The cooling of concrete slabs using water pipe networks

Transcription

1 The cooling of concrete slabs using water pipe networks Dr. Sarah Mitchell MACSI, University of Limerick, Ireland S. L. Mitchell, MACSI, University of Limerick - p. 1/7

2 Piped water is used to remove hydration heat from concrete dams during construction. During this construction large slabs of concrete are poured: typically 3 m 10 m 10 m. Concrete is a mixture of cement, sand and gravel: cement makes up about 10 15%. Cement is made up mainly from limestone, calcium, silicon, iron and aluminium. This mixture is heated to 1482 deg C and ground to a powder. Water is added to the cement and a chemical process occurs as it hydrates: allows it to harden. S. L. Mitchell, MACSI, University of Limerick - p. 2/7

3 Chemical reaction leads to large temperature rises which continue for months, or even years. These high temperatures often lead to internal cracking which weakens the dam structure. One way to prevent this is to embed the concrete blocks with an array of pipe networks. Chilled water is then pumped through the pipes to cool down the blocks more quickly. After one block is cooled, more blocks are added, so it is crucial for first block to be cooled quickly. After the cooling, the pipes are then filled in with concrete. S. L. Mitchell, MACSI, University of Limerick - p. 3/7

4 Wish to estimate temperature within concrete slab and analyse effect of pumping water through it. Engineer wishes to reduce maximum temperature in concrete to an "acceptable" level, whilst using least expensive pipe network. Clear that efficiency of heat removal will decrease as temperature increases. Needs to be balance between thermal efficiency and cost. Ultimate goal: to provide a strategy for improving the heat removal and estimate optimal spacing of pipes and pipe length. S. L. Mitchell, MACSI, University of Limerick - p. 4/7

5 Set up a simple cylindrical model for a single pipe cooling in an insulated concrete cylinder. Suppose pipe, of radius a(m), is embedded in a long insulated cylindrical slab of concrete of radius R(m), length L. z = L d T c d r = 0 z = 0 Water flux Q r = a r = R S. L. Mitchell, MACSI, University of Limerick - p. 5/7

6 The concrete produces hydration heat at a prescribed rate q per unit volume. Cool water, at temperature T 0, enters pipe at z = 0 and removes hydration heat from slab. Volume flux of water flowing through the pipe is Q. Choose an insulated b.c., T c = 0, at r = R to take r into account the local periodicity of pipe network. Ultimate aims of this model are to estimate: Optimal spacing R in elements of pipe network; Flux levels Q required to keep concrete temperature in prescribed bounds; Appropriate length of piping. S. L. Mitchell, MACSI, University of Limerick - p. 6/7

7 Use above assumptions to determine system describing temperatures in both concrete and pipe. Non-dimensionalise system and use this information to obtain a simplified model. Use appropriate mathematical techniques to solve the resulting equations. Examine the effect of including neglected higher order terms. Extension to more realistic model which has an array of pipes and allows for non-cylindrical geometry. Include fact that pipes tend to loop back and forth. S. L. Mitchell, MACSI, University of Limerick - p. 7/7