Laminar boundary layer on a sphere in hypersonic flow of equilibrium dissociating air

Murzinov, I. N.

doi:10.1007/bf01013841

Cited by 24 publications

(8 citation statements)

References 2 publications

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“…This is done for each test case. An example is shown in Figure 4 we expect from the heat flux distribution around a sphere according to Murzinov's result [39],…”

Section: Mesh Independence Studymentioning

confidence: 95%

Characterization of reflected shock tunnel air conditions using a simple method

Olivier

Wen

et al. 2022

Physics of Fluids

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A new method to characterize air test conditions in hypersonic impulse facilities is introduced. It is a hybrid experimental-computational rebuilding method which uses the Fay-Riddell correlation with corrections based on thermochemical nonequilibrium computational fluid dynamic results. Its benefits include simplicity and time-resolution, and, using this method, a unique characterization can be made for each individual experimental run. Simplicity is achieved by avoiding the use of any optical techniques and overly expensive numerical computations while still maintaining accuracy. Without making any assumptions to relate the reservoir conditions to the nozzle exit conditions, the work done characterizing four test conditions in a reflected shock tunnel is presented. In this type of facility, shock compression is used to produce an appropriate reservoir which is then expanded through a nozzle to produce hypersonic flow. Particular focus is given to the nozzle exit total enthalpy where a comparison is made with the reservoir enthalpy obtained using the measured shock speed and pressure in the shock tube. Good agreement is observed in all cases providing validation of the new approach. Additionally, static pressure measurements showed clearly that conditions III and IV have a thermochemical state which likely froze shortly after the nozzle throat. Also, the nozzle flow is shown to be almost isentropic. Due to the simplicity of the current method, it can be easily implemented in existing facilities to provide an additional independent estimate alongside existing results.

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“…This is done for each test case. An example is shown in Figure 4 we expect from the heat flux distribution around a sphere according to Murzinov's result [39],…”

Section: Mesh Independence Studymentioning

confidence: 95%

Characterization of reflected shock tunnel air conditions using a simple method

Olivier

Wen

et al. 2022

Physics of Fluids

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“…Bothp and ς are functions of θ and are able to be obtained with different approaches, such as analytical theories or data correlations [1,[3][4][5]. Taking p 0 ≈ γM 2 ∞ p ∞ in the hypersonic limit, Eq.…”

Section: Ratio Of Skin Friction To Heat Transfer In Rarefied Flowsmentioning

confidence: 99%

“…Considering the downstream region of the stagnation point, Kemp et al [3] made an improvement to extend the theory to more general conditions. In practice, empirical formulas of the heat transfer distribution were also constructed for typical nose shapes such as circular cylinders and spheres [4,5].…”

mentioning

confidence: 99%

General Reynolds Analogy for Blunt-Nosed Bodies in Hypersonic Flows

Chen

Wang

2015

AIAA Journal

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proportional factor of the analogy relation; Eq. (6) f 0 = nondimensional velocity along x axis; u∕u e g = nondimensional total enthalpy; H∕H e H = total enthalpy per unit mass, J∕kg k = thermal conductivity, W∕m · K M ∞ = Mach number in freestream n = index of the power-law shape leading edge Pr = Prandtl number p = wall pressure, N∕m 2 p 0 = pressure gradient parameter at the stagnation point; −d 2 p∕p 0 ∕dθ 2 θ0 p = normalized pressure distribution function; Eq. (13) _ q w = heat flux to the wall, W∕m 2 r 0 = section radius of the body of revolution, m; Eq. (1) R = curvature radius of the surface, m R c = radius of the inscribed circle of the base of the body, m Re l = local Reynolds number; ρ ∞ U ∞ R∕μ ∞ Re ∞ = freestream Reynolds number; ρ ∞ U ∞ R c ∕μ ∞ T = temperature, K T 0 = stagnation temperature in freestream, K U ∞ = velocity in freestream, m∕s u, v = flow velocity along x and y, m∕s W r = rarefied flow criterion; M 2ω ∞ ∕Re l x, y = local coordinate in physical space, m β = gradient parameter; 2dln u e ∕dln ξ Γ 1;2 = coefficients in Eq. (19) γ = specific heat ratio η, ξ = local coordinate in Lees-Dorodnitsyn transformation space θ = slope angle of the surface θ c = surface slope angle at the base of the body μ = viscosity, kg∕m · s ρ = density, kg∕m 3 ς = normalized heat transfer distribution function; Eq. (13) τ w = skin shear stress, N∕m 2 ω = index of the viscosity-temperature power law Subscripts e = boundary-layer edge condition free = free molecular flow condition r = reference state w = wall condition 0 = stagnation point condition ∞ = freestream condition Superscripts(1) = first-order approximation based on Navier-Stokes-Fourier equations (2) = second-order correction based on Burnett equations

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“…where p 0 and qw,0 are the pressure and the heat flux at the stagnation point, respectively. Both p and ς are functions of θ and are able to be obtained with different approaches such as analytical theories or data correlations [1,[3][4][5]. Taking p 0 ≈ γM 2 ∞ p ∞ in hypersonic limit, then Eq.…”

Section: Ratio Of Skin Friction To Heat Transfer In Rarefied Flowsmentioning

confidence: 99%

General Reynolds Analogy for Blunt-nosed Bodies in Hypersonic Flows

Chen

Wang

2015

Preprint

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In this paper, the relation between skin friction and heat transfer along windward sides of blunt-nosed bodies in hypersonic flows is investigated. The self-similar boundary layer analysis is accepted to figure out the distribution of the ratio of skin friction to heat transfer coefficients along the wall. It is theoretically obtained that the ratio depends linearly on the local slope angle of the wall surface, and an explicit analogy expression is presented for circular cylinders, although the linear distribution is also found for other nose shapes and even in gas flows with chemical reactions. Furthermore, based on the theoretical modelling of the second order shear and heat transfer terms in Burnett equations, a modified analogy is derived in the near continuum regime by considering the rarefied gas effects. And a bridge function is also constructed to describe the nonlinear analogy in the transition flow regime.At last, the direct simulation Monte Carlo method is used to validate the theoretical results. The general analogy, beyond the classical Reynolds analogy, is applicable to both flat plates and blunt-nosed bodies, in either continuous or rarefied hypersonic flows.

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Laminar boundary layer on a sphere in hypersonic flow of equilibrium dissociating air

Cited by 24 publications

References 2 publications

Characterization of reflected shock tunnel air conditions using a simple method

Characterization of reflected shock tunnel air conditions using a simple method

General Reynolds Analogy for Blunt-Nosed Bodies in Hypersonic Flows

General Reynolds Analogy for Blunt-nosed Bodies in Hypersonic Flows

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