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An simple explicit approximation of the Prandtl-Karman equation for the friction factor of smooth pipes, λ＝ 1/（－61＋36.84Re0.1）, was obtained by using CurveExpert for regression analysis. The data of friction factors were accurately calculated from the inverse function of the Prandtl-Karman equation, instead of approximate values by the usual iterative method. The obtained approximation has a standard deviation of relative errors to the Prandtl-Karman equation of 0.082% over the whole range of desired Reynolds numbers （Re＝105～107）, with all relative errors being within the range of －0.239%～ ＋0.180%. Such errors are shown to be about one order of magnate smaller than those of all other simple approximate equations compared., 滑らかな円管の管摩擦係数λの計算に用いるPrandtl-Karmanの式に対し，回帰解析ソフトウェアCurveExpertを用いて，簡易な陽的近似式λ＝ 1/（－61＋36.84Re0.1）を得た。回帰に用いたλの値は従来の繰り返し法による近似値ではなく，Prandtl-Karmanの式の逆関数から直接計算した精確な値であった。 この簡易な近似式の予測値は所定レイノルズ数Re＝105～107内において，Prandtl-Karmanの式との相対誤差の標準偏差は0.082％のみで，全ての相対誤差は－0.239％～＋0.180％の範囲内におさまることと，この誤差範囲は比較されたほかの比較的簡易な近似式または実験式に比べ， 1 ケタ程度小さいものであることがわかった。

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航空宇宙技術研究所 24-26 Jun. 1998 東京 日本, National Aerospace Laboratory 24-26 Jun. 1998 Tokyo Japan, 回転曲管内の流体の流れは遠心力、コリオリ力および浮力の3種類の体積力を受ける。加熱された回転コイル管における完全層流について、類似論拠および数値的研究を通して、調べる。壁における熱的境界条件は軸方向に熱流束一定、周方向に壁温一定とする。流れと熱伝達の特徴は、これらがディーン数、プラントル数、体積力比および浮力パラメータの4つのパラメータによって支配される場合に対して、明らかにする。速度場および温度場の詳細な構造をこれらパラメータの広範囲にわたって示す。摩擦因子および平均熱伝達速度に関する計算結果も示す。, The fluid flowing in rotating heated curved pipes is subjected to three body forces: centrifugal, Coriolis and buoyant forces. Fully developed laminar flow in heated rotating coiled pipes is investigated through similarity arguments and computational studies. The thermal boundary conditions at the wall are uniform wall heat flux axially and uniform wall temperature peripherally. Flow and heat transfer characteristics are elucidated for the case when they are governed by four parameters: Dean number, Prandtl number, body force ratio and buoyancy parameter. Detailed structures of velocity and temperature fields are shown for wide range of these parameters. Computed results on the friction factor and the mean heat transfer rate are also given., 資料番号: AA0001958060, レポート番号: NAL SP-41

An experimental investigation on heat transfer enhancement was performed for a smoothed and a straight-ribbed tube. Two trypes of wire-coil and a twisted tape as heat transfer promoters were inserted in both tubes, and the effects of heat transfer enhancement were examined. Heat transfer coefficients were obtained by means of Wilson Plot's method in range of 300 to 30000 for the Reynolds number. The friction factor was calculated from the pressure drop between both ends of a tube under the condition of the same pumping power.In this study, heat transfer performance was evaluated by comparing with a snoothed tube.All promoters were more effective in the laminar flows than in the turbulent flows. It was found that the augmentation of heat heat transfer for twisted tape in a straight rib-tube, caused by turbulence due to spiral flows, is sensitive., ここ数年，エネルギー資源は需給のバランスから安定期にあったが，近い将来には，化石燃料資源は枯渇の問題を抱えている。そのため化石燃料に代わるエネルギーの開発や太陽光エネルギー利用などが模索されている。しかし，代替エネルギーの開発は困難でり，未だ化石燃料に依存する部分が多い。このような状況の中，高炉ガス関係や燃料電池関係などの高温廃熱および低熱源の廃熱など熱エネルギー源となるものは種々あり，これらの廃熱回収などは熱エネルギー有効利用の一つにあげられる。そのため，廃熱回収などこれからの熱交換器は高温度差のみでなく，低温度差での熱交換が要求される。近年，省エネルギーのために熱交換器の性能向上は特に重要視され，そのためにも，伝熱促進技術は熱エネルギー有効利用に欠くことのできないもののひとつである。伝熱促進技術のうち管内伝熱促進法を大別すると，(A)伝熱面近傍に比較的小さな突起物（円柱，三角柱，半円柱など）を設け伝熱面近傍の境膜を撹乱させる方法，(B)ねじれテープ等を管内に挿入し主流を旋回させ，主流と管壁近傍の流れを入れ替える方法，(C)比較的大きな円環などを管路に一定間隔で並べ，主流を撹乱させる方法などがある。いずれの伝熱促進法においても伝熱の向上が認められ，熱交換器の高性能化及び小型化に寄与する。伝熱促進を図る簡便な方法のひとつとして，伝熱促進体を用いる方法が上げられるが，最適促進体形状の追求においては，促進体を挿入した場合の総合的な性能評価が必要になる。経済性，安定性，信頼性等を考慮する必要があるが，一般的に基準となる性能評価はないのが実情である。促進体挿入による圧力損失の増大はエネルギーの有効利用の見地よりマイナスとなる。そこで当研究室では，伝熱促進（プラス面）と圧力損失の増大（マイナス面）の両者を考慮した性能の評価方法として，等ポンプ動力基準の性能比を評価の基準として行う方法を用いる。実験は管内構造条件（管内壁面構造，ワイヤーコイル，リボンの有無）を変えて行った。

Fully developed steady laminar flow of viscous fluid in straight rectangular ducts rotating about a parallel axis is analyzed numerically. Thermal boundary condition of axially uniform wall heat flux is considered. Numerical results of flow and temperature field in ducts with aspect ratio from 0.2 to 5 are obtained for ReRa_Ω number upto 6.725×106 (for Re numbers upto 1346) and Prandtl number from 0.3 to 400. At low to moderate ReRa numbers, a double-vortex secondary flow is exist under the influence of buoyancy due to centrifugal force field. It is found that a pair of additional vortices appear and disappear for higher range of ReRa_Ω numbers. It is shown that tritical number of ReRa_Ω for onset of additional vortices is affected by Prandtl number and aspect ratio. The friction factor and Nusselt number are pressented. The solution is compared with other analyses.

Sea level change and global warming may cause increasing of external forces due to tides, currents and waves acting on breakwaters. Increase of breakwater weights or additional weight behind of present breakwaters become necessary against such external forces. A counter-weight block is newly developed to increase the resistance against horizontal sliding of breakwaters located at entrance of harbors. In the paper, a physical experiment is carried out to evaluate the friction factor of the counter-weight blocks and to compare with a normal type flat armor concrete block. The friction factor of counter-weight block with rubbles inside the center hole becomes larger than that of the normal one. A simple expectation formula calculating the effect of counter-weight block is proposed according to the experimental result.

Numerical analysis is conduced on the forced convection heat transfer in rectangular ducts with aspect ratios 0.2, 0.5, 2.0 and 5,0, rotating at a constant angular velocity about an axis perpendicular to its axis. Navier-Stokes and energy equations are solved by a finite-difference method in the fully developed region of laminar flow. Velocity and temperature fields are obtained for various rotation rates and Reynolds numbers at each aspect ratio of the duct. A double-vortex secondary flow appears at low to moderate rotation rates. An additional pair of vortices appeared and disappeared for a higher range of Reynolds numbers due to aspect ratios of the ducts. The friction factor and Nusselt number are influenced by the Coriolis force and aspect ratio. Numerical results of the friction factor for aspect ratios equal to 0.5 and 2.0 are in good agreement with experimental results by other researchers.

A numerical investigation was made on fully developed laminar forced convective heat transfer in curved rectangular ducts rotating at a constant angular velocity about an axis through the center of curvature of ducts. Thermal boundary conditions of fluid flow are assumed to be subject to uniform wall heat flux. Navier-Stokes and energy equations are solved by the finite difference method for air. The case for the negative rotation of a duct is considered. Velocity and temperature fields are obtained for various rotation rates and Re numbers. It is found that an additional pair of vortices appears in the vicinity of the inner wall under the influence of Coriolis force and in the vicinity of the outer wall under the influence of centrifugal force. The friction factors and Nusselt numbers are also obtained. The numerical results in regard to the friction factors are in good agreement with experimental results obtained by other researchers.

Fully developed steady laminar flow of viscous incompressible fluid in straight square ducts rotating at a constant angular velocity about an axis perpendicular to its axis under thermal conditions of axially uniform wall heat flux and peripherally uniform wall temperature at any axial position is studied. Numerical solutions were obtained for R_eR_Ω numbers from 10 to 10^5 (for R_e numbers form 1 to 4200). At low to moderate R_eR_Ω numbers, a double^vortex secondary flow appears under the influence of the Coriolis force. For higher R_eR_Ω numbers it is found that an additional counter-rotating pair of vortices appeared and disappeared for the range of R_Ω numbers from 10 to 100. Correlation equations for friction factors and Nusselt numbers are obtained from numerical results. The numerical results in regard to the friction factor and Nusselt number are in good agreement with experimental and analytical results by other reseachers for circular pipe.

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