Injection mold cooling analysis estimates

Cooling system is an important part of the injection mold. For most mold is cooled by cooling fluid flowing within the network to achieve the cooling pipe . Analysis calculated cooling pipe network, the basic parameters are given in the basis , to determine the pressure and flow of each node of each tube section. Significance analysis of the network , that not only the cooling fluid can be determined whether the pressure pump to provide sufficient pressure to ensure that the flow pipe ( mostly water pump ) , and when the internal branch pipe , the flow distribution can be calculated for each branch . In general, the pipe network analysis methods can be broadly grouped into two categories: the loop method and node method. Loop method that loops around the column loop equation for each pipeline flow is the unknown quantity . The basic approach is to assume that each pipeline flow , and then  the pressure unbalance of each loop flow correction repeated until a sufficient amount of correction small < 1 > This method has introduced almost all the  injection moulding fluid mechanics textbooks , is also the most widely applied < 2 > disadvantage of this method is the need to determine in advance all of the network loop. Literature < 3 > to find all the loops through graph theory methods for pipe network analysis is a creative work , but also led to the complexity of the algorithm reduces the readability of the program. Moreover, the iterative algorithm loop method employed, essentially within the back-projection method, the number of iterations and more inefficient. When the inlet pipe pressure control input parameters , it is also handling more inconvenient . Method is based on the node ( Node ) pressure pipeline crossing point as an unknown quantity to flow out of the node is equal to the sum of the external input ( a ) establish the flow equation , its principle author made ​​a brief introduction. However, the node method also has shortcomings: both ends of the pipe when the pressure is equal to a certain period , when there is no fluid flow , fluid conductivity matrix is ​​singular . This paper will present a new algorithm for node method : Fix traffic node method. This method can bypass the graph theory , not sure that all circuits , while Reducing Tee mould  maintaining the advantages of the traditional node method , you can not deal with singular matrix , and the iteration speed, has practical value. A network analysis of the basic equations of coolant flow in the pipeline Q by the Darcy-Weis bach equation ( head loss equation ) gives : hf = pg = LDV 2 2g (1) flow is defined as Q =! D 2 V 4. Substituting into formula ( 1) to obtain p = 8 L! 2 D 5 Q 2, remember ? = 8 L! 2 D 5, then p =? Q 2 is the pressure drop ( friction loss along the way ); p is the pressure difference across the cooling duct ; coolant density ; g is the gravitational acceleration ; L is the length of coolant holes ; D is the diameter of the cooling duct ; V cooling flow rate ; drag coefficient along the way . Among them, the drag coefficient and Reynolds number along the way (Re = 4 Q # D, # of coolant viscosity ! ) About : = 64 / Re (Re 2 000) 0 000 016 (4 000 - Re) + 0 000 019 89 ( Re-2 000) (2 000 Re 4 000) 0 316 4 / Re 0 25 (4 000 < basic principles Re) 2 node method < 4,5 > node method is based on the pipeline crossing point (node ​​) of pressure as unknown quantity to flow out of the node is equal to the sum of the external input ( out ) flow established equation. For an plastic pipe fitting mould  independent network , by a plurality of first nodes into a plurality of pipe sections, as shown later in Figure 2. The principle of division, is the intersection of different circuits and import and export must be as a node that can not have a branch within a pipe section ; in the pipe section has been divided into good , you can add any number of nodes as needed. The tube section by the nodes i and j define its internal traffic by equation ( 2 ) calculated : Q 2 = | pi - pj | flow ij (3) defines the outflow node positive inflow is negative , and note Q ij is flows from the node i to node j of flow of formula ( 3 ) can be further rewritten as the directional flow form : Q ij = pi - pj ij | Q ij | = g ij (pi - pj). Wherein , g ij = 1?
ij | Q ij | (4) is similar to the conductance of electrical engineering , g ij here can be called liquid lead . For any network node i, the sum of the liquid from the interior of the tube should be equal to the net inflow and outflow of external input and output sum of qi, therefore, j Q ij = jg ij. (Pi - pj) = q i for all network similar equations are established node obtained an equation : Gp = q (5) G is the conductance matrix solution , which is a non-linear set of equations for a given initial pressure or flow , and then solved iteratively until convergence , you can get pressure on each node , and then get the flow of each pipe section . Overall, the Formula Node law expression , calculation procedures and computational efficiency are superior loop method .
Improved Method 3 can be seen from the node (4 ) , when the pressure is equal at both ends of a pipe , the pressure is zero, the flow inside the pipe is zero , and thus guide the liquid tends to infinity, the finally obtained liquid guide singular matrix . To solve this problem, we propose an improved method .