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PARTICLE-LADEN FLOW - ERCOFTAC SERIES Phần 3

Tham khảo tài liệu 'particle-laden flow - ercoftac series phần 3', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Heat and water vapor transport 77 3 Numerical model implementation The model proposed here makes use of the transient heat conduction equation 9 and the general gamma distribution 16 . The one-dimensional flow equation can be solved by the implicit finite difference method as discussed below in section 3.1 whereas the generation of random deviates for arrival times and approach distances is described in section 3.2. 3.1 Finite difference model setup The one-dimensional transient system of equation 9 with boundary conditions 10 can easily be written in finite differences 15 . In this case the implicit system of equations can be written as a tridiagonal matrix equation that is easily and quickly solved with the Thomas algorithm. In order to make the model as realistic as possible a grid was used consisting of 1000 elements with properties as summarized in Table 1. A temperature solution array of 1000 elements is produced at each time step and an average H was determined for each set of parameters after each simulation run. 3.2 Gamma distribution A basic procedure to generate random deviates with a gamma distribution is given by 16 . However since this procedure assumes that 3 1 a more general procedure gamdev a 3 was developed which returns random deviates as a function of both a and Ị3. The average approach distance hp avg was used instead of 3 as a parameter during the simulation runs. Parameter 3 is then calculated as hp avg a. The Brutsaert model 1 can be implemented by drawing the arrival rates with gamdev 1 1 and resetting the entire temperature T array to the lower temperature upon arrival of the eddies. The more general procedure consists of drawing arrival rates as in the Brutsaert model with gamdev 1 1 and then after selecting hp avg and a drawing an approach distance hp with gamdev a 3 . 4 Results Table 1 below shows the basic parameter set with their chosen values. The parameters such as K p Cp and V depend to a minor extent on temperature. However this .