4,71) Jaeckel coi là một vụ nổ khối lượng không đổi. Trong một trường hợp thực sự điển hình, một vụ nổ bụi có lẽ không phải là một áp lực tinh khiết cũng không phải là một quá trình thuần túy khối lượng liên tục, kể từ khi áp lực sẽ dần dần xây dựng trong đám mây không cháy, mặc dù ngọn lửa có thể không hoàn toàn bị giới hạn về khối lượng. Như có thể nhìn thấy từ phương trình (4,69) và (4,71),. | Propagation of flames in dust clouds 321 Tị is the ignition temperature of the dust cloud L is the heat losses by radiation and conduction By equating the two sides and rearranging one obtains the expression for the minimum explosible concentration G G ể 5 - Ổ - cẶTi - To Ổ - q T - To v For dust concentrations above the stoichiometric concentration the heat production is constant and equal to Q X Cs whereas the heat consumption increases with the dust concentration. In this case the condition for self-sustained flame propagation will be Cj X ặ L Tj Tq C X cd dg X cv By rearranging Jaeckel s theoretical upper explosible limit becomes equal to CSQ - L d X cv Cu z - u Tị T0 cd cd Jaeckel considered a constant volume explosion. In a typical real case a dust explosion is probably neither a pure constant pressure nor a pure constant volume process since pressure will gradually build up in the unburnt cloud although the flame may not be fully confined in volume. As can be seen from Equations and a substitution of cv by Cp increases G and decreases Cu. The loss L is difficult to estimate and Jaeckel suggested as a first approximation that the loss factor L be neglected. If this is done and cv is replaced by Cp Equations and can be written c Tj - Tữ dg X Cp 1 Q - cd T - To c _ dg X Cp u Tj - T0 cd cd If the left-hand sides of the Equations and representing the heat production are denoted Hp it is seen that for 0 c Cs Hp is a linear function of c and for c G it is constant and independent of dust concentration. If the ignition temperature is considered to be independent of dust concentration and the loss L is neglected and the right-hand sides of the equations and representing the heat consumption are denoted Hc Hc becomes a linear function of the dust concentration. According to Jaeckel s simple model the condition of self-sustained flame propagation is Hp Hc Zehr 1957 suggested that Jaeckel s theory be .
