# Measurement of Instantaneous Mass Flow Rate of Polypropylene Gasification Products in Airflow
## 3 Data Processing Procedure
### Mass Flow Rate of Gasification Products  
An important step in the data processing technique under consideration is the determination of the mass of PP sample before (\(W_{1}\)) and after (\(W_{2}\)) test fire. The difference between \(W_{1}\) and \(W_{2}\), (\(W_{1}-W_{2}\)), determines the amount of sample material converted to gas, which flows out of the GG in the form of gasification products. The comparison of gas mass flow rates at GG inlet and outlet with the change in the sample total mass allows writing a mass balance equation in the following form:  
\[W_{1}-W_{2}=\varphi\int\limits_{t1}^{t2}(\mu_{2}A_{2}{{}^{*}}\frac{P_{\text{ out}}(\tau)}{\sqrt{T_{\text{out}}(\tau)}}-G_{\text{in}}(\tau))d\tau \tag{5}\]  
Here, the lower integration limit (\(t_{1}\)) corresponds to the beginning of air temperature rise when the igniter is triggered, and the upper one (\(t_{2}\)) corresponds to the shutdown of air supply; and \(\varphi\) stands for discrepancy between two methods of determining the decrease in sample total mass: by weighing (left-hand side of Equation (5)) and by integrating the mass flow rates \(G_{\text{out}}(t)\) and \(G_{\text{in}}(t)\) (right-hand side of Equation (5)). The instantaneous mass flow rate of gasification products, \(G_{\text{PP}}(t)\), can be determined as:  
\[G_{\text{PP}}(t)=\mu_{2}A_{2}{{}^{*}}\frac{P_{\text{0 out}}(t)}{\sqrt{T_{\text {0 out}}(t)}}-G_{\text{in}}(t) \tag{6}\]  
When the value of \(\mu_{2}\) is found by iterative procedure depending on instantaneous temperature, pressure, and initial composition of the PP-air system (see Equation (4)), then \(\varphi\) must be equal to unity. Deviation from the unity indicates a level of measurement error. When the value of \(\mu_{2}\) is unknown, one can take an arbitrary constant value of \(\mu_{2}\) (e.g., \(\mu_{2}=0.0404\) (kg\(\cdot\)K/J)\({}^{1/2}\) for pure air, see Figure 7) and use Equations (5) and (6) for determining the first approximation of \(G_{\text{PP}}(t)\), that is \(G^{\prime}_{\text{PP}}(t)\), and a value of \(\varphi\). This value of \(\varphi\) can be further considered as a correction factor for calculating the corrected mass flow rate of gasification products, \(G^{\prime\prime}_{\text{PP}}(t)\), using the relationship:  
\[G^{\prime\prime}_{\text{PP}}(t)=\varphi G^{\prime}_{\text{PP}}(t) \tag{7}\]  
Figure 8 illustrates the procedure of determining the corrected mass flow rate of gasification products, \(G^{\prime\prime}_{\text{PP}}(t)\), for one of the test fires (test fire #9, see below). By the iteration process mentioned earlier one can obtain a value of \(\mu_{2}=const=0.0349\) (kg\(\cdot\)K/J)\({}^{1/2}\) for this test case. The corresponding curves for \(G_{\text{out}}(t)\) and \(G_{\text{PP}}(t)\) are represented in Figure 8a,b. To avoid iterations, let us assume for \(\mu_{2}\) a constant value of 0.0404 (kg\(\cdot\)K/J)\({}^{1/2}\) corresponding to pure air. The curves \(G^{\prime}_{\text{out}}(t)\) and \(G^{\prime}_{\text{PP}}(t)\) obtained for such a value of \(\mu_{2}\) are represented in Figure 8a,b. Accordingly, the time integral of the mass flow rate of gasification products along curve \(G^{\prime}_{\text{PP}}(t)\) in Figure 8b (i.e., the integral in the right-hand side of Equation (5)) exceeds the value of \((W_{1}-W_{2})\) determined by sample weighing (shaded area in Figure 8a) by a factor of 1.62. Thus, coefficient \(\varphi\) in Equation (5) takes a value of  
Figure 7: Coefficient \(\mu_{2}\) for calculating gas mass flow rate at GG outlet depending on the PP-to-air mass ratio at 1 MPa. \(1/1.62=0.617\). The corrected mass flow rate \(G_{\mathrm{PP}}^{\prime\prime}(t)\) was then calculated from Equation (7) and represented by curve \(G_{\mathrm{PP}}^{\prime\prime}(t)\) in Figure 8b. Now, one can see a fairly accurate agreement between curves \(G_{\mathrm{PP}}^{\prime\prime}(t)\) and \(G_{\mathrm{PP}}(t)\) in Figure 8b. The difference between these curves is represented by curve \(G_{\mathrm{PP}}^{\prime\prime}(t)-G_{\mathrm{PP}}(t)\) in Figure 8b.