The effects of laminar heat-transfer losses on piston gas-heater performance have been studied theoretically and experimentally. For the analysis, the gas is separated into an isentropic "core" and a developing thermal layer over the "wetted" wall. The heat-transfer rate and thermal boundary-layer thickness are computed in a boundary-layer integral approach, using a zero-order similarity profile for the gas density. The equations were solved with the help of a digital computer and several interesting solutions were obtained. Experiments were conducted with helium and argon in a specially built gas compressor, with a pneumatically driven piston, generally performing one complete forward stroke and one reverse stroke. The experimentally measured time history of the gas pressure (i.e., the average energy density) was found to agree remarkably well with theoretical predictions. The presented computational scheme could potentially be applied to such shock tube and shock tunnel piston compressors where the piston velocity is much smaller than the speed of sound of the gas, as well as to a wide class of laminar gas flow devices using reciprocating pistons.
NomenclatureA = wetted surface area c p = specific heat d 0 = reference length, d Q = 4 To Mo D = piston diameter E -total internal energy of gas / = gas-density similarity function, /(??) = (p -P^)/(PWPco) g = dimensionless piston-motion function, t -g(£) G = dimensionless function, defined in Eq. (14) h ~ specific enthalpy L = dimensionless energy loss, defined in Eq. (24) p -gas pressure q = heat flux q = dimensionless heat flux, defined in Eq. (25) Qioss = total heat-transfer loss, defined in Eq. (19) t = time from start of piston motion T = temperature u = dimensionless piston velocity, defined in Eq. (25) v = flow velocity perpendicular to the plane y = 0 V = compressor volume (time dependent) W = work addition parameter, defined in Eq. (23) x = coordinate in the direction of piston motion y = coordinate in the direction perpendicular to the wall 7 = specific-heat ratio 5 = boundary-layer thickness parameter e = main boundary-layer-growth parameter, defined in Eq. (25) eio = modified boundary-layer-growth parameter, ei 0 = e(l -?io) 1/2 ?7 = dimensionless wall distance parameter, 77 = y/8 A = thermal conductivity £ = dimensionless piston position, £ = X/XQ P -gas density \f/ = fraction of compressor volume occupied by boundary layer gas, defined in Eq. (27) Subscripts 0 = reference condition at £ = 1.0 for isentropic compression 1 = initial condition at time t = 0