JP4797157B2 - Method and program for estimating fluid and thermal characteristics of turbulent flow with buoyancy - Google Patents
Method and program for estimating fluid and thermal characteristics of turbulent flow with buoyancy Download PDFInfo
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本発明は，各種機械，電子機器等の流体による放熱設計や，冷暖房時の室内気流の解析等において必要となる，熱移動によって発生した浮力を伴う乱流の流体的及び熱的諸特性を推定する方法およびコンピュータによって実行可能な，浮力を伴う乱流の流体的及び熱的諸特性の推定プログラムに関するものである． The present invention estimates the fluid and thermal characteristics of turbulent flow with buoyancy generated by heat transfer, which is necessary for heat dissipation design by fluids of various machines, electronic devices, etc., and analysis of indoor airflow during cooling and heating. And a program for estimating the fluid and thermal properties of turbulent flow with buoyancy that can be executed by a computer.
熱移動を伴う流れ場を有する場合の，放熱特性や流体の圧力損失を算出することは，たとえば電気機器等の電子部品の実装密度を高め，省スペースに設計する場合などに必要である．これらを実験的に求めることが一般に行われているが，試作等を要するため多くの時間とコストがかかるという問題がある．
熱移動を伴う流れ場を，シュミレーションし解析的に解く為には，連続の方程式，運動の方程式であるナビエストークス方程式及びエネルギー式を解く必要がある． 流れが層流である場合は，流れの現象をあらわす運動方程式等は乱流の場合に比較して簡単であり，方程式を解くことにより計算できる場合が多いが，実際の機器においては，多くの場合流れは乱流となっており，解析的に解を求めることはできないのが実情である．
乱流の場合にこれらの方程式を解くことを困難にしているのは，レイノルズ平均化されたナビエストークス方程式のなかにあるレイノルズ応力項と，同じくレイノルズ平均化されたエネルギー式の中にある乱流熱流束項である．レイノルズ応力項は速度変動部分の積の平均であり，乱流熱流束項は速度変動と温度変動の積の平均であるから，乱流現象を厳密に小変動にいたるまで計算しなければ算出できない．厳密に解析する方法として，ＤＮＳ（Direct Numerical Simulation）があるが，計算できるのはレイノルズ数の小さな（つまり寸法と，速度の積が小さな）場合に限られ，機器設計等での実際の流れ場においては，
計算すべき格子点数が膨大になりコンピューターの計算容量から計算は実質的には不可能である．
そこで，このレイノルズ応力項や乱流熱流束項を簡単な式に代表させ，方程式を解くことが行われている．この簡単な式をモデル式と言っている．従来モデルの例としてMKCOモデル式がある．以下にMKCOモデル式を示す．レイノルズ応力項は次のように表される．
It is necessary to calculate heat dissipation characteristics and fluid pressure loss when there is a flow field with heat transfer, for example, to increase the mounting density of electronic parts such as electrical equipment and to design in a space-saving manner. These are generally obtained experimentally, but there is a problem that it takes a lot of time and cost because it requires trial production.
In order to simulate and solve the flow field with heat transfer analytically, it is necessary to solve the continuity equation, the Navier-Stokes equation, which is the equation of motion, and the energy equation. When the flow is laminar, the equations of motion representing the flow phenomenon are simpler than those for turbulent flow, and can often be calculated by solving the equations. The situation is that the flow is turbulent and the solution cannot be obtained analytically.
What makes it difficult to solve these equations in the case of turbulence is the Reynolds stress term in the Reynolds averaged Navier-Stokes equations and the turbulence in the Reynolds averaged energy equation. It is a heat flux term. The Reynolds stress term is the average of the products of the velocity fluctuations, and the turbulent heat flux term is the average of the products of the velocity fluctuations and the temperature fluctuations, so it cannot be calculated unless the turbulent phenomenon is strictly calculated up to small fluctuations. . There is DNS (Direct Numerical Simulation) as a rigorous analysis method, but it can be calculated only when the Reynolds number is small (that is, the product of size and speed is small), and the actual flow field in equipment design etc. In
The number of grid points to be calculated becomes enormous, and calculation is virtually impossible due to the computational capacity of the computer.
Therefore, the Reynolds stress term and the turbulent heat flux term are represented by simple equations and the equations are solved. This simple formula is called a model formula. An example of a conventional model is the MKCO model formula. The MKCO model formula is shown below. The Reynolds stress term is expressed as follows.
ここで，
here,
は，速度場における浮力のダンピング関数であって，次式で表される．
Is the damping function of buoyancy in the velocity field and is expressed by the following equation.
乱流熱流束項は次式で表される．
The turbulent heat flux term is expressed by the following equation.
ここで，
here,
は，速度場における浮力のダンピング関数であって，次式で表される．
Is the damping function of buoyancy in the velocity field and is expressed by the following equation.
以上のMKCOモデル式の記号の意味は以下のとおりである．
The meanings of the symbols in the above MKCO model equation are as follows.
はそれぞれ乱流エネルギーkの速度平均勾配における生成項，浮力による生成項，散逸率である．大文字Cで表される項は係数であり，式または値で与えられる．その他の記号は他の式の場合とあわせ，この後に記載する．
このモデル式は浮力を伴う乱流を計算するのに優れたモデル式とされているが，次の欠点がある．
1)乱流熱流束項
Are the generation term in the velocity average gradient of turbulent energy k, the generation term due to buoyancy, and the dissipation factor. The term in capital C is a coefficient, given as an expression or value. Other symbols are described after this, along with other expressions.
Although this model formula is an excellent model formula for calculating turbulent flow with buoyancy, it has the following drawbacks.
1) Turbulent heat flux term
が平均温度勾配
Is the average temperature gradient
に比例するため，平均温度勾配がほとんどない場合に乱流熱流束が計算上ゼロになるが，実際はゼロでない．つまり，現象を正しく表していないため，この項が影響する場合の計算精度が悪くなる．
2)式が場合分けによって選択する形になっているため，座標依存性があり，座標軸と重力方向によって，同一の式で計算ができない．つまり重力方向に対し流路が斜め形状の場合などでは計算が困難である．
Since the formula (2) is selected according to the case, there is a coordinate dependency, and the same formula cannot be calculated depending on the coordinate axis and the direction of gravity. In other words, calculation is difficult when the flow path is slanted with respect to the direction of gravity.
本発明の目的は，機械の放熱設計等に必要な，ヌッセルト数や摩擦係数などを求めるための，熱移動を伴う流れ場の乱流の流体的かつ熱的性質を，高精度で，重力方向がいかなる場合でも，同一の式で予測できる推定方法及び推定プログラムを提供することである． The purpose of the present invention is to determine the fluid and thermal properties of the turbulent flow in the flow field with heat transfer to determine the Nusselt number and friction coefficient necessary for heat dissipation design of the machine, etc. The purpose is to provide an estimation method and an estimation program that can be predicted with the same formula in any case.
請求項１記載の発明は，熱移動を伴う流れ場についての乱流の2方程式モデルを用いて，乱流流れ場の速度分布，温度分布，レイノルズ応力，乱流熱流束等の特性値を推定するコンピュータによって実行される，流れ場の速度分布，温度分布，レイノルズ応力，乱流熱流束等の特性値の推定方法であって，
前記コンピュータは，流れ場の温度，速度等を定める条件となる必要なデータを入力するための入力手段と，乱流流れ場の速度分布，温度分布，レイノルズ応力，乱流熱流束等の特性値を求める演算手段とを有しており，
前記演算手段が，前記入力手段によって入力されたデータに基づいてレイノルズ応力
The invention described in claim 1 estimates the characteristic values of the turbulent flow field velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, etc., using a turbulent two-equation model for the flow field with heat transfer. A method of estimating characteristic values such as flow field velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, etc., executed by a computer,
The computer is provided with input means for inputting necessary data as conditions for determining the temperature, velocity, etc. of the flow field, and characteristic values such as velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, etc. of the turbulent flow field. And calculating means for obtaining
The computing means is based on the data input by the input means and the Reynolds stress
を，強制対流に関する項をF，浮力に関する項をGとすると
Where F is the forced convection term and G is the buoyancy term
の式を用いてレイノルズ応力を算出して，速度場の計算をし，乱流熱流束を
The Reynolds stress is calculated using the following equation, the velocity field is calculated, and the turbulent heat flux is calculated.
，乱流熱流束の強制対流に関する項をFt，乱流熱流束の浮力に関する項をGtとすると，
, Where Ft is the term for forced convection of turbulent heat flux and Gt is the term for buoyancy of turbulent heat flux,
の式を用いて乱流熱流束を算出して，上記速度場における温度場の計算をすることを特徴とする，乱流流れ場の速度分布，温度分布，レイノルズ応力，乱流熱流束等の特性値の推定方法である． 本発明に従えば，レイノルズ応力を強制対流に関する項Fと浮力に関する項Gの和で表し，乱流熱流束を強制対流に関する項Ftと浮力に関する項Gtの和で表しているので，乱流の諸量を正確に予測することができ，かつこれらの式が重力の方向にかかわらず統一された式なのでいかなる重力方向であっても，同一式で計算し予測することが可能となる．
請求項２に記載の本発明は熱移動を伴う流れ場についての乱流の2方程式モデルを用いて，乱流流れ場の速度分布，温度分布，レイノルズ応力，乱流熱流束等の特性値の推定するコンピュータを，流れ場の温度，速度等を定める条件となる必要なデータを入力するための入力手段，入力手段によって入力されたデータに基づいて
The turbulent heat flux is calculated using the above equation, and the temperature field in the above velocity field is calculated. The turbulent flow field velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, etc. This is a characteristic value estimation method. According to the present invention, Reynolds stress is represented by the sum of the term F for forced convection and the term G for buoyancy, and the turbulent heat flux is represented by the sum of the term Ft for forced convection and the term Gt for buoyancy. Various quantities can be accurately predicted, and since these formulas are unified regardless of the direction of gravity, it is possible to calculate and predict with the same formula regardless of the direction of gravity.
The present invention according to claim 2 uses a two-equation model of turbulent flow for a flow field accompanied by heat transfer, and provides characteristic values such as velocity distribution, temperature distribution, Reynolds stress, and turbulent heat flux of the turbulent flow field. Based on the data input by the input means and the input means for inputting the necessary data, which are the conditions for determining the flow field temperature, speed, etc.
の式を用いてレイノルズ応力を算出して，速度場の計算を行い，
The Reynolds stress is calculated using the following formula to calculate the velocity field,
の式を用いて乱流熱流束を算出して，上記速度場における温度場の計算をすることを特徴とする，乱流流れ場の速度分布，温度分布，レイノルズ応力，乱流熱流束等の特性値を求める演算手段，および演算手段によって求められた速度分布，温度分布，摩擦係数，ヌッセルト数，レイノルズ応力，乱流熱流束等の特性値を表示する出力手段，として機能させるコンピュータによって実行可能な熱移動を伴う流れ場の速度分布，温度分布，摩擦係数，ヌッセルト数，レイノルズ応力，乱流熱流束等の特性値の推定プログラムである．本発明に従えば，コンピュータにより上記乱流諸元の推定プログラムが実行され、入力手段により，乱流諸元を生成するために必要な，たとえば，流れ場の形状，流体的及び熱的条件を特定するための諸元，格子点などの各種データが入力されると，演算手段は前記入力手段から入力されたデータに基づいて
The turbulent heat flux is calculated using the above equation, and the temperature field in the above velocity field is calculated. The turbulent flow field velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, etc. Executable by a computer that functions as a calculation means for obtaining characteristic values and an output means for displaying characteristic values such as velocity distribution, temperature distribution, friction coefficient, Nusselt number, Reynolds stress, turbulent heat flux, etc. obtained by the calculation means. This is an estimation program for characteristic values such as velocity distribution, temperature distribution, coefficient of friction, Nusselt number, Reynolds stress, turbulent heat flux, and so on. According to the present invention, the turbulent flow parameter estimation program is executed by the computer, and the flow field shape, fluid and thermal conditions necessary for generating the turbulent flow parameter are generated by the input means. When various types of data for specifying, such as grid points, are input, the calculation means is based on the data input from the input means.
の式を使って，速度場支配方程式と温度場支配方程式を解き，速度及び温度等の乱流諸元を演算し，出力手段にその演算結果を表示することができる．このようにして，出力手段に乱流の速度及び温度に関するの諸元が表示されるので，乱流の予測ツールをコンピュータ上に実現することができる． Using this equation, the velocity field governing equation and the temperature field governing equation can be solved, the turbulent flow parameters such as velocity and temperature can be computed, and the computation results can be displayed on the output means. In this way, the turbulent velocity and temperature specifications are displayed on the output means, so a turbulent flow prediction tool can be realized on a computer.
請求項１の本発明に従えば，レイノルズ応力を強制対流に関する項Fと浮力に関する項Gの和で表し乱流熱流速を強制対流に関する項Ftと浮力に関する項Gtの和で表しているので乱流の諸量を正確に予測することができ，かつこれらの式が重力の方向にかかわらず統一された式なのでいかなる重力方向であっても、同一式で計算し予測することが可能となる．請求項２の本発明に従えば，コンピュータにより上記乱流諸元の推定プログラムが実行され，入力手段により，乱流諸元を生成するために必要な，例えば，流れ場の形状，流体的及び熱的条件を特定するための諸元，格子点などの各種データが入力されると，演算手段は前記入力手段から入力されたデータに基づいて
According to the first aspect of the present invention, the Reynolds stress is represented by the sum of the term F for forced convection and the term G for buoyancy, and the turbulent heat velocity is represented by the sum of the term Ft for forced convection and the term Gt for buoyancy. It is possible to accurately predict various quantities of flow, and since these equations are unified regardless of the direction of gravity, it is possible to calculate and predict with the same equation regardless of the direction of gravity. According to the second aspect of the present invention, the computer program executes the turbulent flow parameter estimation program, and the input means generates the turbulent flow parameters, for example, the flow field shape, When various data such as specifications and grid points for specifying the thermal conditions are input, the calculation means is based on the data input from the input means.
の式を使って，速度場支配方程式と温度場支配方程式を解き，速度及び温度等の乱流諸元を演算し，出力手段にその演算結果を表示することができる．このようにして，出力手段に乱流の速度及び温度に関するの諸元が表示されるので，乱流の予測ツールをコンピュータ上に実現することができる． Using this equation, the velocity field governing equation and the temperature field governing equation can be solved, the turbulent flow parameters such as velocity and temperature can be computed, and the computation results can be displayed on the output means. In this way, the turbulent velocity and temperature specifications are displayed on the output means, so a turbulent flow prediction tool can be realized on a computer.
熱移動を伴う乱流の流体的及び熱的現象は周知のレイノルズ平均化された以下の式
連続の式
The turbulent fluid and thermal phenomena with heat transfer are well-known Reynolds averaged equations
ナビエストークスの式
Navi Estokes formula
及びエネルギー式
And energy formula
で表される．
ただし，式には，周知のBoussinesq近似が施されている．以上の式で，繰り返される添え字はテンソルの総和規約に従う．実際のケースでは，主流の温度
It is represented by
However, the well-known Boussinesq approximation is applied to the equation. In the above formula, repeated subscripts follow the tensor sum rules. In the actual case, the mainstream temperature
を与条件として与えると，重力加速度
Is given as a given condition, gravitational acceleration
，や流体の物性値である流体の密度
, Or fluid density, which is a physical property value of fluid
，粘性係数
, Viscosity coefficient
，熱拡散係数
, Thermal diffusion coefficient
は既知であり，レイノルズ応力
Is known and Reynolds stress
と乱流熱流束
And turbulent heat flux
の値を算出できると，未知数が平均圧力
If the value of can be calculated, the unknown is the average pressure
(1つ)，平均速度ベクトル
(One), average velocity vector
(3方向で3つ)，平均温度
(3 in 3 directions), average temperature
(１つ)の合計6つであるのに対し，式の数が連続の式（１つ），ナビエストークス式（3方向で3つ），エネルギー式(１つ）で合計6つとなり式を解くことができる．
本発明の特色とするところはこのレイノルズ応力と乱流熱流束を算出する式を物理現象を最もよく表すと見られる次の式としたところにある．レイノルズ応力を
While there are a total of six (one), the number of formulas is continuous (one), Naviestokes formula (three in three directions), and energy formula (one) for a total of six. Can be solved.
The feature of the present invention is that the equation for calculating the Reynolds stress and the turbulent heat flux is the following equation that appears to best represent the physical phenomenon. Reynolds stress
，強制対流に関する項をF，浮力に関する項をGとすると
, The term for forced convection is F and the term for buoyancy is G
の式を用いてレイノルズ応力
Reynolds stress using the formula
を算出する．また，乱流熱流束を
Is calculated. In addition, the turbulent heat flux
，乱流熱流束の強制対流に関する項をFt，乱流熱流束の浮力に関する項をGtとすると，
, Where Ft is the term for forced convection of turbulent heat flux and Gt is the term for buoyancy of turbulent heat flux,
の式を用いて乱流熱流束
Turbulent heat flux using
を算出する．
以上の式の計算に必要な乱流エネルギー
Is calculated.
Turbulence energy required for the above calculation
，乱流エネルギー散逸率
, Turbulent energy dissipation rate
，温度乱れ強度
, Temperature turbulence intensity
，温度乱れ強度散逸率
, Temperature turbulence intensity dissipation rate
の輸送方程式はそれぞれ次式で与えられる．
The transport equations for are given by
ここで，
here,
は乱流エネルギーの生成項，
Is the generation term of turbulent energy,
は浮力項，
Is the buoyancy term,
は温度乱れ強度の生成項である．
Is the generation term of the temperature turbulence intensity.
の乱流拡散項については，一般化されたこう配拡散近似に基づき，以下のようにモデル化されている．
The turbulent diffusion term is modeled as follows based on the generalized gradient diffusion approximation.
式中のモデル関数，およびモデル定数を以下にまとめて示す．
The model functions and model constants in the equation are summarized below.
ここで，
here,
は無次元距離
Is dimensionless distance
（局所レイノルズ数でもある）と乱流レイノルズ数
(Also local Reynolds number) and turbulent Reynolds number
の調和平均形で定義された修正レイノルズ数である．次に式中におけるモデル関数，およびモデル定数を以下にまとめて示す．
Here is a modified Reynolds number defined by the harmonic mean form of. The model functions and model constants in the equation are summarized below.
ここで用いられている記号の意味するところは以下の通りである．
The meanings of the symbols used here are as follows.
以下に具体的方法について説明する．
図１は本発明の実施の一形態である乱流の熱的・流体的諸元を求めるフローチャートである．図２は乱流の熱的・流体的諸元の推定プログラムを実行して，シュミレーションするために用いられるコンピュータ１の電気的構成を示すブロック図である．ステップa1で，コンピュータ１により当該プログラムが実行され，計算すべき流体，形状，温度等の与条件が入力手段２により入力されて初期設定される．乱流の熱的・流体的諸元の推定プログラムは記憶手段３に記憶され演算処理装置４からの実行指令によって読み出されて実行し，出力手段である表示手段５に計算結果を表示させ，乱流の熱的・流体的諸元の推定システムを構築する．
計算は流路を多数の格子状の微小体積に分割し，各微小体積で上記の各式が成り立つように未知の項を求める方式で行う．上記の各式は，実質微分D/Dtや偏微分(
The specific method is described below.
FIG. 1 is a flowchart for obtaining thermal and fluid specifications of a turbulent flow according to an embodiment of the present invention. FIG. 2 is a block diagram showing the electrical configuration of the computer 1 used for executing the simulation program for the thermal and fluid parameters of the turbulent flow. In step a1, the program is executed by the computer 1, and given conditions such as fluid, shape and temperature to be calculated are input by the input means 2 and initialized. The thermal / fluid specification estimation program for turbulent flow is stored in the storage means 3 and read and executed in accordance with an execution command from the arithmetic processing unit 4, and the calculation result is displayed on the display means 5 as output means. Establish a system for estimating turbulent thermal and fluid dimensions.
The calculation is performed by dividing the flow path into a large number of grid-like microvolumes and obtaining unknown terms so that the above equations hold for each microvolume. Each of the above formulas can be expressed as real differential D / Dt or partial differential (
など)を含んでいるのでこのままでは解けないのでこれらを何らかの形で近似化する必要があり，このような近似化の手法として差分法，有限要素法，有限体積法などがある．たとえば，有限体積法では各微小部分についての積分と直線近似を用いて離散化し，多元一次方程式に置き換えて計算する．これらの手法は周知である．平均圧力
Therefore, it is necessary to approximate them in some form. Differences, the finite element method, the finite volume method, etc. are available as approximation methods. For example, in the finite volume method, it is discretized using integration and linear approximation for each minute part, and is replaced with a multidimensional linear equation. These techniques are well known. Mean pressure
は連続の式とナビエストークスの式から周知のＳＩＭＰＬＥ解法等で求める．この手法も周知である．
DNSによる厳密な解との比較のために実施した例の場合について説明する．
図3に示す本形態は，一方が高温で，他方が低温である２枚の垂直平板間の乱流流れについてその熱的・流体的諸元を推定する方法について説明する．計算式は三次元の場合を記載するが，計算はＤＮＳ計算のできる，二次元の完全発達流について行うので，実質的には一次元である．計算格子は流れに直角方向に145点とした．計算手法は有限体積法によった．熱的流体的予条件はレイノルズ数150，グラスホッフ数9.6×10 ５ である．
ステップａ１で初期設定すると，ステップａ２で，入力された諸条件に基づいて，以上に述べた各方程式を解き乱流の解を求める計算が開始される．
まず，ステップａ２１でレイノルズ応力
Is obtained by the well-known SIMPLE method, etc. from the continuous equation and the Navi Estokes equation. This technique is also well known.
The case of the example implemented for comparison with the exact solution by DNS is explained.
This form shown in Fig. 3 describes a method for estimating the thermal and fluid characteristics of a turbulent flow between two vertical plates, one of which is hot and the other is cold. The calculation formula describes a three-dimensional case, but the calculation is performed on a two-dimensional fully developed flow that can be calculated by DNS, so it is substantially one-dimensional. The calculation grid was 145 points perpendicular to the flow. The calculation method was based on the finite volume method. The thermal fluid preconditions are Reynolds number 150 and Grashof number 9.6 × 10 5 .
When the initial setting is made in step a1, in step a2, calculation for solving the above-described equations and finding the solution of the turbulent flow is started based on the inputted conditions.
First, in step a21, Reynolds stress
を計算する．計算に必要な，式の中に現れる各項は，繰り返し算の１回目は，適当に仮定した値を用い，繰り返し算の２回目以降はそれ以前に求めた値を使うことにより計算される．計算は格子の各点について行われる．レイノルズ応力
This computes Each term appearing in the expression necessary for the calculation is calculated by using the value assumed appropriately for the first iteration, and using the value obtained before the second iteration. The calculation is performed for each point on the grid. Reynolds stress
が求まると，次に，ステップａ２２でナビエストークス式を計算し，平均速度ベクトル
Next, in step a22, the Naviestokes equation is calculated and the average velocity vector
を求める．次にステップａ２３で乱流エネルギー
Is obtained. Next, in step a23, turbulent energy
，乱流エネルギー散逸率
, Turbulent energy dissipation rate
を前述の輸送方程式を同様に有限体積法で解くことにより求める．さらに以上の計算の結果を使い，平均圧力を求め，その他の以降の計算のために必要な項の値を求める．ステップａ２４で乱流熱流束
Is obtained by solving the above transport equation by the finite volume method. In addition, use the results of the above calculations to find the mean pressure and other term values needed for subsequent calculations. Turbulent heat flux at step a24
の計算を既述の式を使い有限体積法で解き，その結果を用いてステップａ２５エネルギー式を同じく有限体積法で解き平均温度
The finite volume method is used to solve the calculation of the step a25 energy equation using the result and the average temperature is solved using the finite volume method.
を得る．次にステップａ２６で温度乱れ強度
Get Next, in step a26, the temperature turbulence intensity
，温度乱れ強度散逸率
, Temperature turbulence intensity dissipation rate
の輸送方程式を解きこれらの値を求める．ステップａ３で以上のようにして求めた平均速度ベクトル
Solve these transport equations to find these values. Average velocity vector obtained as described above in step a3
，乱流エネルギー
, Turbulent energy
，乱流エネルギー散逸率
, Turbulent energy dissipation rate
，平均温度
, Average temperature
，温度乱れ強度
, Temperature turbulence intensity
，温度乱れ強度散逸率
, Temperature turbulence intensity dissipation rate
らの値が収束するまで，ステップａ２を繰り返す．収束すれば，乱流の熱的・流体的状態が求められる．以上の結果を用いて，工学的に必要な数値をステップａ４で求めることができる．たとえば流体の圧力損失係数は壁近傍の平均速度分布から求めることができる．壁近傍の温度分布からヌッセルト数を求めることができる．
図４は本計算によって得られたレイノルズ応力の一成分
Repeat step a2 until these values converge. Once converged, the thermal and fluid state of the turbulent flow is required. Using the above results, numerical values necessary for engineering can be obtained in step a4. For example, the fluid pressure loss coefficient can be obtained from the average velocity distribution near the wall. The Nusselt number can be obtained from the temperature distribution near the wall.
Figure 4 shows one component of Reynolds stress obtained by this calculation.
を実線で示し，厳密解であるＤＮＳ値を丸印で示し，従来のＭＫＣＯ法によるものを破線で比較している．図５は乱流熱流束
Is indicated by a solid line, the DNS value which is an exact solution is indicated by a circle, and the conventional MKCO method is compared by a broken line. Figure 5 shows turbulent heat flux
について本計算結果を実線で示し，厳密解であるＤＮＳ値を丸印で示し，従来のＭＫＣＯ法によるものを破線で比較している．
レイノルズ応力について，差は少ないが，乱流熱流束について，従来は算出できなかったのが，できるようになり，乱流の構造の推定が，より詳細にできるようになったことがわかる．
This calculation result is shown by a solid line, DNS value which is an exact solution is shown by a circle, and the conventional MKCO method is compared by a broken line.
Although the difference in Reynolds stress is small, it can be understood that the turbulent heat flux can be calculated in more detail, and the structure of the turbulent flow can be estimated in more detail.
以上説明したように，本発明によるレイノルズ応力と、乱流熱流速のモデル式は，乱流の物理現象を従来のモデルより正確に表現し，しかも流れと重力の方向にかかわらず同じ式で計算できるので，機械の放熱設計などにおいて，実験の手間を削減し，より予測精度を上げ，摩擦係数や，ヌッセルト数を計算し，圧力損失や放熱量の正確な予測を可能とし，速やかにコンパクトで効率のよい機械を設計する手段を提供するものである． As described above, the Reynolds stress and turbulent heat flow velocity model equations according to the present invention represent the turbulent physical phenomenon more accurately than the conventional model, and are calculated using the same equation regardless of the direction of flow and gravity. Therefore, in the heat dissipation design of machines, etc., the labor of experiments is reduced, the prediction accuracy is further increased, the friction coefficient and the Nusselt number are calculated, and the pressure loss and the heat dissipation amount can be accurately predicted. It provides a means to design efficient machines.
１ コンピュータ
２ 入力手段
３ 記憶手段
４ 演算処理装置
５ 表示手段
DESCRIPTION OF SYMBOLS 1 Computer 2 Input means 3 Storage means 4 Arithmetic processor 5 Display means
Claims (2)
前記コンピュータは，流れ場の温度，速度等を定める条件となる必要なデータを入力するための入力手段と，乱流流れ場の速度分布，温度分布，レイノルズ応力，乱流熱流束等の特性値を求める演算手段とを有しており，
前記演算手段が，前記入力手段によって入力されたデータに基づいてレイノルズ応力を
，強制対流に関する項をF，浮力に関する項をGとすると
の式を用いてレイノルズ応力を算出して，速度場の計算をし，乱流熱流束を
，乱流熱流束の強制対流に関する項をFt，乱流熱流束の浮力に関する項をGtとすると，
の式を用いて乱流熱流束を算出して，上記速度場における温度場の計算をすることを特徴とする，乱流流れ場の速度分布，温度分布，レイノルズ応力，乱流熱流束等の特性値の推定方法 A flow implemented by a computer that estimates the turbulent flow field velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, and other characteristic values using a turbulent two-equation model for a flow field with heat transfer A method for estimating characteristic values of field velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, etc.
The computer is provided with input means for inputting necessary data as conditions for determining the temperature, velocity, etc. of the flow field, and characteristic values such as velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, etc. of the turbulent flow field. And calculating means for obtaining
The computing means calculates the Reynolds stress based on the data input by the input means.
, The term for forced convection is F and the term for buoyancy is G
The Reynolds stress is calculated using the following equation, the velocity field is calculated, and the turbulent heat flux is calculated
, Where Ft is the term for forced convection of turbulent heat flux and Gt is the term for buoyancy of turbulent heat flux,
The turbulent heat flux is calculated using the above equation, and the temperature field in the above velocity field is calculated. The turbulent flow field velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, etc. Method for estimating characteristic values
乱流流れ場の速度分布，温度分布，レイノルズ応力，乱流熱流束等の特性値の推定するコンピュータを，流れ場の温度，速度等を定める条件となる必要なデータを入力するための入力手段，入力手段によって入力されたデータに基づいてレイノルズ応力を
，強制対流に関する項をF，浮力に関する項をGとすると
の式を用いてレイノルズ応力を算出して，速度場の計算を行い,乱流熱流束を
，乱流熱流束の強制対流に関する項をFt，乱流熱流束の浮力に関する項をGtとすると，
の式を用いて乱流熱流束を算出して，上記速度場における温度場の計算をすることを特徴とする，乱流流れ場の速度分布，温度分布，レイノルズ応力，乱流熱流束等の特性値を求める演算手段，および演算手段によって求められた速度分布，温度分布，レイノルズ応力，乱流熱流束等の特性値を表示する出力手段，として機能させるコンピュータによって実行可能な熱移動を伴う流れ場の速度分布，温度分布，レイノルズ応力，乱流熱流束等の特性値の推定プログラム Using a two-equation model of turbulence for a flow field with heat transfer,
An input means for inputting necessary data that is a condition for determining the temperature, velocity, etc. of the flow field to a computer that estimates the characteristic values of the velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, etc. of the turbulent flow field , Based on the data input by the input means, the Reynolds stress
, The term for forced convection is F and the term for buoyancy is G
The Reynolds stress is calculated using the following formula, the velocity field is calculated, and the turbulent heat flux is calculated.
, Where Ft is the term for forced convection of turbulent heat flux and Gt is the term for buoyancy of turbulent heat flux,
The turbulent heat flux is calculated using the above equation, and the temperature field in the above velocity field is calculated. The turbulent flow field velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, etc. Flow with heat transfer that can be executed by a computer that functions as a calculation means for obtaining characteristic values and an output means for displaying characteristic values such as velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, etc. obtained by the calculation means Estimation program for characteristic values of field velocity distribution, temperature distribution, Reynolds stress, turbulent heat flux, etc.
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