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as minus the end restraint forces due to the loads acting in the element, when the ends are held fixed. The equivalence between this definition and that given by Tong from the variation of Eq. (2) can easily be shown by means of the virtual work equation where the virtual displacements are taken as the actual displacements in the element when one of the end displacements, q^ is equal to one and all others are zero:where G is the vector of internal forces associated with the degrees of freedom of the problem (a function of x) due to the element loads for fixed end condition, and Qi is the generalized force associated with #». Since G constitutes a state of stress that corresponds to a fixed end condition, it immediately follows that the first term in the right-hand side of the preceding equation vanishes. The validity of Eq. (8) can also be proved without reference to variational considerations by pointing out that the internal forces G satisfy equilibrium and compatibility inside each element and that the interelement compatibility and displacement boundary conditions are satisfied by definition of the generalized displacements; thus it only remains to insure equilibrium at the element ends and to satisfy the force boundary conditions that may be prescribed, which is done through Eq. (8). Finally, it may be concluded in agreement with Tong, that the solution of Eq. (8) for the nodal displacements is exact because both K and Q are exact. R -reattachment line, OS = oblique shock, MD = Mach disk, SS = single shock, MS = multishock, SL = subsonic layer.subsonic reattachment line defined by oil-film technique was located much further from nozzle x = 1.8 for D p /Dt = 1.58 than the supersonic one, x = 0.33. The cyclic oscillation of the reattachment region is associated with strong pressure and shock-wave cyclic oscillation. The change of flow pattern is also cyclic, and therefore the wall is being touched by the supersonic and subsonic stream in turn. The oscillation is self-excited, and for each value of D p /Di it appears in a definite range of p w . These and some other features of the oscillating flow are described in detail in Refs. 2 and 3. It is therefore of interest to know how exact was the coincidence of reattachment line location with the heat-transfer maximum and to what types of reattachment the results given in Figs. 8-10 correspond.Nomenclature Di = igniter nozzle throat diameter Dp = test-section diameter p Q = stagnation pressure upstream nozzle p w = static pressure in the dead-air region p w = PW/PO x = coordinate along test section x = x/D p W HEN investigating heat transfer during head-end hotgas ignition, the authors 1 distinguished only two cases of flow pattern (Figs, la and Id). One case corresponds to the reattachment of supersonic jet (Fig. la) and the other one has no reattachment at all (Fig. Id). This is an oversimplification because there are two other intermediate cases. 2 One is significant for subsonic reattachment (Fig. Ic) and the other for mixed reattachment and oscillating flow ...