Proceedings of the5th ASME/JSME Joint Thermal Engineering Conference

March 15-19, 1999 San Diego, California

AJTE99-6302

PROGRESS IN DIRECT NUMERICAL SIMULATION OF TURBULENT HEATTRANSFER

NOBUHIDE KASAGIDepartment of Mechanical Engineering

The University of TokyoHongo 7-3-1, Bunkyo-kuTokyo 113-8656, Japan

E-mail: kasagi@thtlab.t.u-tokyo.ac.jp

OAKI IIDADepartment of Mechanical Engineering

Nagoya Institute of TechnologyGokiso-cho, Showa-ku

Nagoya 466-8555, JapanE-mail: iida@heat.mech.nitech.ac.jp

Keywords: Turbulent Heat Transfer, Direct Numerical Simulation, Prandtl Number, Buoyancy, Control

ABSTRACT

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With high performance computers, reliable numericmethods and efficient post-processing environment, dirnumerical simulation (DNS) offers valuable numericaexperiments for turbulent heat transfer research. In particuone can extensively study the turbulence dynamics atransport mechanism by visualizing any physical variable space and time. It is also possible to establish detailed dataof various turbulence statistics of turbulent transpophenomena, while systematically changing important flow ascalar field parameters. The present paper illustrates thnovelties of DNS by introducing several examples in recentstudies. Future directions of DNS for turbulence and hetransfer research are also discussed.

In the following, with introductory remarks oncomputational requirement for respectable DNS, progressnumerical techniques is first reviewed. Then, an effort to revthe effect of Prandtl number on turbulent heat transfer sketched with an emphasis on the new techniques developedmaking DNS over a wide range of Prandtl number possibBoth methods of saving grid points and Lagrangian partictracking are found very useful in the future work on turbuleheat and mass transfer.

The complex buoyancy effects on turbulent transport adiscussed in a series of DNSs of horizontal and vertical chanflows. It is found that the buoyancy effect appears mudifferently depending upon the directional alignment of th

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buoyant force and the mean flow. In the vertical flow, tbuoyancy effect results in an increased or decreased Reynnumber effect, which appears through a change in the Reynstress distribution and hence in the shear production ratturbulent kinetic energy near the wall. In the horizontal flohowever, it causes substantial alternation in the turbulestructures and transport mechanism so that the resultant transfer coefficient would behave in a much more compmanner. The thermal plumes and internal gravity wavcharacteristic of these flows play an important role in tinteraction with the quasi-coherent structures of wturbulence.

DNSs of the channel flow under active turbulence and htransfer control are discussed finally. In these simulations,array of micro deformation actuators on a wall surface intelligent micro particles are tested as control schemes. shown that these sophisticated devices possibly bring anotable friction drag reduction and heat transfer enhancemA perspective view is given that DNS will be even more usein evaluating future turbulence control methodologies basednew algorithms such as optimum control theory and neunetworks. These simulations have been triggered by the rdevelopment of microelectromechanical systems (MEMtechnology, but hopefully future DNSs will lead furthedevelopment of MEMS-based controller units integrating micsensors, micro actuators and IC.

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INTRODUCTIONTurbulent momentum and scalar transport plays a key

in many engineering applications and will be of growiimportance in global environmental problems. For instanceis necessary to predict flow and heat transfer characteriunder design conditions, if one has to establish efficient safe industrial systems such as aircrafts, ships, automobilespower plants. Control of thermo-fluids phenomena in varioequipment and production processes is crucial to keeping quality, reliability and safe operation of products. Hence, meffort has been devoted to developing methodologies prediction and control of various turbulent flows and associatransport phenomena.

In the early 1980’s, with the advancement of large sccomputers, direct numerical simulation (DNS, hereafter)turbulent flow and heat transfer became possible. Later, theof DNS rapidly spread in the turbulence research communDNSs are three-dimensional, time-dependent numersolutions of the Navier-Stokes and scalar transport equatthat govern the evolution of flow and scalar fields. Thegoverning equations do not involve any turbulence modHence, a DNS must be executed on a fine grid systemcapture all scales arising in turbulent processes. Despitedemanding nature, DNS has proved to be a valuable tool fofundamental research of turbulent transport phenom(Reynolds, 1990; Kasagi & Shikazono, 1995; Moin & Mahe1998; Kasagi, 1998).

In this paper, numerical methods for DNS are fireviewed briefly and then the recent progress in the applicatof DNS is illustrated by introducing typical examples. NameDNSs of turbulent heat transfer in a plane channel at varPrandtl numbers are sketched. Then, the complex effectbuoyancy on turbulence and heat transfer are explored wseries of DNSs. Finally, trial computations for possible actturbulence control are presented. The authors’ view on fudevelopment is given, when appropriate.

NUMERICAL METHODS OF DIRECT NUMERICALSIMULATION

Because a turbulent flow phenomenon contains a brrange of dynamically significant scales, its DNS must executed in a computational domain large enough to containlargest eddies, while keeping the grid spacing fine enougresolve the smallest eddies. The ratio of the largest to smalength scales in a turbulent flow is roughly estimated toproportional to the 3/4 power of the flow Reynolds number Rein each direction, so that the total number of grid pointsNrequired in a DNS is proportional to Re9/4. The time incrementin advancing the numerical integration must be as small assmallest eddy’s turnover time (and a Courant number also

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sufficiently small), whilst the total length of integration shoube much larger than the largest eddy’s turnover time in ordobtain well converged turbulence statistics. The ratio of thlargest to smallest time scales is roughly proportional to Re1/2.Thus, as the Reynolds number increases, the numbers opoints and time steps inevitably increase rapidly.

The above requirement of DNS is even more serious, additional scales, which are out of the range of turbulescales, are introduced or imposed. For example, theturbulence microscales should also be captured when turbheat transfer is to be simulated (Kim & Moin, 1989; KasagShikazono, 1995), but this becomes difficult when the Pranumber is very large. The essentially same problem ariseflows with mass transfer and chemical reactions. In a falong a wall surface with artificial micro-groves (riblets),large computational volume is hard to retain, because morepoints are required in order to represent the riblet shape wsharp ridge (Choi et al., 1993a). In the simulations multiphase flows, characteristic scales of interfacial dynam(or waves) and of distributed particles and bubbles do always stay within the range of turbulence scales, yet hremarkable interactions with turbulence. In flows unarbitrarily imposed unsteadiness, associated time scales also be captured. These facts should be a major difficultDNSs of complex turbulent flows.

Continuous efforts have been directed toward improvemof the numerical methods of DNS. Spatial discretizatschemes for DNS are categorized into spectral (Canuto e1987), spectral element (Patera, 1984) and finite differe(Peyret & Taylor, 1983) methods. Among them, the specmethod should be most suitable to DNS because ofexponential convergence. It needs, however, linearizatiogoverning equations with explicit or semi-implicit timadvancement schemes. The channel flow simulation of Kimal. (1987) is based on a pseudo-spectral method, which emFourier series in the two periodic directions and Chebyspolynomial expansion in the wall-normal direction. Tspectral method can be applied to geometrically complex flby using mapping (coordinate transformation) or patch(Orszag, 1980). The former is used in the adaptive spemethod, which has been successfully employed in the DNSturbulent boundary layers (Spalart & Leonard, 1987), squduct flows (Madabhushi et al., 1993), turbulent flows obumps (Carlson & Lumley, 1996) and gas-liquid interfacturbulence (Lombardi et al., 1996).

The spectral element technique can be interpreted high-order finite element method (Peyret & Taylor, 1983)has been applied to a DNS of turbulent flow over riblets (C& Karniadakis, 1993). Since it has both flexibility of finielement method and high accuracy of spectral method, it

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be more widely used in the future DNSs of engineering inte(Karniadakis & Henderson, 1998).

High-order finite difference schemes (Rai & Moin, 199Rai & Moin, 1993) and a compact finite difference sche(Adam, 1977; Hirsh, 1977; Lele, 1992) have been extensiused and tested. The former was employed in the DNSturbulent boundary layers by Rai & Moin (1993). In additiothe second-order finite difference scheme has been emplwith a fractional step method in various flows, e.g., turbulflows in a square duct (Gavrilakis, 1992), over riblets (Choal., 1993a), in a curved square duct (Zang et al., 1994) along an oscillatorily deforming wall (Mito & Kasagi, 1998).

Temporal discretization schemes adopted so far areexplicit scheme, a semi-implicit scheme (a combinationimplicit and explicit schemes), and a fractional step met(Chorin, 1969; Temam, 1984). The semi-implicit scheme, wAdams-Bashforth method used for the nonlinear terms Crank-Nicolson method for the linear terms, is often adop(Kim et al., 1987), whilst the third-order Runge-Kutta meth(Spalart et al., 1991) has also become popular. A fractionalmethod developed by Chorin (1969) and Temam (1984employed in many DNSs. With this scheme, solutions velocity and pressure fields can be separated, and this leaappreciable reduction in computational load. Kim & Mo(1985) uses a semi-implicit type fractional step method, wAdams-Bashforth method for the nonlinear terms and CraNicolson method for the linear terms. This method has bmodified to a high-order version by Rai & Moin (1991) and & Moin (1991), i.e., with a low-storage third-order RungKutta method and a Crank-Nicolson method.

It is noted that recent DNS applications are also foundthe research on multiphase turbulent flows. Gas-liqinterfaces, bubbles and particles are taken into accounsophisticated numerical techniques, e.g., level set (Sussmal., 1994), CIP (Yabe & Aoki, 1991) and force (FogelsonPeskin, 1988) methods. In particle-laden flows, interactitake place between fluid and particles, which should properly taken into account (McLaughlin, 1994). When particle concentration is dilute, only the force experiencedparticles is calculated; this treatment is called one-way coup(Pedinotti et al., 1992). Care must be taken of the degreapproximation in the equation of particle motion and also ofinterpolation technique for the velocity field calculated DNS. Current effort is being made to calculate also particforces acting on fluid (two-way coupling) for higher particconcentrations and in more general cases particle collisalthough only a few results have been reported (see, Elghobashi & Truesdell, 1993; Pan & Banerjee, 19Yamamoto et al., 1998).

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APPLICATIONS OF DIRECT NUMERICALSIMULATION

Novelty of DNSA DNS can be regarded as a numerical experiment w

replaces a laboratory experiment. Although the Reynnumber remains small to moderate, there are many attrafeatures in DNS, and some of them are to be worth mentiobelow (Kasagi & Shikazono, 1995):

(1) Unlike experimental measurement, DNS allows oneprobe all the instantaneous flow variables such as velocpressures, and temperatures in space. Hence, turbstructures and transport mechanisms can be analyzedetails through various theoretical and visualizattechniques (Robinson, 1991; Kasagi et al., 1995).

(2) Even experimental measurement techniques canvalidated in simulated turbulent flow and thermal fiel(Moin & Spalart, 1989; Suzuki & Kasagi, 1992).

(3) DNSs provide precise turbulence statistics includpressure and any spatial derivatives, which are extremdifficult to measure. They are undoubtedly helpful evaluating and developing turbulence models. The statiand their budgets in various types of flows are availabltabulated forms at ftp sites (e.g., http://www.thtlab.ttokyo.ac.jp).

(4) The effects of various influential parameters can be stusystematically by DNS. Namely, dimensionless paramesuch as Reynolds, Prandtl, Richardson, Rossby, Hartmann numbers, can be systematically changedDNSs. Wall injection/suction effects on turbulent hetransfer have been examined by Sumitani & Kasagi (199

(5) Lastly, DNS can offer a chance to study even a virtual fand heat transfer. This is particularly meaningful evaluating possible turbulence control methodologies (Jet al., 1992; Choi et al., 1994; Satake & Kasagi, 1996).

DNS of Turbulent Heat Transfer at Various PrandtlNumbers

If we extensively exploit DNS of turbulent heat transfthe numerical as well as physical accuracy of DNS shouldfirst confirmed. In particular, the velocity field should habeen well examined before any argument in the heat traaspect is put forward. The DNS results have been repeacompared to the experimental data over the last decademost comprehensive verification has been made in the developed channel flow. In general, various statistquantities and the turbulent structures visualized in simulation are in close agreement with the experimental and observation both qualitatively and quantitatively.

Copyright ©1999 ASME

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As a typical example, the friction coefficients reportedseveral workers are compared with empirical formula in FigFour early simulations were made by using a pseudo-spemethod with Fourier series in the streamwise and spandirections and a Chebyshev polynomial expansion in the wnormal direction, whilst two recent simulations were made bsecond-order central finite difference method. Although DNSs of Kim et al. (1987) and of Kuroda et al. (1989, 95the bulk Reynolds number of Reb = 2ubδ/ν < 6000 usesufficiently large computational volumes (4~5πδ x 2δ x 2πδ),the two of Kim (1990) and Kawamura et al. (1998) adopsmaller volume (2πδ x 2δ x πδ) at Reb ~14,000 for savingcomputer storage. Here, δ is the channel half width. In thessimulations, the spatial and temporal resolutions are sufficieor marginally fine to capture all dynamically significant scaof turbulence. In spite of the difference in computatioconditions, the calculated friction coefficients agree well wthe formula of Dean (1978). Strictly speaking, all numerresults are smaller by a small fraction than the empirformula, and this is because the aspect ratio of the channmostly about 10 in the experiments, but assumed to

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Figure 1 Friction coefficient

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infinitely large in the DNSs.Another example is shown in Fig. 2, where three roo

mean-square velocity fluctuations divided by a local mvelocity are compared between the DNS of Kim et al. (19and experimental data of Kreplin & Eckelmann (1979) aNishino & Kasagi (1989). Although the comparison in thfigure is critical since both numerator and denominator huncertainties, almost complete collapse is observed betweeDNS and the data of Nishino & Kasagi, who used a thdimensional particle tracking velocimeter. There are discernerrors in the near-wall data of Kreplin & Eckelmann’s hot-fimeasurement. The reason for this has been found by SuzKasagi (1992) through their virtual calibration of hot-wires inDNS data that those errors are inherent in finite dimensionhot-wires, which can not assumed to be ideally small compwith the scales of turbulence diminishing toward the wComparison has also been extended from mean velocity tto the fourth-order moments of velocity fluctuations, aexcellent agreement has been confirmed. Thus, it can bethat, as long as respectable computational schemesnumerical conditions are employed, DNS offers reliastatistical quantities of turbulence (also see, KasagiShikazono, 1995).

Owing to a grid requirement, high Reynolds number Dis a difficult task, but DNS of turbulent heat and mass tranbecomes even more difficult as the Prandtl (or Schmnumber is increased. The ratio of the largest to smallest lescales in thermal turbulence is roughly proportional to Re3/4

Pr1/2 at high Prandtl numbers (Batchelor, 1959; TennekeLumley, 1972) and this means that the ratio of the grid porequired for thermal field Nθ to that for velocity field N isproportional to Pr3/2. For instance, Nθ/N is about 30 and 103 forPr = 10 and 100, respectively. Thus, the DNS of turbulent htransfer becomes much harder as Pr is increased. It is alsonoted that, when Pr is decreased, less grid resolution wouldrequired, but a care must be taken so that the computatvolume should be enlarged to capture larger scales of theturbulence.

Since the DNSs of turbulent heat transfer in channel fat Pr ~ 1were made at Reτ = 180 by Kim & Moin (1989), and aReτ = 150 by Lyon & Hanratty (1991) and Kasagi et al. (199those at lower Pr were also carried out at Reτ = 150 by Kasagi& Ohtsubo (1993) and later at Reτ = 180 by Kawamura et a(1997). Here, Reτ (= uτδ/v) is the Reynolds number based on tfriction velocity and the channel half width. The statistiquantities of thermal turbulence have been collected and the budget terms in the transport equations of temperavariance, its dissipation rate and turbulent heat fluxes have quantitatively evaluated. In particular, Kasagi & Ohtsu(1993) claim that a major sink term for the turbulent heat

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pressure temperature-gradient correlation, which mainly bredown the heat flux at higher Pr numbers. Furthermore, theyhave found that even for low Pr the major transportmechanisms are closely related with the quasi-coherent vortstructures of wall turbulence (Kasagi et al., 1995).

High Pr heat transfer is a classical, but challenginproblem, of which DNS several recent workers have attemptWith a large scale parallel computer system, Kawamura et(1997) extended their DNS of turbulent heat transfer in uniformly heated channel to Pr = 5 at Reτ = 180; this DNS isthe first that has been run at sufficiently high Re and Prnumbers. The number of grids used for a computational voluof 6.4δ x 2δ x 3.2δ is 256 x 128 x 256, which is twice as manas that sufficient for the velocity field. The resultant grispacing is 4.5 and 2.25 wall units in the streamwise aspanwise directions, respectively, while non-uniform spacifrom 0.44 to 13.0 wall units is used in the wall-normadirection. They have reported systematic changes in statistical quantities such as the mean temperature, turbuheat flux and turbulent Prandtl number as Pr is increased. It isfurther confirmed that, at high Prandtl numbers, the presstemperature-gradient correlation is found dominant insteadthe molecular dissipation as a sink term in the turbulent hflux budget.

The Nusselt numbers calculated by the DNSs mentionabove and those of Hanratty and his colleagues (Lyons et 1991; Brooke, 1994; Na et al., 1998) are shown in Fig. 3. HeNu has been divided by Reb

0.8 so as to compare the data adifferent Reynolds numbers as a function of Prandtl numbAll the results are in good agreement with the valurecommended by Kays & Crawford (1980).

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Kays & Crawford (1980): Reb = 5000, qw= const Reb = 5000, Tw= const Reb = 15000, qw= const

Reb = 4540: Brooke (1994) Reb = 4540: Papavassiliou & Hanratty (1997) Reb = 4540: Na et al. (1998)

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Figure 3 Dependence of heat transfer coefficient onPrandtl number

An interesting attempt at high Pr DNS has been made byYano & Kasagi (1997). The idea they pursued was that, sinc

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only the spectra of thermal turbulence are broadened with Pr, itwould be possible to run only the simulation of thermturbulence on a finer grid, while using the original gsufficient for fluid turbulence. They ran DNSs of forchomogeneous isotropic turbulence with a constant tempergradient at Re = k2/νε = 30 - 85 and Pr = 0.7 - 100, and foundthat it is actually possible to perform DNS at a Prandtl nummuch larger than unity with moderate increase in computatiload. This was done by employing, only for the temperafield, approximately Pr 3/2 times more grid points than thosrequired for the velocity field.

As an example, instantaneous thermal fields at Pr = 0.7and 20 are compared in Fig. 4, where the contours of sqtemperature gradient Gi

2 = ∂θ / ∂xi( )2 are represented. Thdistribution of Gi

2 at Pr = 0.7 is somewhat blurred, whilst that Pr = 20.0 clearly exhibits finer structures. However, bglobal patterns are indifferent; the fine thermal structures

(a) Pr = 0.71

(b) Pr = 20

Figure 4 Instantaneous distributions of squaretemperature gradient at different Prandtl numbers

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also associated with continuous deformation due to large-scvortical motions. This association of the temperature gradieinto a vortical motion, which is called wrapping (Guezennec al., 1990), becomes more remarkable at higher Pr numbers.Thus, the low-wave number components of velocity fluctuatioseem to cause mainly the cascade of temperature fluctuatThis qualitative understanding has been separately verifiedan analysis of the transfer functions of temperature variancewave number space. It indicates that, irrespective of Prannumber, two close wave number modes of temperature anlower wave number mode of velocity should be responsible the cascade transfer in the way similar to the cascadeturbulent kinetic energy. Also note that the microscale temperature fluctuation is found to be proportional to Pr1/2 ingood agreement with the prediction of Batchelor (1959).

Although the above method of saving grid points at higPr has not been accessed systematically in the DNS of wturbulence, De Angelis et al. (1997) have adopted a simitechnique for a DNS of free surface turbulence with matransfer at Schmidt numbers of 10 and 25. At these Sc numbers,they limit their simulation of mass transfer to a near-wall regioat y+ < 43 where significant mean gradients are expected, whsolving the turbulent flow field at y+ < 171 with the samenumber of grid points. Hence, a more grid density is given the concentration field than the velocity field. They havobtained mass transfer coefficients in good accordance wlaboratory experiments.

Another promising technique of simulating high Prnumber thermal turbulence has been proposed by Papavass& Hanratty (1997). Their method is Lagrangian simulation othe dispersion of heat markers from wall sources, with whithey carry out DNSs of turbulent heat transfer at Pr = 0.1 –2400. The flow field at Reτ = 150 is simulated by an EularianDNS with a 128 x 65 x 128 grid, and the trajectories of hemarkers from a wall are calculated by assuming that a markeeach time step ∆t has the velocity of the fluid particle, whichconsists of convective and molecular effects. The convectvelocity is estimated from the DNS, while the moleculadiffusion is simulated by imposing a three-dimensional randowalk of a Gaussian distribution with zero mean and standadeviation 2∆t / Pr in wall units. They successfully observedthe transfer mechanism in the close vicinity of the waincluding the wall-limiting behavior of turbulent fluxes atextremely high Pr numbers. Their results of heat transfecoefficient are also included in Fig. 3, where it is evident ththey are consistent with other DNSs.

Buoyancy Effect on Turbulent Heat TransferTwo distinct modes of forced and natural convection ofte

appear combined together in engineering applications a

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environmental flows, e.g., in heat exchangers, turbine blasolar panels, nuclear reactors, electronic equipment geophysical flows. Among this type of convective flows, whthe mean flow is driven in the horizontal direction, it is callstratified flow, of which stratification is either stable ounstable. When unstable stratification is imposed, turbulencenhanced, whilst under stable stratification turbulendiminishes and eventually becomes relaminarized (Narashi& Sreenivasan, 1979; Tritton, 1988). It is also known thunder strong stratification, characteristic fluid motiogenerated by buoyancy, i.e., the internal gravity waves thermal plumes, interact with turbulence (Turner, 197Although detailed measurements are extremely difficult, solaboratory experiments have been carried in horizonboundary layer and channel flows to reveal buoyancy effectswall turbulence (Kasagi and Hirata, 1977; Komori et al, 19Fukui et al., 1983, 1991).

On the other hand, upward flows along heated and covertical walls are respectively referred to as aiding aopposing flows depending upon the combination of directions of flow and buoyancy. The experiments in literatshow that in the aiding flow both the turbulence and the htransfer rate are suppressed in spite of the increased meanvelocity, whereas in the opposing flow the turbulence activityenhanced with the mean velocity decreased (Jackson e1989).

The buoyancy effects on turbulence and heat transfer hbeen intensively studied by DNSs, but in many caseshomogeneous shear flows with stable stratification (Gerz et1989; Holt et al., 1992; Jacobitz et al., 1997). There are onfew DNSs of wall turbulence under stable (Coleman et 1992; Iida et al., 1997a) and unstable (Domaradzki & Metca1988; Iida & Kasagi, 1997) stratification, and of the aiding aopposing flows (Kasagi & Nishimura 1997).

Hereafter, two kinds of channel flows are examined. Tfirst one is a fully developed horizontal turbulent channel fl(Iida & Kasagi, 1997; Iida et al., 1997a), and the second onthe vertical channel (Kasagi & Nishimura 1997); in both cathe walls are kept at different, but isothermal temperaturesthe former the buoyancy due to stable or unstable denstratification does not affect directly the mean field, but othrough the turbulent fluctuations, whereas in the latter buoyancy force has a substantial effect on the mean fbalance. This distinct mechanisms can be inferred examining the transport equations of the second-order momof turbulent fluctuations (Launder, 1978).

The geometry and coordinate system of horizontal chanflow are shown in Fig. 5. The Reynolds number Reτ (= uτδ/v)was kept at 150, while the Prandtl number was assumed t0.71. In the DNS of the unstably stratified flow, the Grash

Copyright ©1999 ASME

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number Gr (= gβ (∆T)(2δ)3/ν2), which is based on thetemperature difference between the two walls ∆T (= Th - Tc)and the channel width 2δ, was varied from 0 to -4.8x106. On theother hand, in the stably stratified flow, Gr was varied from 0to 2x107. All of these DNSs at different Grashof numbers acalculated by a pseudo-spectral method (Kim et al., 1987) relatively coarse grid, i.e., 64 x 49 x 64 in the x-, y- and z-directions, respectively. These results are mainly usedexamine qualitatively the dependence of the flocharacteristics on the imposed buoyancy. In order to assesnumerical accuracy, a fine grid of 128 x 97 x 128 is usedsome typical cases.

Figures 6 and 7 show the changes in the normalifriction coefficient and Nusselt number versus the bRichardson number Rib (= Gr/Reb

2), respectively. In Fig. 7, twokinds of Nusselt numbers are plotted, i.e., Nu* represents thedimensionless heat transfer coefficient based on temperature difference between the two walls, while Nu isbased on the wall to bulk mean temperature difference. Uunstable stratification, as the Richardson number is increathe friction coefficient first decreases and takes a minimaround Rib = 0.05. This is because the buoyancy-drivsecondary flow deteriorates the near-wall turbulence increases the thickness of the viscous sublayer as disculater. When Rib further increases, Cf starts to increase becausthe contribution of the secondary flow to the momenttransfer is more enhanced. On the other hand, the Nunumber Nu simply increases with Rib, although it shows aplateau around Rib = 0.05. In the stably stratified channel, boCf and Nu decrease markedly with increasing Rib. It has beenconfirmed separately that, when Rib reaches 0.54, the flowbecomes almost relaminarized (Iida et al., 1997a). Itinteresting that in both cases of stratification the buoyaforce causes a larger change in the Nusselt number than iskin friction coefficient. Note also that the DNSs agree wwith previous experimental results (Fukui et al., 1983).

The logarithmic plots of the mean velocity and temperat

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distributions are shown in Figs. 8 and 9, respectively. Inunstably stratified cases, the mean velocity in the chacentral region tends to decrease. However, at Gr = -1.3x106, themean velocity increases in the buffer as well as logarithregions; this is associated with the aforementioned decreathe friction coefficient. Although not shown here, this increaof the mean velocity is mainly due to the reduction of Reynolds shear stress in the region at y+ < 30. When themagnitude of Gr is further increased to Gr = -4.8x106, the meanvelocity decreases in almost all regions. As a result, the sproduction of Reynolds shear stresses decreases over the channel cross section, and both the pressure and turbdiffusions become more important. This is similar to ttransport mechanism in the wall turbulence with a redushear rate (Kuroda et al., 1995; Hunt, 1984).

In the stably stratified channel, the mean velocity tendincrease in the region y+ > 10. Namely, the thickness of thbuffer region increases and the logarithmic region disappeThis should be because, under stable stratification,

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

Cf /

Cf0

5 6 7 8 9

10-2

2 3 4 5 6 7 8 9

10-1

2 3 4 5

|Gr/Reb2|

DNS (fine) DNS (coarse) Iida & Kasagi (1996) Iida et al. (1997a)

Stable

Unstable

Fukui et al. (1983)

Figure 6 Dependence of the normalized skin frictioncoefficients on bulk Richardson number

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

Nu

/ Nu 0

, N

u* / Nu 0

*

5 6 7 8 9

0.012 3 4 5 6 7 8 9

0.12 3 4 5

|Gr/Reb2|

DNS (fine) DNS (coarse) Nu / Nu0 Iida & Kasagi (1996) Nu*/ Nu0

* Iida & Kasagi (1996) Nu / Nu0 Iida et al. (1997a) Nu*/ Nu0

* Iida et al. (1997a)

Fukui et al. (1983)

Unstable

Stable

Figure 7 Dependence of the normalized Nusseltnumbers on bulk Richardson number

Copyright ©1999 ASME

tc

mmdt

uanthnk

nt

n

ae

rmalergecesnentinedt thesi-ous

tion are

asmberf the

turbulence structure becomes smaller and indifferent to distance from the wall, i.e., Z-less scaling of the turbulen(Stull, 1988), and the assumption of the standard logarithlaw becomes invalid. The disappearance of the logarithregion is also confirmed in the DNS of a rotating pipe (Orlan& Fatica, 1997), and this fact supports analogy between effects of rotation and stratification (Bradshaw, 1969).

The effects of stratification on the mean temperatdistributions are similar to those observed in the mevelocity profiles, so that the similarity between the turbuleheat and momentum transfer is almost valid even in horizontally stratified flows. However, the change in tmean temperature profile is more marked in the chancentral region, where the gradient Richardson number tathe largest value.

A typical example of instantaneous velocity vector atemperature distributions in a cross-stream plane of unstable channel flow at Gr = -1.3 x 106 is shown in Fig. 10;this is the case in which the skin friction coefficient is fouto decrease compared to the case without buoyancy. Bthermal plumes and quasi-streamwise vortices can be cleidentified. The large-scale downward and upward plum

25

20

15

10

5

0

U +

100

2 3 4 5 6 7 8 9

101

2 3 4 5 6 7 8 9

102

2

y +

Gr =0 : Kuroda et al. (1993)

Gr = -1.3x106 : Iida & Kasagi (1997)

Gr = -4.8x106 : Iida & Kasagi (1997)

Gr = 4.4x106 : Iida et al. (1997a)

Gr = 1.0x107 : Iida et al. (1997a)

U+ = 2.5 ln y + + 5.0

Stable

Unstable

Figure 8 Logarithmic plot of the mean velocity

25

20

15

10

5

0

Θ ΘΘΘ +

100

2 3 4 5 6 7 8 9

101

2 3 4 5 6 7 8 9

102

2

y +

Gr =0 : Kasagi et al. (1992)

Gr = -1.3x106 : Iida & Kasagi (1997)

Gr = -4.8x106 : Iida & Kasagi (1997)

Gr = 4.4x106 : Iida et al. (1997a)

Gr = 1.0x107 : Iida et al. (1997a)

Stable

Unstable

Figure 9 Logarithmic plot of the mean temperature

heeicici

he

rent

heeeles

dhe

dothrlys

are seen at the center and two sides of Fig. 10. The theplumes as large as the width of the channel height emfrom the near-wall region. The quasi-streamwise vortiseem to be swept out by the spanwise flow compoinduced by the plumes and concentrated into the confregions where another thermal plume emerges. Note thaturbulent skin friction is closely associated with the quastreamwise vortices (Robinson, 1991). Hence, the viscsublayer thickens due to the plumes and the skin friccoefficient decreases. However, the large-scale plumesalso effective in transporting heat between two wallsshown in Fig. 10, so that the decrease of the Nusselt nushould not appear despite the increased thickness o

z

y

Figure 10 Instantaneous velocity vectors andtemperature fluctuations in the y-z plane ( ∆∆∆∆y+ x ∆∆∆∆z+ =300 x 943) of the unstably stratified channel ( Gr = -

1.3x106): blue to red; θθθθ /∆∆∆∆T = -0.15 to 0.15

x

y

(a) With pressure fluctuations:blue to green, p+ = -4 to 0

x

y

(b) With temperature fluctuations:blue to red, θθθθ /∆∆∆∆T = -0.15 to 0.15

Figure 11 Instantaneous velocity vectors ( U + u, 12v)in the x-y plane ( ∆∆∆∆x+ x ∆ ∆ ∆ ∆ y+ = 2356 x 300 with the x-

axis compressed to one half) of the stably stratifiedchannel ( Gr = 1x107)

Copyright ©1999 ASME8

e nn

96;

lowuresu

Fth

luidnccity-encity, th th wsu af thticeeti(bar

irec thn tiedvestia

eatall-

e

sublayer. The deterrence of the near-wall turbulence duthe secondary flow is also observed in the turbulent chaflow under system rotation (Nishimura & Kasagi, 19Bech & Andersson, 1996).

The stable stratification generates the unique fstructures, which contribute little to heat transfer. Fig11(a) shows an example of velocity vectors and prescontour in the x-y plane at Gr = 1 x 107, while Fig. 11(b)shows temperature fluctuations at the same instance. In11(a), the wave-like motions are clearly observed in channel central region. The characteristics of this fmotion are studied statistically by the phase differebetween the streamwise and wall-normal velofluctuations, which shifts from zero to +π/2. They are the socalled internal gravity waves, because the phase differbetween the temperature and wall-normal velofluctuations also becomes +π/2 (Stull, 1987; Komori et al1983) and their correlation diminishes to almost zero inchannel central region. Figure 11(a) also shows thatelongated low-pressure regions are formed between theand the crest of the internal waves. These low-presregions correspond to the streamwise vortices, whichextended down to the wall and entrained into the crest owaves. The internal gravity waves and streamwise vorinteract through pressure, by which the turbulent kinenergy is exchanged. However, it is found from Fig. 11that the intensive temperature fluctuations, which associated with the internal gravity waves, are not in dcontact with the heated and cooled wall, but confined inchannel central region. Hence, the heat transfer betweetwo walls is seriously impeded. In the stably stratifchannel, the dynamically important internal gravity wado not contribute to the heat transfer and works substanas an adiabatic layer.

-0.2

-0.1

0.0

0.1

0.2

Gai

n

L

oss

140120100806040200

y +

Iida et al. (1997) Gr = 4.4x106

Production

Buoyant Pruduction

Pressure Diffusion Turbulent Diffusion

Pressure-Temperature Gradient Correlation

Figure 12 Budget of the wall-normal turbulent heatflux

toel

re

ig.e

e

ce

ee

allrerees

c)etehe

lly

The effects of stable buoyant force on the turbulent htransfer are also observed in the budget terms of the wnormal turbulent heat flux, i.e., vθ , as shown in Fig. 12. Inthe budget of vθ (<0), the dominant source term is th

Th

Flow

2δ

Heated wall

(Aiding flow)

g

Cooled wall

(Opposing flow)

xy z

2πδ

5 πδ

Tc

Figure 13 Flow geometry and coordinate system forthe vertical channel

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

Cf /

C f 0

10-32 3 4 5 6 7

10-22 3 4 5 6 7

10-1

Gr/Reb2

Kasagi & Nishimura (1997) Aiding flow: DNS (fine) DNS (coarse) Opposing flow: DNS (fine) DNS (coarse)

Aiding flow: Nakajima et al. (1980) Opposing flow: Nakajima et al. (1980)

Cf /Cf0 = 1.006-10.26Gr/Reb2 : Easby (1978)

Figure 14 Dependence of normalized frictioncoefficient on buoyancy

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

Nu/

Nu 0

10-32 3 4 5 6 7

10-22 3 4 5 6 7

10-1

Gr/Reb2

Aiding flow: Nakajima et al. (1980) Opposing flow: Nakajima et al. (1980)

Kasagi & Nishimura (1997) Aiding flow: DNS (fine) DNS (coarse) Opposing flow: DNS (fine) DNS (coarse)

Nu/Nu0 = 1.009+17.82Gr/Reb2 : Easby (1978)

Figure 15 Dependence of normalized Nusselt numberon buoyancy

Copyright ©1999 ASME9

onure

tion

ntra aedve

entnd

ren 64geswn by

n.ethe

idinoodusbyrge

islek

ean theseltuming

oldssedeaningor andtheoldss athe

viateancyy the

production term due to the wall-normal velocity fluctuatiand the mean temperature gradient, while the pressscrambling term (pressure-temperature gradient correlacontributes to destruction of vθ . When stable densitystratification is imposed, the buoyant production, −gβθ 2 ,appears in the budget of vθ . It is evident in Fig. 12 that thisbuoyancy term takes the largest value in the channel ceregion, where the pressure diffusion term also works asadditional sink. Hence, the turbulent heat flux is dampsignificantly there. This fact is associated with the abomentioned internal gravity waves.

The buoyancy effect appears in an essentially differmanner in the vertical channel flow. The flow geometry acoordinate system are shown in Fig. 13. DNSs at diffeGrashof numbers were carried out on coarse (64 x 49 xas well as fine (128 x 97 x 128) grids. The relative chanof the friction coefficient and the Nusselt number are shoin Figs. 14 and 15, respectively. They are calculatedusing the following equations:

Nu = 2qwδ /(<T> - Tw)/λ, (1)Cf = 2τw /ρ<U>2, (2)

where < > denotes a bulk-averaged quantity over d, which isthe interval from the wall to the maximum velocity locatioIt is evident that Cf increases in the aiding flow (on thheated wall), while decreased in the opposing flow (on cooled wall), with increasing Gr/Rib

2. However, Nu exhibitsan inverse trend; it is decreased and increased in the aand opposing flows, respectively. These facts are in gagreement with the results found in the previoinvestigations, although the empirical formula of Eas(1978) seems to over predict the buoyancy effect at lavalues of Gr/Reb

2.The mean velocity profile in the global coordinates

shown in Fig. 16. It is evident that the velocity profibecomes more asymmetric as Gr increases. The pea

15

10

5

0

U*

-1.0 -0.5 0.0 0.5 1.0

y/δδδδ

Case 1 (Gr = 0)

Case 2 (Gr = 6.4×105)

Case 3 (Gr = 9.6×105)

Case 4 (Gr = 1.6×106)

(Aiding flow) (Opposing flow)

Figure 16 Mean velocity profile in global coordinates

1

-)

ln

t)

g

location shifts toward the aiding-flow side, where the mvelocity is accelerated by the buoyant force, and henceskin friction coefficient increases. The decrease of Nusnumber is also associated with the shift of the maximmean velocity toward the aiding flow side. On the opposflow side, the opposite changes take place.

In Figs. 17 and 18, Cf and Nu in both the vertical andhorizontal channels are plotted against the bulk Reynnumber Reb. Note that the bulk Reynolds number is now baon the distance from the location of the maximum mvelocity to the wall. The results of the opposing and aidflows agree fairly well with the standard correlation experimental data, i.e., Dean (1978), Patel & Head (1969)Kays & Crawfords (1980). Hence, the relaminarization in aiding flow should be due to the decreased bulk Reynnumber, while the opposing flow should be interpreted ahigher bulk Reynolds number flow. On the other hand, results of both stable and unstable density stratification demarkedly from the standard correlation, because the buoyforce and the associated secondary flow alter substantiall

10-3

2

4

68

10-2

2

4

68

10-1

Cf

103

2 3 4 5 6 7 8 9

104

Reb

Laminar

Dean (1978)

Patel & Head (1969)

Gr = -1.3x106 : Iida & Kasagi (1997)

Gr = -4.8x106 : Iida & Kasagi (1997)

Gr = 4.4x106 : Iida et al. (1997a)

Gr = 1.0x107 : Iida et al. (1997a)

Iida et al. (1997b) Kuroda et al. (1989) Kuroda et al. (1995) Kim (1990)

Kasagi & Nishimura (1996)

Gr = 9.6x105

: Aiding Flow : Opposing Flow

Figure 17 Skin friction coefficient versus bulkReynolds number

100

2

4

68

101

2

4

68

102

Nu

103

2 3 4 5 6 7 8 9

104

Reb

Kays & Crawford (1980)

Kasagi & Nishimura (1996)

Gr = 9.6x105

: Aiding Flow : Opposing Flow ---------------------------------------

Gr = 0 : Kasagi et al. (1992)

Gr = -1.3x106 : Iida & Kasagi (1997)

Gr = -4.8x106 : Iida & Kasagi (1997)

Gr = 4.4x106 : Iida et al. (1997a)

Gr = 1.0x107 : Iida et al. (1997a)

Figure 18 Nusselt number versus bulk Reynoldsnumber

Copyright ©1999 ASME0

thdbes

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turbulence structures and transport mechanism.

SMART CONTROL OF TURBULENT HEAT TRANSFERControl of turbulence and heat transfer has been one of

central issues in modern scientific, engineering anenvironmental research efforts. Its potential benefits can easily recognized if one thinks about the significance of thartificial manipulation of turbulent drag, noise, heat transfer awell as chemical reaction, to name a few. Over the sevedecades, many intensive investigations have been undertafocusing on possible heat transfer control techniques. Althouthere is a considerable degree of knowledge on such methodroughness/grooves, twisted tapes, blowing/suction and polymadditives, the major difficulty exists in controlling momentumand heat transfer independently. Namely, most heat transenhancement techniques are associated with an excess amof pressure loss penalty, and the real enhancement is usulimited to a low Reynolds number regime. An exception is thspirally fluted tube (Yampolsky, 1979), in which the swirlingvelocity caused by the flute on the inner tube surface maintacore-region turbulence low while enhancing heat transfer high Pr number fluids with the secondary flow in the flutecavity (Cheah et al., 1993). Dissimilarity between heat anmomentum transfer (Inaoka et al., 1998) does not take plaeasily without a particular flow arrangement, which may noalways be possible in real applications.

Efforts are now directed toward to active or interactivcontrol schemes, particularly those exploiting emerginmicromachining technology, called microelectromechanicasystems (MEMS) (Moin & Bewley, 1994; Ho & Tai, 1996;Jacobson & Reynolds, 1993). The turbulent structures in reflows are very small in size, typically several hundred micronin width and a few mm in length in wall turbulence. Theilifetime is also very short. In the past, direct manipulation othese structures was very difficult, but is now expected become possible with miniature sensors and actuators micron size fabricated by MEMS. This new technology offers batch production process, through which micromechanical paare produced in large quantities. A MEMS controller unit, withits integrated mechanical parts and IC, will be able to sense physical world, process the information, and then manipulathe physical phenomena through actuators. From thviewpoint, studies of active turbulence control now begin to usDNSs extensively for analyzing the effectiveness of proposcontrol algorithms (Choi et al., 1994; Moin & Bewley, 1995Satake & Kasagi, 1997; Lee et al., 1997) to lead the futudevelopment of MEMS controllers and systems. Two examplof latest DNSs are introduced below.

Endo et al. (1999) assumes an array of micro deformabactuators on a wall of turbulent channel flow for possible drareduction and heat transfer augmentation as shown in Fig.

1

e

e

lenhasr

runtlly

sf

e

l

f

s

e

s

e

9.

Choi et al. (1994) employed local blowing and suction, baon the instantaneous wall-normal velocity near the wall, obtained about 30% drag reduction by interfering with longitudinal vortices. Similarly, the velocity at the center each actuator is determined in the same manner as follows:

vwn+1 = −αyw

n + β vsn− < vs

n >( ) (3)

Here, vs is the wall-normal velocity detected at y/δ = 0.1 (y+ ~15), while vw is the velocity of the center of each wall actuatof which shape is given as a Gaussian distribution. The bra<χ> denotes an ensemble average of quantity χ in the x-z planeat each time step n. The first term on the RHS of Eq. (3) is damping term to suppress excessive wall deformation. Wheβis negative, the wall deformation would decelerate the flmovement near the wall.

The size of each actuator is to be optimized so that it wogive the best control result with the least number of actuatoris, however, anticipated to be on the order of the size oflongitudinal vortices, which play a primary role in momentuand heat transport in wall turbulence (Kasagi et al., 1995time trace of the relative change in pressure loss is showFig. 20, where the actuator is assumed to have a size of 50 × 7.3wall units in the x- and z-directions, respectively, with α = 2

Figure 19 Arrayed micro actuators (2x4) on a wall forturbulence control

1.2

1.0

0.8

0.6

0.4

0.2

0.0

<-dp

/dx >

c/<

-dp/

dx> 0

___

___

10008006004002000

t*

Without control

Laminar flow

With control

Figure 20 Time trace of normalized pressure gradientin channel flow

Copyright ©1999 ASME1

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kel-ureul 0 %male- thlesody

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t is by, is thece.sferientonss. Itthetessfer

itherureall

ctive iscted

and β = -1. It is evident that the array of elongated micactuators with a simple control algorithm works efficiently drag reduction.

In a recent experimental investigation of turbulent htransfer in a gas-particle two-phase flow, Hishida and Ma(1994) tried to exploit soft magnetic particles made of niczinc-ferrite, which lost magnetism when their temperatexceeded the Curie temperature. They were successfenhancing the local heat transfer coefficient as much as 6This idea can be conceptually extended to fabrication of sparticles with the aid of MEMS. Hence, DNS of a particladen channel flow has been made to further explorepossibility of enhancing heat transfer with intelligent particby Arai et al. (1998). The particles are endowed with a bforce on-off switching depending on temperature.

The motion of each particle is calculated in a Lagrangframe by using the equation of motion:

dup,i+

dt+=

1

τ p+ uf ,i

+ − up, i+( )+ ae

+ θ p*( )δi ,2

(4)

where all variables are made dimensionless with the variables, and subscripts f, p and 2 denote fluid, particle and th

8

7

6

5

4

3

2

1

0

P( y

p | y

< y

p< y+

dy)

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

y/δδδδ

without body force θ sw

* = 0.05 θ sw

* = 0.1 θ sw

* = 0.15

Figure 21 Particle Number Density Distribution

1.0

0.8

0.6

0.4

0.2

0.0

<v pθ θθθ p>

/ vp,

rm

sθ θθθ p, r

ms

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9

100

y+

without body force θ sw

* = 0.1

θ sw

* = 0.05 θ sw

* = 0.15

Figure 22 Relative Correlation Coefficient of Wall-Normal velocity and Temperature Fluctuations of

Particle

1

ta

in.

rt

e

ll

wall-normal direction, respectively. Note also that the first asecond terms on the RHS of Eq. (4) are the Stokes drag and the virtual body force, respectively. It is assumed thatflow field is affected by the particles only thermally, but ndynamically. The heat transfer coefficient around the particgiven by the empirical formula of Ranz (1952). The virtuforce term in Eq. (4) is a function of the temperatnormalized by the temperature difference between two chawalls as follows:

ae+ θ p

*( )=− 0.5 0≤θ p

* ≤θsw*( )

+ 0.125 θsw* < θ p

* < 0.5( )

(5)

where θp* is the threshold temperature, at which the body fo

changes its acting direction. Namely, the particle is pusaway from the wall in the near-wall region, whilst attractoward the wall in the central region of the channel. Tmagnitude of body force is assumed to be on the same ordthat of the Stokes drag, so that the work of driving the partishould be small enough to assure the net heat traaugmentation.

The particles’ conditions are given by referring to Hishand Maeda: i.e., the density ratio, ρp/ρf = 4460; the specific hearatio, cp/cf = 0.76; the relaxation time constant of particle, τp

+ =(ρp/ρf)/(dp

+2/18) = 5.2; the thermal relaxation time constantparticle, τθ

+ = 3(cp/cf) τp+Pr/Nup = 4.2; the dimensionles

particle diameter, dp+ = 0.1448; the mass loading ratio, φm =

0.069; Reτ = 150, and Pr = 0.71. The threshold temperaturechanged as θp

* = 0.05, 0.1 and 0.15, which roughly correspoto the mean temperatures at y+ = 2.5, 5 and 10, respectively.

As a result, it is found that the heat transfer coefficienincreased by 3.3% by simply introducing particles, but even16%, 11.7%, and 9% when θp

* = 0.05, 0.1 and 0.15respectively. The probability density of particles’ locationshown in Fig. 21. The peak concentration moves away fromwall as θp

* is increased, otherwise it exists on the wall surfaThe contribution of these intelligent particles to heat trancan be evaluated in Fig. 22, where the correlation coefficbetween the wall-normal velocity and temperature fluctuatiof the particle is compared with that of the inactive particleis evident that the correlation is significantly improved by body force at y+ < 10, where the conductive heat flux dominathe turbulent heat flux. Note that the magnitude of heat tranaugmentation should increase with the mass loading ratio.

Instantaneous flow fields are shown in Fig. 23. Wvirtual body force, the distribution of particle is no longuniform, but exhibits clustering along the high-temperat(low-speed) streaks (Iritani et al., 1984) in the viscous wregion. Thus, the particles transport heat outside the condusublayer more efficiently. Since the particle’s diameterassumed to be very small in these simulations, it is expe

Copyright ©1999 ASME2

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that its dynamical effect is mainly dissipative so that thturbulent friction drag would not increase, but may decreasThis point remains to be fully resolved in the future work.

As modern knowledge on the structure of turbulent flow isuccessfully exploited in choosing the effective mode omanipulation in the above DNSs, an attempt at controlling thturbulent heat transfer is based on empiricism or intuition many cases. Hence, it is a desirable option to cast this problinto the framework of optimal control theory; i.e., the spatiotemporal distribution of control input should be optimized inthe sense that the maximum control performance is achievwith the least control input energy. Recently, by simplifying theoptimal control theory (Abergel & Temam, 1990), Choi et a(1993b) devised a suboptimal feedback control algorithm fothe Navier-Stokes equations and applied it to the stochasBurgers equation. Later, this suboptimal control scheme wsuccessfully used in optimizing proposed control modes fdrag reduction in channel flows by Choi (1995), Moin &Bewley (1995), and Satake & Kasagi (1997). Different types active feedback control algorithms based upon adaptischemes and dynamical systems theory are also being stud(Moin & Bewley, 1994). For instance, a nonlinear adaptiv

x

z

(A) without body force

x

z

(b) with body force ( θθθθsw* = 0.05)

Figure 23 Particle concentration at y+ < 7 andtemperature fluctuation at y+ = 2.9 (∆∆∆∆x+ x ∆∆∆∆y+ = 2356 x

300): blue to red corresponds to low to hightemperatures

1

.

d

c

d

algorithm, called neural networks, has a wide range applicability (Jacobson & Reynolds, 1993; Lee et al., 199since it does not require precise mathematical description ofsystem nor empirical knowledge on physical mechanismThese new proposals for smart turbulent heat transfer conshould also be tested and evaluated through the further usDNSs.

CONCLUDING REMARKSDirect numerical simulation offers valuable numerica

experiments for turbulence heat transfer research. With hperformance computers, reliable numerical methods aefficient post-processing environment, a variety of applicatioof DNS are possible. In particular, one can extensively stuthe turbulence dynamics and transport mechanism visualizing any of physical variables in space and time. It also possible to establish detailed database of variturbulence statistics in turbulent transport phenomena, whsystematically changing important flow and scalar fieparameters.

The present paper has illustrated such novelties of DNSintroducing several examples of recent studies. An effort reveal the Prandtl number effect on turbulent heat transfesketched with the new techniques developed for making Dover a wide Prandtl number range possible. Both methodssaving grid points and Lagrangian particle tracking are veuseful in the future research on turbulent heat and mtransfer. The complex buoyancy effects on turbulent transpare systematically investigated in a series of DNSs of horizonand vertical channel flows. It has been observed that buoyancy effect appears distinctly depending upon tdirectional alignment of the buoyant force and the mean floIn the vertical flow, the buoyancy can be interpreted as increased or decreased Reynolds number effect, whilst in horizontal flow it can cause substantial alternation in tturbulence structures and transport mechanism so that resultant heat transfer coefficient would behave in a much mcomplex manner. The thermal plumes and internal gravwaves characteristic of these flows play an important role in interaction with the quasi-coherent structures of waturbulence.

Finally, DNSs have been introduced to the work on actiturbulence and heat transfer control, in which an array of mideformation actuators on a wall surface or intelligent micparticles are tested. It is shown that these control schempossibly bring about notable turbulent friction drag reductioand heat transfer enhancement. A perspective view is given DNS will be even more useful in evaluating future turbulencontrol methodologies based on new algorithms such optimum control theory and neural networks. These simulatio

Copyright ©1999 ASME3

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tal

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have been triggered by the rapid development of MEMtechnology, but hopefully future DNSs will lead furthedevelopment of MEMS-based controller units integrating micsensors, micro actuators and IC. There are yet many combut important problems of turbulent transport such multiphase flows and those with chemical reactions, of whDNSs should be challenged. Thus, there is no doubt that Dwill serve continuously as a powerful tool for fundamenturbulence research in the coming century.

ACKNOWLEDGEMENTSThe authors are grateful to Professors T. J. Hanratty,

Kawamura and Y. Nagano for offering their DNS data to tpresent work.

REFERENCESAbergel, F., and Temam, R., 1990, “On Some Cont

Problems in Fluid Mechanics,” Theor. Comput. Fluid Dyn.,Vol. 1, pp. 303-325.

Adam, Y., 1977, “High Accurate Compact ImplicMethods and Boundary Conditions,” J. Comput. Phys., Vol. 24,pp. 10-22.

Arai, Y., Mizuya, T., Kasagi, N., and Suzuki, Y., 199“Numerical Simulation of Turbulent Hear Transfer Controlleby Dispersed Solid Particles, Proc. 35th Natl. Heat TransferSymp. Japan, Nagoya, Vol. 3, pp. 775-776.

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