Rohsenow W., Hartnett J., Young Cho. Handbook of Heat Transfer (776121), страница 103
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For theboundary conditions of Fig. 6.19, two solutions are possible for negative values of 13pnear separation. It is argued in Ref. 42 that true similarity with negative 13p cannot occur physicallybecause Eq. 6.115 would require Ue ~ oo as ~ ~ 0. Thus, similar solutions with negative 13pcanonly be approached after a period of nonsimilar flow, and depending on the conditions, oneor the other of the similar solutions for a given 13pcan be attained.
In Ref. 42, experimentalevidence from Ref. 43 for turbulent flow is cited for the possible existence of double-valuedflow-field behavior. The velocity profiles shown are characteristic of those for either a cooledsurface or one at the total enthalpy of the fluid. For a heated surface and 13p> 0, it is possiblefor the velocity ratio f ' in the outer portion of the boundary layer to attain a value greaterthan unity before approaching unity at the outer edge. The physical reason for this is that theacceleration of lower-density fluid by the favorable pressure gradient exceeds the retardationby the viscous forces.~1.0y010.6/0.4i~" -0.38840.20I23456{FIGURE 6.19 Similarvelocity distributions for body with surface pressure gradient 13pdefined by Eq. 6.103, iw = 0, ?s= 1 [42].FORCED CONVECTION, EXTERNAL FLOWS6.33The total enthalpy distribution in terms of the velocity is shown in Fig.
6.20 for lw = 0 andts = 1. A pressure gradient can cause significant departures from the Crocco relationship (Eq.6.40, represented by the straight line labeled 13p= 0). The latter is often used for approximatecalculations even when pressure gradients are present.I'0""-o.36-0.3884~00.20.40 .6-o.3657Ol 8i'F I G U R E 6.20 Enthalpy and velocity relationship withinsimilar boundary layers on a body with pressure gradient13pdefined by Eq. 6.103, iw = 0, ?s = 1 [42].Figure 6.21 shows the wall shear parameter f " required to evaluate the local skin frictioncoefficients by Eq. 6.106 or 6.108. These curves apply for the case where ts = 1.
The doublevalued nature of f " for a cooled surface (I w= 0) for 13pnear separation ( f " = 0) is evident. Generally, f'w' is more sensitive to variations in 13pfor a hot surface. In fact, for cold wall conditions(lw = 0), the variation of f " with 13pfor [3p > 0 is quite modest. Also, a cooled surface tends toretard separation; that is, f " = 0 at a smaller value of ~p.j2.52oL-2I.(30.5-05,,-/J,.-.-00.,~1.01.52.0Bp2.53.03.54.0R G U R E 6.21 Effect of pressure gradient on the skin friction parameter f " for various wall temperature levels, ?s= 1 [42].6.34CHAPTER SIX0.80.7Iw=20.6ot0.5r~0.40.30.2-0.5//00.5IO1.52.02.53.03.54.0tipFIGURE 6.22 Effect of pressure gradient on the heat transfer parameter [" for various walltemperature levels, ?s= 1, Pr = 1 [42].The heat transfer parameter required in Eq.
6.111 or 6.112 to calculate Stanton number isshown in Fig. 6.22 for ts = 1. It should be noted that because of the similarity of Eqs. 6.101 and6.102 for Pr = 1,I'-W~ - lw - Iaww(6.116)Hence, the ordinate in Fig. 6.22 can also be used in conjunction with Eq. 6.107 or 6.109 to calculate the cross flow skin friction coefficient for cases of very small yaw angles (ts --- 1). Notethat_ law is equal to unity because the solution of Eq. 6.102 with Pr = 1 and an insulated surfaceis I -= 1. Although the trends exhibited in Figs. 6.21 and 6.22 are generally similar, it must becautioned that such large variations in the Reynolds analogy factor occur that the latter is nolonger a useful concept.
The heat transfer parameter for a cooled surface shows a rather smallvariation with [3p for [3p > 1A, a fact first utilized in Ref. 44 to obtain relatively simple expressions for the local heat flux to blunt bodies in hypersonic flow.Cylinder Normal to the Free Stream, Fluid With Constant Properties. For constant fluidproperties, Eqs. 6.100 and 6.102 reduce tof'" + i f " = [3p(f,2 _ 1)[" + Pr f [ ' = 2Pr ¢ f ' [ ;(6.117)(6.118)For a cylinder normal to the free stream, the inviscid velocity distribution is given bywithue=Ax m(6.119)[3p- 12m+m(6.120)The term on the right side of Eq. 6.118 has been added to account for a nonuniform surfacetemperature.FORCED CONVECTION, EXTERNAL FLOWS6.35Similar solutions for Prandtl numbers other than unity may be obtained from Eqs. 6.117and 6.118 or their equivalent.
A major simplification is the independence of the momentumequation (Eq. 6.117), from the energy equation_(Eq. 6.118), which makes findependent of [.Also, the linear form of the energy equation in I permits handling arbitrary surface temperature distributions as in the case of the fiat plate. (See the section on the two-dimensional laminar boundary layer.)Solutions of the momentum equation (Eq.
6.117) [45] yield velocity distributions generallysimilar to those of Fig. 6.19, and the skin friction parameter f~ shown by the<b>Текст обрезан, так как является слишком большим</b>.
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