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en:grundlagenhandbuch:entgasungsoberflaechenberechnung [2026/02/07 14:59] – deppe2en:grundlagenhandbuch:entgasungsoberflaechenberechnung [2026/08/03 13:36] (aktuell) – [Degassing efficiency of the process] paal
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 ====== Calculation of the degassing surface====== ====== Calculation of the degassing surface======
  
-==== Degassing Basic knowledge (Theory) ====+==== Material degradation and degassing ====
  
-Material degradation and degassing 
   * Thermal (oxidative, mechanical)   * Thermal (oxidative, mechanical)
   * Hydrolytic degradation   * Hydrolytic degradation
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 The calculations of the free surface and renewal time are based on the mathematical model of Schuler. The calculations of the free surface and renewal time are based on the mathematical model of Schuler.
  
-{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberlfaechenberechnung_002.png?nolink |}}+{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberflaechenberechnung_002.png?nolink |}}
  
 **Figure 2:** The left figure shows the formation of a melt pool in the screw channel and the right figure shows the position of the melt film in the screw channel. **Figure 2:** The left figure shows the formation of a melt pool in the screw channel and the right figure shows the position of the melt film in the screw channel.
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 The surface (2) is the result of the multiplication of the height and the development of the channel, taking into account that no melt pool is formed in the contact zone. The surface (2) is the result of the multiplication of the height and the development of the channel, taking into account that no melt pool is formed in the contact zone.
  
-$$A_{Pool} = 2 \frac{\pi - \alpha_E}{\pi} \cdot \frac{2hL}{\sin \varphi} \tag{2}$$+$$A_{Pool} = 2 \frac{\pi - \alpha_F}{\pi} \cdot \frac{2hL}{\sin \varphi} \tag{2}$$
  
 For the determination of the melt film, the difference of the shell surface of the eight-shaped housing (filled with melt) and comb surfaces of the screw is drawn up, thereby the surface of the film is determined (see equation 3). For the determination of the melt film, the difference of the shell surface of the eight-shaped housing (filled with melt) and comb surfaces of the screw is drawn up, thereby the surface of the film is determined (see equation 3).
  
-$$A_{Film} = 2 \frac{\pi - \alpha_E}{\pi} D_a \pi L \left(1 - \frac{2e}{t \cos \varphi}\right)(1 - \varepsilon) \tag{3}$$+$$A_{Film} = 2 \frac{\pi - \alpha_F}{\pi} D_a \pi L \left(1 - \frac{2e}{t \cos \varphi}\right)(1 - \varepsilon) \tag{3}$$
  
 The surface renewal time is calculated by using Equation (4). The surface renewal time is calculated by using Equation (4).
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 During the modification, it is assumed that the polymer is completely melted in the last third of the screw channel and there's a bubble-free layer flow. The essential difference is that here the height of the melt is present as a function of the filling degree, as shown in equation 5. During the modification, it is assumed that the polymer is completely melted in the last third of the screw channel and there's a bubble-free layer flow. The essential difference is that here the height of the melt is present as a function of the filling degree, as shown in equation 5.
  
-{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberlfaechenberechnung_003.png?nolink |}}+{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberflaechenberechnung_003.png?nolink |}}
  
 **Figure 3** shows that the channel is divided into three sections. The grey area is the product of the pool. **Figure 3** shows that the channel is divided into three sections. The grey area is the product of the pool.
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 On the basis of the course of the analytical and approximated solution it becomes clear that in the required interval [e/2; B/2], the solution is sufficiently precise, see Figure 4. The irregularity appears only outside the boundary. On the basis of the course of the analytical and approximated solution it becomes clear that in the required interval [e/2; B/2], the solution is sufficiently precise, see Figure 4. The irregularity appears only outside the boundary.
  
-{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberlfaechenberechnung_004.png?nolink |}}+{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberflaechenberechnung_004.png?nolink |}}
  
 **Figure 4:** Comparison of the analytical and approximated solution **Figure 4:** Comparison of the analytical and approximated solution
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 It is clear from Figure 6 that the theoretical calculation is based on the degree of filling. The filling level includes the current operating parameters of the extruder. This basic knowledge makes it possible to determine the channel height on the basis of the approximation equation with the necessary X-coordinate of the melt in equation 7. It is clear from Figure 6 that the theoretical calculation is based on the degree of filling. The filling level includes the current operating parameters of the extruder. This basic knowledge makes it possible to determine the channel height on the basis of the approximation equation with the necessary X-coordinate of the melt in equation 7.
  
-{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberlfaechenberechnung_005.png?nolink |}}+{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberflaechenberechnung_005.png?nolink |}}
  
 **Figure 5:** Methodology for determining the renewal of surfaces on the basis of theoretical foundations **Figure 5:** Methodology for determining the renewal of surfaces on the basis of theoretical foundations
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 Figure 6 shows the schematic sequence of the surface calculation for implementation in SIGMA. Figure 6 shows the schematic sequence of the surface calculation for implementation in SIGMA.
  
-{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberlfaechenberechnung_006.png?nolink |}}+{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_entgasungsoberflaechenberechnung_006.png?nolink |}}
  
 **Figure 6:** Implementation of the surface renewal time and free surface calculation in SIGMA **Figure 6:** Implementation of the surface renewal time and free surface calculation in SIGMA
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 ===== Degassing efficiency of the process ===== ===== Degassing efficiency of the process =====
  
-The degassing efficiency is evaluated with the degassing reference parameter of Schuler (Equation 1. In this case taken place the determination for wetting and non-wetting polymer.+The degassing performance can be calculated using the following equation:
  
-$$\frac{c_{Start} - c_{End}}{c_{Start} - c_{Gleichgewicht}} = \frac{\left(\frac{A_{POOL}}{t_{POOL}} + \frac{A_{FILM}}{t_{FILM}} + \frac{A_{GRUND}}{t_{GRUND}}\right)}{\dot{m}} \tag{Equation 1}$$+$$\eta^* = \frac{c_{Start} - c_{End}}{c_{Start} - c_{Equilibrium}} = 2\rho\sqrt{ \frac{ D }{ \pi } } \frac{\left(\frac{A_{POOL}}{\sqrt{t_{POOL}}} + \frac{A_{FILM}}{\sqrt{t_{FILM}}} + \frac{A_{GROUND}}{\sqrt{t_{GROUND}}}\right)}{\dot{m}} \tag{8}$$
  
 After transposing of the equation can be the end concentration of low molecular component determined. Thereby is it possible to take a statement about the degassing efficiency. After transposing of the equation can be the end concentration of low molecular component determined. Thereby is it possible to take a statement about the degassing efficiency.
 +The degassing efficiency is evaluated with the degassing reference parameter of Schuler (Equation 9). 
  
-For wetting polymer is the Equation 2and for non-wetting polymer is the Equation 3 used.+$$\frac{c_{Start} - c_{End}}{c_{Start} - c_{Equilibrium}} \sim \frac{\left(\frac{A_{POOL}}{\sqrt{t_{POOL}}} + \frac{A_{FILM}}{\sqrt{t_{FILM}}} + \frac{A_{GROUND}}{\sqrt{t_{GROUND}}}\right)}{\dot{m}} \tag{9}$$
  
-$$EK_{Benetzend} = \frac{\left(\frac{A_{POOL}}{t_{POOL}} + \frac{A_{FILM}}{t_{FILM}} + \frac{A_{GRUND}}{t_{GRUND}}\right)}{\dot{m}} \tag{Equation 2}$$+In this case taken place the determination for wetting and non-wetting polymer. For wetting polymer is the Equation 10 and for non-wetting polymer is the Equation 11 used.
  
-$$EK_{Nicht-Benetzend} = \frac{\left(\frac{A_{POOL}}{t_{POOL}} + \frac{A_{FILM}}{t_{FILM}}\right)}{\dot{m}} \tag{Equation 3}$$+$$EK_{Wetting} = \frac{\left(\frac{A_{POOL}}{\sqrt{t_{POOL}}} + \frac{A_{FILM}}{\sqrt{t_{FILM}}} + \frac{A_{GROUND}}{\sqrt{t_{GROUND}}}\right)}{\dot{m}} \tag{10}$$ 
 + 
 +$$EK_{Non-Wetting} = \frac{\left(\frac{A_{POOL}}{\sqrt{t_{POOL}}} + \frac{A_{FILM}}{\sqrt{t_{FILM}}}\right)}{\dot{m}} \tag{11}$$
  
 The difference between both equation is that the surface area und renewal time at screw root is neglected, because in non-wetting case are not melt at screw root available. The difference between both equation is that the surface area und renewal time at screw root is neglected, because in non-wetting case are not melt at screw root available.