b for turbulent liquid flow

... approach for turbulent mixing was restricted to describing canonical turbulent flows (Corrsin 1951a; Corrsin 195 1b; Corrsin 1957; Gibson and Schwarz 1963a; Gibson and Schwarz 196 3b; Lee and Brodkey ... of large numbers of samples and bins, the bi-variate histogram can be used to compute an estimate for the joint PDF of φA and B : lim N ,MA ,MB →∞ h A ,B (ψA , B ) → fˆA ,B (ψA , B ) (1.33) We ... with turbulent flows are encouraged to review Part I of the recent text Turbulent Flows by Pope (2000) before attempting to tackle the material in this book In order to facilitate this effort,...

Ngày tải lên: 01/04/2014, 10:48

... M This norm will be denoted K2,α (M, X) Actually the definition below makes sense for any subset M of spacetime Let BN = BN (0, 1) and BN,1 = BN × (−1, 1) denote the open unit balls centered at ... ·) → uniformly on compact sets in spacetime (because d(0, Ui ) → ∞) And as before, the functions K2,α (Mi , ·) are uniformly bounded on compact subsets of RN,1 Thus by passing to a subsequence, ... same proof, that K1,α (M, x) is bounded Spacetime (for parabolic problems) is somewhat more complicated than space (for elliptic problems) Thus for example parabolic dilations and Gaussian densities...

Ngày tải lên: 06/03/2014, 08:21

... Turbulence, 1994) 1.1 Computational Turbulent Incompressible Flow This book is Vol of the Body&Soul series and is devoted to computational fluid dynamics with focus on turbulent incompressible ... polymers The basic mathematical models for turbulence thus appear to be known since very long, but nevertheless turbulence is viewed as the basic open problem of classical mechanics How can it be? The ... analytical mathematical methods to obtain quantitative information about turbulent flow, has been very slow or rather non-existent, because the complexity of turbulent solutions to the Navier–Stokes...

Ngày tải lên: 01/04/2014, 10:49

... may attain for arbitrary L L values of Peclet number More precisely, it has been shown [12,337] that e ' KH ' e is rigorously H L L bounded above and below, for all Peclet number, by certain ... obtain mathematically explicit and unambiguous results which can be used as a sound basis for the scienti"c investigation of more complex turbulent di!usion problems arising in applications for ... possible to construct sharper bounds on the e!ective di!usivity using information from a "nite number of terms in a small Peclet number & expansion, which can be determined by a straightforward formal...

Ngày tải lên: 24/04/2014, 16:48

... vapour flux values for both sites is slightly better for the Carrasqueira where data were obtained on bright clear days than for the Bray where data were collected under changeable weather conditions ... variability of sap flux density at a height of 1.30 m for three trees Bray site The relationship between density and either the number of rings or the proportion of earlywood crossed by the probe ... tests and sampling procedures are detailed by Berbigier et al [2] for the Carrasqueira site and Lamaud et al [21 ]for the Bray site RESULTS 4.1 Azimuthal variability of sap flux density in pine stands...

Ngày tải lên: 09/08/2014, 04:20

... Crafts for Kids: 17 Flower Crafts, Butterfly Crafts, and More Flower Crafts Fingerprint Bouquet By: Amanda Formaro for AllFreeKidsCrafts The Fingerprint Bouquet incorporates the beauty and joy of flowers ... and More Downy Blooming Spring Flowers By: Jill from Meet the Dubiens Spring into crafting with the beautiful, blossoming Downy Blooming Spring Flowers You may not believe it, but these darling ... Crafts for Kids: 17 Flower Crafts, Butterfly Crafts, and More Water Bottle Flower Power By: Crissy from Crissy’s Crafts Spring is in bloom, and so are your water bottles These flowers are absolutely...

Ngày tải lên: 19/03/2015, 15:03

... double-shock region for Double Mach Reflection (background mesh corresponding to h = 1/100) 159 6.23 Sub-element resolution at double-shock region for Double Mach Reflection (background ... contours for shock-Bubble interaction problem at t = 0.2 computed with WWR-WENO scheme 144 6.13 Comparison of 3rd order GWR and QWR WENO schemes applied to shockbubble interaction ... of density for a 3rd order solution of a 3D shock bubble interaction 164 6.28 Iso-surfaces of density for a 3rd order solution of a 3D shock bubble interaction...

Ngày tải lên: 09/09/2015, 18:52

... LBM Table 3.3 Parameters for the bubble rising under buoyancy 67 Table 3.4 Comparison of terminal velocity for bubble rising under 67 buoyancy Table 3.5 Terminal bubble rising velocities with ... simulated by the 150 conventional IBM and boundary condition-enforced IBM Fig 5.6 Streamlines around the cylinder at Re = 40 simulated by the 151 conventional IBM and boundary condition enforced IBM ... structure developed for N-S solvers is used in LBM framework Although the tree-structured grid has been proven to be very efficient for N-S solvers, it may not be suitable for LBM In LBM, the simulation...

Ngày tải lên: 10/09/2015, 09:06

... However, it can be argued that the non-radial flows observed by Bond [8] could be due to the cone’s boundary Indeed, this possibility is supported by his observation that “ the liquid near the ... in subsection 2.1.4 The nondimensionalization is performed in subsection 2.1.5 The final form of the boundary-value problem is stated in subsection 2.1.6 This boundary-value problem will be analyzed ... figure 1.2) can be stable If however, stability only with respect to symmetric disturbances is concerned, then the solutions of type II1 can be stable for higher Reynolds numbers, presumably up to...

Ngày tải lên: 11/09/2015, 09:05

... trilinear form b (or ¯ as, b) b( u, v, w) = (B( u, v), w), ¯ v, w) = (B( u, v), w) ¯ b( u, By simple computation, we can easily check ¯ v, w) = {b( u, v, w) − b( u, w, v)}, ∀u, v, w ∈ H1 (Ω) b( u, (2.1) ... lemma 2.1 and 2.2 are ¯ also true for trilinear form ¯ For simplicity, we focus on B and ¯ in the thesis, but b b all results we obtain later are valid for B and b as well Chapter Some Estimations ... H1 (Ω) b( u, (2.2) Therefore, For the trilinear form b, we can prove the following inequalities by combination of integration of parts, H¨lder’s inequality and Sobolev inequality (see for instance...

Ngày tải lên: 12/09/2015, 10:42

... sector has the ability to absorb labor But high barriers to foreign entry, highly regulated professional categories, and onerous regulations and bureaucratic hurdles faced by new businesses (IMF ... `lg@ j>gl `kg? j?gi `lgh higi `mgB k@gj `hgj `mg@ `@gB `mgi `@gB `@g? `mgB `@g@ `hg? `@gj `@gB `@g> `@g? `@gB `mgi `lg@ `kg? `lgh `mgB `hgj `mgi `@gB `@g? `mgB `@g@ CBEsR&(!G4Ge#X$2PR4&(!'#%012(!P#!R1&(!Hd^2(!1&!>??@o!]G1G$1%Ñ#1G5!^OPÖX4G!P#!124!G4Ge#X$2PR42!3#450J!q4&PG1&I&N%G!1X4!q50&4&P50_4!/$G^12$5&1J ... Ct|KÅ!+*So>E!:9.![L*!9*ä!!ÅT+-U[:[!c;:UU ,b, c:[,-9!K)|!>??jg!:U![L*V!:+*!TU*.!zV!Åã!Z*Zz*+!c-T9[+,*U!:cc-+.,9M![-![L*!K-T9c,;!Ü*MT;:[,-9U!Bjil7>??h!:9.!m @B7 >??jo B? /Change ? ? B@ @ ? @ ? `B? `B? `B@ `>? `B@ >??k `@ (%) (%) `B@ (%)...

Ngày tải lên: 23/09/2015, 08:51

... DISCUSSION As described above, finding the best performanced cross-section of microchannels for two phase flow is the important task to determine the optimal design of two phase flow microchannel ... transfer behaviors for two phase flow In the study, it indicates that the microchannel heat exchanger with the circle cross-section is the best choice for designing There was less than 0.3% error between ... cross-section (case 4) The general parameters for these two cases are summarized in Table Case Table General parameters for cases under study Variable parameters Fixed parameters Rectangular cross-section:...

Ngày tải lên: 16/01/2016, 13:29

... input data-sample in table 3.1 along the associated gas pipeline of flow equations of Weymouth, Panhandle A, Panhandle B and Clinedinst are stored in table 3.2a and 3. 2b Table 3.2a Pressure along ... of flow equations of Weymouth, Panhandle A, Panhandle B and Clinedinst are stored in table 3.3a and 3. 3b Table 3.3a Pressure along associated gas pipeline with input data – sample from table ... input data - sample in table 3.1 along the associated gas pipeline of flow equations of Weymouth, Panhandle A, Panhandle B and Clinedinst are stored in table 3.4a and 3. 4b Table 3.4a Pressure along...

Ngày tải lên: 22/07/2014, 10:21

... results for smooth channel obtained by empirical formula ∗ dimensional quantity + wall units Subscripts results for smooth channel obtained by numerical method xxv Greek symbols α wave number of ... bubble injection is also widely accepted as a useful method for drag reduction (see the review by Ceccio, 2010) Besides, MEMS (Micro-Electro-Mechanical Systems) based feedback control of turbulent ... has also been proposed by Bechert and Bartenwerfer (1989); Choi (1989) Riblet has been flight-tested by Airbus and other companies through the use of special 3M adhesive riblet films on aircrafts...

Ngày tải lên: 10/09/2015, 09:10

... ensure statistically stationary for most cases Besides, doubled averaging time had been used for some cases, but no obvious difference was shown between the doubled averaging time and the original ... long enough for calculation of mean data 58 2.4.1 Grid independence test Both the DNS and DES codes need to be validated and tested for grid independence before employing to calculate for the flow ... and every time step is × 10−9 for both velocity and pressure 54 2.3.2 On Detached Eddy Simulation Detached Eddy Simulation (DES) model is a hybrid technique for turbulent flows with massive separations...

Ngày tải lên: 10/09/2015, 09:11

... this study However, the applicability of reduced order geometry model has to be verified for turbulent channel flow first before we focus on sinusoidal grooves in turbulent channel flow In this section, ... asymptotic limit for flow rate 76 difference can also be obtained as lim ΔQ =0 ⎧ ⎪ ⎪ 3S ⎪ ⎪ ⎪ ⎨ lim ΔQ = α→0 ⎪ ⎪ ⎪ 3S ⎪ ⎪ ⎩ 32 S→0 for both Cases & (3.9) for Case (3.10) for Case 3.2.3 Global performance ... the cases for turbulent flow Meanwhile, DNS is still utilized on three typical cases of turbulent channel flow (marked by ‘*’ in Table 3.2) to verify the accuracy of the results obtained by DES In...

Ngày tải lên: 10/09/2015, 09:11

... Case at h/D = 10% (b) Ga/Ga0 for Case at h/D = 15% 1.6 1.6 1.5 Performance ratio Performance ratio Gv/Gv0 for Dz=0% Gv/Gv0 for Dz=15% symmetric dimple 1.4 Gv/Gv0 for Dz=0% Gv/Gv0 for Dz=15% 1.3 -0.2 ... time-averaged local form drag distribution on the bottom wall for the different sub-cases in Case As is known, positive form drag contributes to increasing the total drag, and conversely negative form drag ... higher form drag for Case 3C.3 compared to the symmetric dimple (Case 3C.2*) Figures 4.19(d)–(f) show that contours of the form drag for Case 3S exhibit fairly similar behavior to that described above...

Ngày tải lên: 10/09/2015, 09:11

... performance factors for protrusions (d) performance factors for dimples Figure 5.3: Effect of h/D on Nusselt number, friction coefficient and performance factors: h/D stands for height ratio for ... distributes asymmetrically about the streamwise centerline of protrusions However, the asymmetry of form drag distribution is less obvious than that for friction drag Being so, the highest form ... can be observed that the Nusselt number for the protrusions with larger height is generally higher than that on the counterpart with lower height It can be also found that Nusselt number distributes...

Ngày tải lên: 10/09/2015, 09:11