Proposal of a simple prediction method

In this session, a simple prediction method, which is used an early engine design process is proposed under the above experimental study.
It is impotant to predict the shaft power in the early engine design process. In such case, The method using Beale Number or West Number is used until now. As a problem of the method, the engine speed must be set for the calculation.

For more useful predicted method, it is noticed to find the relation between the engine speed and the shaft power. It becomes clearly how is the shaft power affected from the physical conditions by above analysis method and experimental results. After many discussions, the engine performance is affected by a shaft work, W_s, a mean pressure, P_m, a swept volume of the expansion space, V_SE, a gas constant, R, gas teperatures, T_E and T_C, a viscosity coefficient, v and engine speed, n. It is desided that belows non-dimentional speed, n^* and non-dimentional shaft work, w_S^* are used after a dimensional analysis.

On the other hand, as the non-dimentional numbers for the operating conditions, a permited pressure ratio, P^* and a non-dimentional temperature, T^* are defined.

A right figure shows a sample of the relation between the non-dimentional speed, n^* and the non-dimentional shaft work, w_S^*. It is confirmed that the experimental results can be reduced with n^* and w_S^* very well.

Under above results, non-dimentional shaft work, W_S^*, non-dimentional shaft power, L_S^* and non-dimentional engine specification, S^* are defined as follows.

A right figure shows the relation between n^* and L_s^* with five kind of Stirling engines. Engine A is the prototype engine in this study. Engine B is an alpha-type Stirling engine with the same pewer level of Engine A. Engine C is a 2 kW class beta-type engine. Engine D is a 300 W class low temperature difference Stirling engine. And, Engine E is a 1 kW class low temperature difference Stirling engine.
This figure shows that there is the optimum value of L_s^* on the each engines. And the optimum value, L_smax^* is related to n^* and S^*.
Next, a right figure shows the relation between n_max^* and L_smax^* including experimental results of high performance Stirling engines developed in the world. From this figure, the relation between n_max^* and L_smax^* is follows equation.

A right figure shows the relation between S^* and L_smax^* including experimental results of the high performance Stirling engines. From this figure, the relation between S^* and L_smax^* is follows equation.

A flowchart for the engine design process is shown in a right figure. First, the engine specification is decided, and the non-dimentional engine specification, S^* is calculated. Next, the maximum shaft power, L_Smax and the optimum engine speed, N_max are lead using above experimental equations. If the maximum shaft power and the optimum engine speed are enough performance, it is advanced to a detail design process.

(1) A simple prediction method, which is used an early engine design process is proposed under the above experimental study.
(2) The method can predict the maximum shaft power and the optimum engine speed.
(3) The prediction method is suitable for the general Stirling engines, using the non-dimentional numbers, n^*, L_S^* and S^*.