proceedings

More documents

Recommendations

Info

FORUM PROCEEDINGS In this manner we finish with as many stacks as there are singularities. They are properly coded with respect to each other. Next they are fed through the collator. Here all cards belonging to the same coordinates are stacked together. This new total stack enters the accounting machine where the values cp, tf' x, yare added together for each coordinate. A new card is summary punched for each addition. The new resulting stack is the solution. Other singularities can be added to it if a modification of it is desired. The solution is not yet in the fon11 in which we need it. We must find the points for a number of (equally spaced) constant values of tf (stream lines). The .t' and y values appearing along these lines furnish coordinates of the physical stream lines. One of these is the profile. What is needed is a fast and simple inverse interpolation for tf and a direct interpolation for .t' and y. In the absence of a fast method, we use the old and time-honored method of cross plotting. We hope to be able some day to do this part by machine. As long as machines become faster there is hope. 60· - 60· Bucket Turn FIGURE 6 Here are some of the more simple examples which we have done. We are collecting experience about the most promising combination of singularities. Figure 5 shows· a very simple flow turn which has a constant velocity on the inside of the turn. By the addition of two singularities, one source and one sink, we arrive at turning streamlines, one of which has constant velocity throughout. The other streamlines decelerate first and then accelerate. None of these streamlines generates a closed profile. The simplest closed curve we could generate is shown in Figure 6. A vortex source flows into a vortex sink and both are 0pP9sed by equal and opposite singularities. This results in a closed curve in both hodograph (circle) and physical plane. Here we have a saddle point which is not situated at minus infinity. As a result, the profile does not have a finite entrance angle at its nose. The velocity there is not zero. There is, by the way, a very simple condition which assures that if you have a closed curve in the hodograph map you will also get a closed physical flow curve. 65
66 All that is necessary is that the strength of the infinity singularities matches the components of the velocity at which they are situated, and that the residue in the closed hodograph figure be zero. I may add that the fate of the compressible counterpart of this computation is now entirely in the hands of IBM. IBM is willing to perform the very complicated calculation of the compressible singularities on the Selective Sequence Electronic Calculator. After these tables are available we can calculate subsonic compressible flow. Supersonic flow is of small interest to us. \Ve leave that to the artillery ! Nothing will help us much, except being able to do two things. One is to compute with a great deal of accuracy. If we could sacrifice accuracy, we could proceed along cheaper ways by experiment alone. The other is to be able to mass. product theoretical results, because what we primarily are after are not solutions for production, i.e., for the immediate turbine that goes into the shop. VYe want series of solutions for experimental purposes. vVe want to get experimental parameters which are related to blade shapes, to the interaction between blade shapes, and to a number of additional variables which now rather obscure a clear conception of the working process of a turbine. If this computation can help here we shall be able to produce a still better performing machine than we have now. SCIENTIFIC COMPUTATION DISCUSSION Dr. Fenn: How justified is your irrotational flow with the blades moving past each other? Mr. Kraft: The flow can be considered completely irrotational as long as it is considered as a two-dimensional problem. Even in three dimensions, when the turbine is designed for constant circulation, you still would have an irrotational problem. It becomes rotational only when you take the boundary layer into account. This must come necessarily after we can calculate irrotationally. We have to follow the procedure which the great'masters of aerodynamics have laid down. \Ve do not think we know anything better. Mr. Stevenson: Have you ever tried the classical aerodynamic scheme using conformal transformation? Mr. Kraft: As I emphasized at the beginning, if it were only the incompressible solution we were after, we would not do this computation as I described it. We do it in this manner only because we can replace it by the compressible calculation as soon as the additional logarithmic singularity tables for compressibility are available. We are well aware that incompressible lattice computations can be performed by simpler procedures.
Page 2 and 3:
PROCEEDINGS Scientific Com putation
Page 4:
FOREWORD ASCIENTIFIC COMPUTATION FO
Page 8:
KING, GILBERT W., Physical Chemist
Page 42 and 43: FO RUM PRO C E E DIN G S g(x) is a
Page 45: 44 cated series of operations, but
Page 52: FORUM PROCEEDINGS means of a differ
Page 60 and 61: FORUM PROCEEDINGS procedure. For in
Page 68: Dynamics of Elliptical Galaxies I N
Page 74: FORUM PROCEEDINGS ments. A molecule
Page 89: 168 G C T GHA h 0 , o 34232.7 1 357
Page 95: 94 through the typewriter would per
Page 99 and 100: 98 listing only. Using the desk cal
Page 102: Use of the IBM Relay Calculator s f
Page 127:
126 these solutions. It turns out t
show all

proceedings

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?