Laminar Boundary Layer behind Strong Shock Moving with Nonuniform Velocity

Mirels, Harold; Hamman, Jesse

doi:10.1063/1.1706496

Cited by 25 publications

(24 citation statements)

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“…Numerous researchers have studied boundary layer growth behind shock waves. Mirels 13,14 developed much of the pioneering work on boundary layer growth behind shock waves. Sturtevant and Okamura 15 solved the boundary layer equation in the shock-fixed frame and explored the effects of shock strength on the boundary layer profile.…”

Section: Introductionmentioning

confidence: 99%

Boundary Layer Profile Behind Gaseous Detonation as it Affects Reflected Shock Wave Bifurcation

Damazo

Odell

Shepherd

2012

42nd AIAA Fluid Dynamics Conference and Exhibit

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The present study explores the flow field created by reflecting detonations using heat transfer and pressure measurements near the location of detonation reflection. Schlieren imaging techniques are used to examine the possibility of shock wave-boundary layer interaction. These measurements are compared to laminar boundary layer theory and a onedimensional model of detonation reflection. Experiments were carried out in a 7.6 m long detonation tube with a rectangular test section using mixtures of stoichiometric hydrogenoxygen with argon dilution of 0, 50, 67, and 83% at an initial pressure of 10, 25, and 40 kPa. Optical observations show that minimal interaction of the reflected shock wave results when propagating into the boundary layer created by the incident wave. The heat transfer rate is qualitatively consistent with the time dependent laminar boundary layer predictions, however the magnitude is consistently larger and substantial (factor of three) peak-to-peak fluctuations are observed. The pressure measurements show good agreement between predicted ideal incident and reflected wave speeds. The pressure amplitudes are under-predicted for no argon dilution cases particularly at 40 kPa, but in reasonable agreement for lower pressures and higher dilutions.

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Section: Introductionmentioning

confidence: 99%

Boundary Layer Profile Behind Gaseous Detonation as it Affects Reflected Shock Wave Bifurcation

Damazo

Odell

Shepherd

2012

42nd AIAA Fluid Dynamics Conference and Exhibit

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“…001, 0.01 atmospheres, and T o= Tw = 522 R (in Ref. 13) and should be valid for air in a low pressure shock tube. Equation (Z7) should also give reliable estimates for the effect of variable pp.…”

Section: Approximate Analytical Integration Of Eq (16)mentioning

confidence: 99%

Test Time in Low-Pressure Shock Tubes

Mirels

1963

The Physics of Fluids

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293

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The reduction of test time in low pressure shock tubes, due to a laminar wall boundary layer, has been analytically investigated.In previous studies by Roshko and Hooker the flow was considered in a contact surface fixed co-ordinate system. In the present study it was assumed that the shock moves with uniform velocity, and the flow was investigated in a shock fixed co-ordinate system. Unlike the previous studies, the variation of free stream conditions between the shock and contact surface was taken into account. It was found that P, a parameter defined by Roshko, is considerably larger than the estimates made byRoshko and Hooker except for very strong shocks. Since test time is proportional to V 2 , previous estimates of test time are too large, particularly for weak shocks. The present estimates for P appear to agree with existing experimental data to within about 10 percent for shock Mach numbers greater than 5. In other respects, the basic theory is in general agreement with the previous results of Roshko.

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“…kirn sm _ sln _ = N sin* (j? (7) Thus one can write the operator R, which substitutes for (2) in expanded form, R = P* and for Eq. (5) as follows:…”

Section: Cos(kir/n)]mentioning

confidence: 99%

“…The parameter /3 is computed from laminar boundary layer solutions obtained by Mirels. 7 The solutions of Mirels are for initial pressures of 0.76 and 7.6 mm Hg and a range of shock Mach numbers between 4 and 14. Outside this range of conditions an extrapolation formula is given.…”

Section: Test Time In a 15-inch-diameter High-stagnation-enthalpy Shmentioning

confidence: 99%

Test Time in a 1.5-Inch-Diameter High-Stagnation-Enthalpy Shock Tube

1963

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The most popular method of solution of boundary-value problems like the foregoing is founded on Green's function. With its help, the moment on the nth support has the value n = G nk G h (4) To modify this method and to change the finite-difference operator L and boundary values (2) into single operator R or to change the boundary-value problem (1) into the algebraic equationthe operator L will be expanded. The eigenvalues can be found from the equation I -XL = 0 or from the equivalent equationwhere X * cos(kir/N)]and N -1 is the number of rows and columns in matrix L. But it is easy to prove that sin(kirn/N) represents the components of the eigenvectors of L. To carry out the normalization, these quantities must be multiplied by a constant factor, and then one gets the "projection tensors". kirm . kirnThus one can write the operator R, which substitutes for (2) in expanded form, R = P* and for Eq. (5) as follows:From (9), with help of the tensor property of P,one gets, after multiplication from the left by Pz, the explicit solution of the "three-moments equation:"The comparison of (11) with (4) yields Green's function G nm = -\iP nm ;i I = 0,1, ....N (12)The comparison of (12) and (8) reveals that R and G are commuting operators. This property distinguishes the operators R and (2). After summation, it is possible to write Green's function (12) in the form W nk = -|n -k\a--2 sinho-. , , . 7N . 2 sinhncr sinh^cr) , . ffln h(n+t) g + tanh^ \ (13) where sinhcr = 3 1/2 . Then the explicit solution (11) takes more compact form: Mn = (14) Adding to (14) regular part, one can write the solution of the boundary value problem M n+1 + 4M n + M n -i = -G n M 0 = M Q M N = M N n = 0,1, . . . N (15) as follows: M n = WnkG k -(-!)"+» (sinrmoysinhA/V) X [(-1) VTlfo -M N ] + (-l (16)To facilitate insight into the structure of Green's function (12) and (13), one can take, as in the previous case, N = 3, ThenAi = J, X 2 = |,and wm wn G nmFor particular numbers G = -10 + -6> 10 6" ' 1~I ' >10Assuming, for example, N = 3 and the load terms, GI = G 2 = JpZ 2 , one obtains from (15) the following expression foi moments:in agreement with previous results.

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Laminar Boundary Layer behind Strong Shock Moving with Nonuniform Velocity

Cited by 25 publications

References 1 publication

Boundary Layer Profile Behind Gaseous Detonation as it Affects Reflected Shock Wave Bifurcation

Boundary Layer Profile Behind Gaseous Detonation as it Affects Reflected Shock Wave Bifurcation

Test Time in Low-Pressure Shock Tubes

Test Time in a 1.5-Inch-Diameter High-Stagnation-Enthalpy Shock Tube

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