Numerical simulation of reciprocating turbulent flow in a plane channel

Abstract

Computational results were obtained for oscillatory flow with zero time mean ͑reciprocating flow͒ in a plane channel using a finite-volume method. A forcing term that varied cosinusoidally in time was imposed, and its frequency and amplitude were made to vary so as to span a range of regimes from purely laminar to fully turbulent. The results were validated against analytical solutions and literature data. In turbulent flow, although the computational grid did not fully resolve all the turbulence scales, the results were judged to be sufficiently accurate to capture all the essential features of the problem. The present computational results confirmed the existence of four main flow regimes ͑laminar, disturbed laminar, intermittently turbulent, and fully turbulent͒, already identified in the previous literature. One of the most interesting results was that the relation between the amplitudes of the forcing term and of the flow rate was found to be approximately linear both in the laminar and in the turbulent regimes; the reasons for this peculiar behavior were investigated and discussed. The influence of oscillation frequency and forcing term amplitude on transition to turbulence was also studied; results were compared with transition criteria proposed in literature, and a flow regime chart was proposed. Finally, the effect of unsteadiness on heat transfer was investigated by imposing different temperatures at the opposite walls of the channel and computing mean and fluctuating temperature distributions and heat transfer rates. The Nusselt number was found to increase significantly even in the disturbed laminar regime and to vary as Re 0.8 ͑as in steady turbulent flow͒ in the turbulent regime.

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“…By means of relations (15) one can calculate [4] the overall raising of each of the N dw's on the reservoir i.e. the h k 's.…”

“…To evaluate the entropy production in the adiabatic steps we must recall that for such steps it has been shown [4] …”

“…It is well known [1][2][3][4][5][6][7][8][9][10] that for some elementary irreversible process, such as the irreversible isothermal expansion of a gas in contact with a heat source T , the work done by the gas out W is related to the reversible isothermal work v W Re (i.e. the work performed by the gas in the corresponding reversible process) by the relation (1) where U S is the total entropy change of the universe (system + environment).…”

“…which is negative and remains negative in the N limit i. e. also for "reversible cycles" [4]. For the (N -(L -1)) th dw, which has been on the piston for the last L steps of the compression and the first step of the expansion (i.e.…”

Dissipated energy and entropy production for an unconventional heat engine: the stepwise ‘circular cycle’

“…It is well known [1][2][3][4][5][6][7][8][9][10] that for some elementary irreversible process, like the irreversible isothermal expansion of a gas in contact with a heat source at temperature T , the work done by the gas (1) where U S ∆ is the total entropy change of the universe (system + environment). …”