## Info

Fig. 7.9. Thermal legeneratoi it: counter-flow operations. la.l Hot Hind A enters matrix at constant inlel temperature during the hot blow, {bl Fluid A leaves matrix at ¡1 variable temperature always below the inlet valve, but increasing with time asymptotically to the inlet valve, (c) After the flow of fluid A ceases, cold fluid C enters the matrix at constant inlet temperature during the cold blow, (di Fluid C leaves the matrix with a variable temperature always above the inlet valve, but decreasing with time asymptotically to the inlet valve

Fig. 7.9. Thermal legeneratoi it: counter-flow operations. la.l Hot Hind A enters matrix at constant inlel temperature during the hot blow, {bl Fluid A leaves matrix at ¡1 variable temperature always below the inlet valve, but increasing with time asymptotically to the inlet valve, (c) After the flow of fluid A ceases, cold fluid C enters the matrix at constant inlet temperature during the cold blow, (di Fluid C leaves the matrix with a variable temperature always above the inlet valve, but decreasing with time asymptotically to the inlet valve flow conditions at the inlet to (or exit from) the matrix are not constant, but vary continually. The pressure, density, and velocity vary over an appreciable range, and the temperature varies over a more limited range.

### Theory of regenerator operation

The most comprehensive treatment of thermal regenerators is that given by Jakobt comprising a distillation of the classical work of Hauson (1929. 1931), Nusselt (1927), Schumann (1929), and An/.elius (1926), Elsewhere, flitTe (1948) has reviewed and extended the work of Hansen and others. Coppage and London (1953) have summarized and compared the various results presented in the literature, and Kays and London (1958) have established a rational basis for the design of regenerators, correlated with the design of other forms of compact heat-exchanger. Valuable contributions have been made also by Johnson (1952) and Tipler (1948). None of the work was directed specifically to the application of regenerators in Stirling engines, but was either of a fundamental nature or specific to gas-turbine applications.

Operating conditions Various modes of regenerator operation may be postulated, but that which is generally of most interest is called the state of cyclic operation. This is the state obtained when, after repeated heating and cooling for a fixed time-cycle consisting of one heating and one cooling period, the temperature at any one point in the fluid (or the matrix) is then the same as it was a full cycle earlier.

I'ig. 7.9 is a representation of a thermal regenerator in counterflow operation. In the state of cyclic operation the regenerator is assumed to function as follows. Hot fluid at a constant inlet temperature-, enterir g from the left-hand end. passes through the matrix, gives up part of its heal, and leaves the right-hand end with a variable temperature, lower

Fig. 7.10. Time-temperature variation of fluid and matrix in a thermal regenerator. The figure shows the possible form of the timc-tcmpernture variation at some interim point in a thermal regenerator m the state of cyclic operation. <a) to (hi is ihc hot-blow period. The fluid temperature increases from A to B as the flow Is switched from the cold lb hot fluid and thereafter increases towards the hot-fluid inlet temperature. The matrix temperature increases from X to Y during the hot-blow period due to heat transferred from the hot fluid to the matrix. Al (b) the flow is switched to cold fluid and the period ibj to (c) is the cold-blow period As the flow is switched the fluid temperature decreases from C to D and thereafter decreases asymptotically towards the constant temperature. During the cold blow the matrix temperature decreases from Y to X as heat is transferred from the matrix to Ihe fluid.

Fig. 7.10. Time-temperature variation of fluid and matrix in a thermal regenerator. The figure shows the possible form of the timc-tcmpernture variation at some interim point in a thermal regenerator m the state of cyclic operation. <a) to (hi is ihc hot-blow period. The fluid temperature increases from A to B as the flow Is switched from the cold lb hot fluid and thereafter increases towards the hot-fluid inlet temperature. The matrix temperature increases from X to Y during the hot-blow period due to heat transferred from the hot fluid to the matrix. Al (b) the flow is switched to cold fluid and the period ibj to (c) is the cold-blow period As the flow is switched the fluid temperature decreases from C to D and thereafter decreases asymptotically towards the constant temperature. During the cold blow the matrix temperature decreases from Y to X as heat is transferred from the matrix to Ihe fluid.

than the inlet temperature. The supply of hot fluid is discontinued, and all the fluid is ejected from the matrix through Ihe exit at the right. Cold fluid now enters at a constant inlet temperature from the right, passes through the matrix, is heated by absorbing heat from the matrix, and leaves at the left-hand end with a variable temperature above the inlet temperature. The cold fluid supply is discontinued, and all of the fluid is ejected from the cold end, to complete the cycle of operations.

Figure 7.1D shows the possible form of variation with time of the matrix temperature and fluid temperature, at one particular station in the matrix, with the regenerator in a state of cyclic operation. Fig. 7.1 I shows the temperature field in a regenerator, for both fluid and matrix, at the instant of flow-reversal. The upper curves represent the temperature of the fluid and matrix at the end of heating-blow and the start of the cooling-blow. The lower curves represent temperature, conditions at the end of cooling-blow and the start of heating-blow. At any particular station along the length of the matrix, the temperatures may fluctuate between the upper and lower curves, in a time-dependent relationship similar to that shown in Fig. 7.10. There are four periods in the cycle. Considering the passage of the hot fluid, the 'blow period' is the time taken for the total quantity of fluid to pass any joint in the regenerator; the 'reversal period' is the time which elapses between the entry of one

Regenerator passage length

Flo. 7.11. Spatial tetnperuturc variation oi fluid and matnx in a thermal regenerator. The tigure shows the spatial temperature variation in a thermal regenerator, at the instant of flow-switching In the state of cyclic operation, with hot and cold lluids having the constant inlet-temperatures P and Q, respectively.

(a) Fluid temperature ut end of the hot blow.

(b) Matrix temperature at end of the hot blow, and start of the cold blow.

(c) Matrix temperature at end of the cold blow.

(d) Fluid temperature at the end of the cold blow.

Points A. C. X. and Y correspond to the conditions represented by A. C. X, and \ m Fig.

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