<i>Analytical Fluid Dynamics</i>

Emanuel, George; Bershader, D.

doi:10.1063/1.2808705

Cited by 22 publications

(15 citation statements)

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“…textbooks. The Prandtl-Meyer expansion analysis presented here is similar to that of Emanuel [7], Ismail [8], and Zebbiche [9], whereas the oblique shock analysis is similar to that of Emanuel [7] and Tatum [10]. However, none of these authors considered wave interactions, which are the focus of the present work.…”

Section: High-temperature Two-dimensional Wave Modelmentioning

confidence: 83%

Reduced-Order Modeling of Two-Dimensional Supersonic Flows with Applications to Scramjet Inlets

Dalle

Fotia

Driscoll

2010

Journal of Propulsion and Power

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Control-oriented models of hypersonic vehicle propulsion systems require a reduced-order model of the scramjet inlet that is accurate to within 10% but requires less than a few seconds of computational time. To achieve this goal, a reduced-order model is presented, which predicts the solution of a steady two-dimensional supersonic flow through an inlet or around any other two-dimensional geometry. The model assumes that the flow is supersonic everywhere except in boundary layers and the regions near blunted leading edges. Expansion fans are modeled as a sequence of discrete waves instead of a continuous pressure change. Of critical importance to the model is the ability to predict the results of multiple wave interactions rapidly. The rounded detached shock near a blunt leading edge is discretized and replaced with three linear shocks. Boundary layers are approximated by displacing the flow by an empirical estimate of the displacement thickness. A scramjet inlet is considered as an example application. The predicted results are compared to two-dimensional computational fluid dynamics solutions and experimental results. Nomenclature a = local sound speed, m=s c = specific heat, J=kg K H = length normal to flow, m h = specific enthalpy, J=kg L = length tangent to flow, m M = Mach number n = number of a given quantity Pr = Prandtl number p = pressure, Pa R = normalized gas constant, J=kg K R = 8314:47 J=kmol K r = radius, m T = temperature, K u = velocity magnitude, m=s W = molecular weight, kg=kmol x = forward body-frame coordinate, m Y = mass fraction z = vertical body-frame coordinate, m = shock angle = ratio of specific heats = thickness of layer, m " = ratio = ln p 0 =p = dynamic viscosity, kg=m s = flowpath angle = =2 = M 2 1 p = sin 1 1=M, Mach angle = Prandtl-Meyer function = density, kg=m 3 = wave angle = flux of subscripted quantity = reference angle Subscripts A, B, . . . = region label a, b, . . . = point label bs = curved portion of bow shock cl = property of inlet cowl e = value at edge of boundary layer ex = expansion i = species index j = index of expansion discretization k = region index le = leading edge p = constant pressure s = constant entropy sp = pertaining to species w = wall value 0 = stagnation value 1 = index for inlet portion of flow 2 = index for inlet outflow 1 = freestream Superscripts = value at Mach number of 1 = reference value for boundary layer

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Section: High-temperature Two-dimensional Wave Modelmentioning

confidence: 83%

Reduced-Order Modeling of Two-Dimensional Supersonic Flows with Applications to Scramjet Inlets

Dalle

Fotia

Driscoll

2010

Journal of Propulsion and Power

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“…It is commonly accepted that blood presents a mostly noncompressible behavior (17). Consequently, the conservation of mass equation for a fluid with constant density requires (18): where ∇ is the divergence operator and $\vec r$ the local velocity…”

Section: Methodsmentioning

confidence: 99%

Four‐dimensional flow‐sensitive MRI of the thoracic aorta: 12‐ versus 32‐channel coil arrays

Stalder

Zhou

Yang

et al. 2011

Magnetic Resonance Imaging

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Purpose: To evaluate the performance of four-dimensional (4D) flow-sensitive MRI in the thoracic aorta using 12-and 32-channel coils and parallel imaging.Materials and Methods: 4D flow-sensitive MRI was performed in the thoracic aorta of 11 healthy volunteers at 3 Tesla (T) using different coils and parallel imaging (GRAPPA) accelerations (R): (i) 12-channel coil, R ¼ 2; (ii) 12-channel coil, R ¼ 3; (iii) 32-channel coil, R ¼ 3. The quantitative analysis included SNR, residual velocity divergence and length and curvature of traces (streamlines and pathlines) as used for 3D flow visualization. In addition, semi-quantitative image grading was performed to assess quality of phase-contrast angiography and 3D flow visualization.Results: Parallel imaging with an acceleration factor R ¼ 3 allowed to save 19.5 6 5% measurement time compared with R ¼ 2 (14.2 6 2.4 min). Acquisition using 12 channels with R ¼ 2 and 32 channels with R ¼ 3 produced data with significantly (P < 0.05) higher quality compared with 12 channels and R ¼ 3. There was no significant difference between 12 channels with R ¼ 2 and 32 channels with R ¼ 3 but for the depiction of supra-aortic branches where the 32-channel coil proved superior.Conclusion: Using 32-channel coils is beneficial for 4D flow-sensitive MRI of the thoracic aorta and can allow for a reduction of total scan time while maintaining overall image quality.Key Words: phase-contrast MRI; 4D flow-sensitive MRI; aorta; parallel imaging; 32-channel coil; GRAPPA J. Magn. Reson. Imaging 2012;35:190-195. V C 2011 Wiley Periodicals, Inc.IN A CONTEXT where functional evaluation of the cardiovascular system is gaining increased importance, four-dimensional (4D) flow-sensitive MRI is getting more widely used (1-8). The technique is characterized by its high-dimensionality (depiction in three dimensions and over time of anatomy and three-directional blood flow velocities) that allows comprehensive blood flow and vessel wall analysis within complete arterial segments. However, the high-dimensionality of 4D-flow-sensitive MRI is limiting the clinical application of the technique by making the image acquisition time-consuming. In this context, recent developments in MRI acceleration techniques such as parallel imaging (9), non-cartesian (10,11), compressed or sparse sensing are promising. Nevertheless, increased acceleration factors are known to potentially degrade image quality (12). Additionally, the use of a high number of surface coils results in high SNR near to the coil but lower SNR with increased distance from the coil (13,14). This aspect is further amplified by the geometry or ''g''-factor, which depends on the acceleration factor and on the coil sensitivity of the multi-coil array. In this context, the benefits of multichannel coil arrays and parallel imaging can be limited when imaging structures centered in the body such as the thoracic aorta.The aim of this study was to evaluate the performance of 4D flow-sensitive MRI in the thoracic aorta with 12-and 32-channel coils using GRAPPA acc...

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“…The last term on the right side of Equation is the buoyancy term. Effective viscosity represents turbulent influences which is the sum of the laminar viscosity µ l and turbulent viscosity µ t :

μ_{normaleff} = μ_{normall} + μ_{normalt} .

…”

Section: Numerical Analysismentioning

confidence: 99%

Numerical study of nanoencapsulated phase change material inside double pipe heat exchanger

Iranfar

Saraei

2019

Heat Trans. Asian Res.

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Nanoencapsulated phase change material (NPCM) slurry is a dispersion where the phase change material (PCM) is dispersed in fluid. Compared with fluid, these nanofluids have a higher heat capacity during the phase change and a possible enhancement, as a result of this phase change, in the heat transfer phenomenon. To appreciate the merits, in terms of energy, a numerical study has been carried out with fluid based on NPCM inside double pipe heat exchanger. The numerical simulation results have been validated using experimental heat transfer data. The Reynolds and Nusselt numbers have been determined using thermal conductivity and viscosity evaluated in the same conditions as those in numerical model. The results obtained show an improvement of this energetic criterion at low mass flow rate compared with the base fluid. Analysis of the numerical and analytical results reveal that higher inlet flow rate and NPCM concentration results in higher heat transfer rate. In addition, increasing NPCM slurry temperature decreases its performance due to fast melting of PCM inside the tube. K E Y W O R D S double pipe, heat transfer, nanocapsule, phase change, slurry

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Analytical Fluid Dynamics

Cited by 22 publications

References 0 publications

Reduced-Order Modeling of Two-Dimensional Supersonic Flows with Applications to Scramjet Inlets

Reduced-Order Modeling of Two-Dimensional Supersonic Flows with Applications to Scramjet Inlets

Four‐dimensional flow‐sensitive MRI of the thoracic aorta: 12‐ versus 32‐channel coil arrays

Numerical study of nanoencapsulated phase change material inside double pipe heat exchanger

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