Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
| Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
| en:grundlagenhandbuch:symbole_und_formelzeichen [2025/05/15 09:28] – angelegt deppe2 | en:grundlagenhandbuch:symbole_und_formelzeichen [2026/01/28 11:18] (aktuell) – deppe2 | ||
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| Zeile 1: | Zeile 1: | ||
| ====== Nomenclature ====== | ====== Nomenclature ====== | ||
| - | | + | ===== Latin Symbols ===== |
| - | | + | |
| - | | + | ^ Symbol ^ Meaning ^ Symbol ^ Meaning ^ |
| - | | + | | $A,B,C$ | Coefficients of the Carreau Law | $S$ | Specific energy input | |
| + | | $A$ | Overall cross section of the screw channel | $S_{Ma}$ | Overall specific energy input of the entire machine | | ||
| + | | $A$ | Parameter for the temperature calculation in the melt film | $S_{Ve}$ | Specific energy input in the processing unit | | ||
| + | | $A_{1-4}$ | Area | $T$ | Temperature | | ||
| + | | $A_{1-4}$ | Variables for the calculation of the starting temperature profile | $T_{A,E}$ | Temperature at the beginning, end | | ||
| + | | $A_{\Delta}$ | Area of the triangular gap between kneading discs | $T_B,T_0$ | Reference temperature | | ||
| + | | $A_f$ | Filled cross section within a screw channel | $T_i$ | Mass temperature at the location i | | ||
| + | | $A_{fr}$ | Free cross section | $T_F$ | Solids temperature | | ||
| + | | $A_{Pr}$ | Cross section of the screw profile | $T_1$ | Reference temperature | | ||
| + | | $\overline{A_{zw}}$ | Average free surface in the intermeshing region | $T_{Fl}$ | Flow temperature | | ||
| + | | $A_{Zyl}$ | Cross sectional area of the barrel | $T_G$ | Glass transition temperature | | ||
| + | | $B$ | Variables for the calculation of the starting temperature profile | $T_K$ | Crystalline melt temperature | | ||
| + | | $C$ | Machine constant | $T_M, \overline{T}, | ||
| + | | $C_{x, | ||
| + | | $D$ | Inner barrel diameter | $T_S$ | Melt temperature | | ||
| + | | $D_F$ | Pressure screen value | $\overline{T_{Start}}$ | Average start temperature | | ||
| + | | $D_N$ | Nominal screw diameter | $T_Z$ | Barrel temperature | | ||
| + | | $D_S$ | Outer screw diameter | $T_{Z,1-5}$ | Barrel temperature at the location 1–5 | | ||
| + | | $E$ | Extensive material data | $U_{max}$ | Maximum wetted circumference ($s_R = 0$) | | ||
| + | | $F$ | Distribution function | $U_{min}$ | Minimum wetted circumference ($s_R = 0$) | | ||
| + | | $F$ | Factor | $\overline{U}$ | Average wetted circumference ($s_R = 0$) | | ||
| + | | $F$ | Screen area | $U(\Theta^*)$ | Wetted circumference dependent on $\Theta^*$ | | ||
| + | | $\Delta H$ | Difference of enthalpies | $\dot{V}$ | Volumetric flow rate | | ||
| + | | $K$ | Coefficient of the power law | $\dot{V}_{ei}$ | Volumetric flow rate in the intermeshing region | | ||
| + | | $K_{Spalt}$ | Coefficient of the power law in the clearance | $\dot{V}_{fr1, | ||
| + | | $K_{Kanal}$ | Coefficient of the power law in the channel | $\dot{V}_{Leck}$ | Volumetric leakage flow rate | | ||
| + | | $K_{0T}$ | Consistency | $\dot{V}_{Kanal}$ | Volumetric flow rate in the screw channel | | ||
| + | | $L$ | Axial length, screw length | $\dot{V}_p$ | Pressure flow | | ||
| + | | $L_{Ele}$ | Axial length of the pair of screw elements | $V_{real}$ | Realistic free volume | | ||
| + | | $L_{ei}$ | Axial length of the intermeshing region | $V_{theor}$ | Theoretical free volume | | ||
| + | | $L_{fr}$ | Axial length of the free channel section | $\dot{V}_S$ | Drag flow rate | | ||
| + | | $L_{Kn}$ | Overall axial length of the kneading blocks | $\dot{V}_{Steg}$ | Leakage flow rate | | ||
| + | | $L_R$ | Axial backpressure length | $\dot{V}_x$ | Volumetric flow rate in x-direction | | ||
| + | | $L_{Zw}$ | Axial length of the intermeshing area | $\dot{V}_z$ | Volumetric flow rate in z-direction | | ||
| + | | $M_{1,2}$ | Centerpoints | $V_{Zw}$ | Average volume of the intermeshing region | | ||
| + | | $M_D$ | Torque | $X$ | Concentration of the additive | | ||
| + | | $M_{D\%}$ | Proportional torque | $X$ | Width of the solid bed | | ||
| + | | $P$ | Power | $X$ | Ratio of element length and lead | | ||
| + | | $P_{1-3}$ | Power in the functional sections | $X_{1,2}$ | Width of the solid bed | | ||
| + | | $P_{1-4}, P_{M1-M4}$ | Points | $Y_1$ | Parameter of the pressure-throughput equation | | ||
| + | | $P_{Ma., | ||
| + | | $P_{Ve., | ||
| + | | | | $Z_{ei}$ | Unwound length of the intermeshing region | | ||
| + | | | | $Z_{fr}$ | Unwound length of the channel region | | ||
| + | | | | $Z,z$ | Cartesian coordinate (channel direction), length | | ||
| + | |||
| + | ^ Symbol ^ Meaning ^ Symbol ^ Meaning ^ | ||
| + | | $\alpha$ | Staggering angle of the kneading discs | $\pi_{p, | ||
| + | | $\beta$ | Temperature shift factor (Arrhenius law) | $\pi_{p, | ||
| + | | $\dot{\gamma}$ | Shear rate | $\pi_{p, | ||
| + | | $\dot{\gamma}_{min}$ | Minimum shear rate | $\pi^{\dot{V}}$ | Dimensionless flow rate | | ||
| + | | $\dot{\gamma}_{max}$ | Maximum shear rate | $\pi^{\dot{m}}$ | Dimensionless mass flow rate | | ||
| + | | $\overline{\delta}$ | Average thickness of the melt film | $\pi^{\dot{V}}_{Kanal}$ | Dimensionless flow rate in the screw channel | | ||
| + | | $d$ | Thickness of the melt film | $\pi^{\dot{V}}_x$ | Dimensionless flow rate in x-direction | | ||
| + | | $\overline{\delta_0}$ | Average initial thickness of the melt film | $\pi^{\dot{V}}_{Spalt}$ | Dimensionless flow rate in the radial clearance | | ||
| + | | $\delta_0$ | Initial thickness of the melt film | $\pi^{\dot{V}}_z$ | Dimensionless flow rate in z-direction | | ||
| + | | $\varepsilon$ | Accuracy | $\pi^{\dot{V}}_{Ele}$ | Dimensionless flow rate in a pair of screw elements | | ||
| + | | $z$ | Dimensionless z-coordinate | $\pi^{\dot{V}}_{ei}$ | Dimensionless flow rate in the intermeshing region | | ||
| + | | $\eta$ | Melt viscosity | $\pi^{\dot{V}}_{fr}$ | Dimensionless flow rate in the free channels | | ||
| + | | $\overline{\eta}$ | Average effectivity | $\rho_0$ | Density at reference temperature (melt regime) | | ||
| + | | $\eta_{Ge}$ | Effectivity of the gear box | $\rho_m$ | Slope of the density at reference temperature (melt regime) | | ||
| + | | $\eta_{Mo}$ | Effectivity of the motor | $\rho, \rho_S$ | Density, bulk density | | ||
| + | | $\Theta$ | Polar coordinates | $\rho_{Schütti}$ | Bulk density at the element i | | ||
| + | | $\overline{\Theta}$ | Average dimensionless residence time | $\sigma^2$ | Variance of the residence time distribution | | ||
| + | | $\Theta$ | Dimensionless residence time | $\sigma_M$ | Axial mixing coefficient | | ||
| + | | $\Theta$ | Dimensionless temperature | $\overline{\sigma_M}$ | Average axial mixing coefficient | | ||
| + | | $\Theta_0$ | Initial temperature | $\tau$ | Shear stress | | ||
| + | | $\Theta_1$ | Minimum dimensionless residence time | $\overline{\tau}$ | Average shear stress | | ||
| + | | $\Theta_B$ | Dimensionless width of the residence time distribution | $\overline{\tau_W}$ | Average wall shear stress | | ||
| + | | $\Theta_S$ | Self cleaning number | $\tau_{0x}$ | Wall shear stress in x-direction | | ||
| + | | $\lambda_0$ | Thermal conductivity at $T_0$ (melt regime) | $\tau_{0z}$ | Wall shear stress in z-direction | | ||
| + | | $\lambda_1$ | Slope of the linearized thermal conductivity | $\tau_{yi, | ||
| + | | $\lambda$ | Thermal conductivity | $\Phi,\phi$ | Flight angle | | ||
| + | | $\xi$ | Dimensionless coordinate in y-direction | $\Psi$ | Standardised melt film thickness | | ||
| + | | $\pi_{0,1}$ | Dimensionless number | $\omega$ | Angular velocity | | ||
| + | | $\pi_{geo}$ | Dimensionless geometrical number | $\Omega$ | Intermeshing angle | | ||
| + | | $\pi_p$ | Dimensionless pressure gradient | $\phi_{1A}, | ||
| + | | $\pi_{pKanal}$ | Dimensionless pressure gradient in the channel | $\varphi$ | Lead angle | | ||
| + | | $\pi_{px}$ | Dimensionless pressure gradient in x-direction | $\varphi_S$ | Lead angle at the outer screw diameter | | ||
| + | | $\pi_{pSpalt}$ | Dimensionless pressure gradient in the radial clearance | $\varphi_{S, | ||
| + | | $\pi_{pz}$ | Dimensionless pressure gradient in z-direction | $\overline{\Psi}$ | Standardised thickness of the melt film | | ||
| + | | $\pi_{p, | ||
| + | | | | $\Psi_S$ | To $\delta_0$ standardized radial clearance | | ||
| + | | | | $\Psi_{1, | ||
| + | |||
| + | |||
| + | ===== Dimensionless numbers ===== | ||
| + | |||
| + | ^ Symbol ^ Meaning ^ | ||
| + | | $Br$ | Brinkmann Number | | ||
| + | | $Gz$ | Graetz Number | | ||
| + | |||
| + | ===== Indices and Abbreviations ===== | ||
| + | |||
| + | ^ Symbol ^ Meaning ^ Symbol ^ Meaning ^ | ||
| + | | A, B, C | Corner points | ber. | Calculated | | ||
| + | | Ele | Element, pair of elements | ei. | Value in the intermeshing region | | ||
| + | | ESE | Single screw extruder | exp. | Experimentally determined | | ||
| + | | Kanal | Channel section | fr. | Value in the free channel section | | ||
| + | | Ma | Machine | i, j | Counter variable | | ||
| + | | Spalt | Radial clearance | min, max | Minimum, maximum | | ||
| + | | Ve | Processing unit | r., l. | Right, left | | ||
| + | | Zw | Intermeshing region | | | | ||
| + | |||