz}$ | Velocity of the solid bed |
| $\overline{v_{Fz}}$ | Average velocity of the solid bed |
| $v_j$ | Velocity of the screws in j-direction |
| $v_x$ | Velocity of the screws in x-direction |
| $v_z$ | Velocity of the screws in z-direction |
| $w$ | Distance between the points of inflection of the residence time distribution |
| $x$ | Cartesian coordinate orthogonal to the channel direction |
| $x_f$ | Position of the melt interface in the screw channel |
| $x_{pmax}$ | Maximum radial pressure |
| $y$ | Dimensionless solid bed width |
| $y_j$ | Averaged dimensionless solid bed width for the element j |
| $z_j$ | Length of the unwound channel for the element j |