船舶設(shè)計(jì)外文翻譯---船舶最大下沉量

1、<p>　　The Maximum Sinkage of a Ship</p><p>　　T. P. Gourlay and E. O. Tuck</p><p>　　Department of Applied Mathematics, The University of Adelaide, Australia</p><p>　　A ship movi

2、ng steadily forward in shallow water of constant depth h is usually subject to downward forces and hence squat, which is a potentially dangerous sinkage or increase in draft. Sinkage increases with ship speed, until it r

3、eaches a maximum at just below the critical speed . Here we use both a linear transcritical shallow-water equation and a fully dispersive finite-depth theory to discuss the flow near that critical speed and to compute th

4、e maximum sinkage, trim angle, and stern displace</p><p>　　Introduction</p><p>　　For a thin vertical-sided obstruction extending from bottom to top of a shallow stream of depth h and infinite wi

5、dth, Michell (1898) showed that the small disturbance velocity potential (x,y) satisfies the linearized equation of shallow-water theory(SWT)</p><p><b>　　(1)</b></p><p>　　Where, with

6、 the Froude number based on x-wise stream velocity U and water depth h. This is the same equation that describes linearized aerodynamic flow past a thin airfoil (see e.g., Newman 1977 p. 375), with replacing the Mach nu

7、mber. For a slender ship of a general cross-sectional</p><p>　　shape, Tuck (1966) showed that equation (1) is to be solved subject to a body boundary condition of the form</p><p><b>　　(2)&

8、lt;/b></p><p>　　where S(x) is the ship’s submerged cross-section area at station x. The boundary condition (2) indicates that the ship behaves in the (x ,y) horizontal plane as if it were a symmetric thin

9、 airfoil whose thickness S(x)/h is obtained by averaging the ship’s cross-section thickness over the water depth. There are also boundary</p><p>　　conditions at infinity, essentially that the disturbance vel

10、ocity vanishes in subcritical flow ().</p><p>　　As in aerodynamics, the solution of (1) is straightforward for either fully subcritical flow (where it is elliptic) or fully supercritical flow (where it is

11、hyperbolic). In either case, the solution has a singularity as , or .In particular the subcritical (positive upward) force is given by Tuck (1966) as</p><p><b>　　(3)</b></p><p>　　wit

12、h B(x) the local beam at station x. Here and subsequently the integrations are over the wetted length of the ship, i.e., where L is the ship’s waterline length.</p><p>　　This force F is usually negative, i.

13、e., downward, and for a fore-aft symmetric ship, the resulting midship sinkage is given hydrostatically by</p><p><b>　　(4)</b></p><p>　　where is the ship’s displaced volume, and<

14、/p><p><b>　　(5)</b></p><p>　　where is the ship’s waterplane area. The nondimensional coefficient has been shown by Tuck & Taylor(1970) to be almost a universal constant, depending

15、only weakly on the ship’s hull shape.</p><p>　　Hence the sinkage appears according to this linear dispersionless theory to tend to infinity as .However, in practice, there are dispersive effects near which

16、limit the sinkage, and which cause it to reach a maximum value at just below the critical speed.</p><p>　　Accurate full-scale experimental data for maximum sinkage are scarce. However,, according to linear i

17、nviscid theory, the maximum sinkage is directly proportional to the ship length for a given shape of ship and depth-to-draft ratio (see later). This means that model experiments for maximum sinkage (e.g., Graff et al 196

18、4) can be scaled proportionally to length to yield full-scale results, provided the depth-to-draft ratio remains the same.</p><p>　　The magnitude of this maximum sinkage is considerable. For example, the Tay

19、lor Series A3 model studied by Graff et al (1964) had a maximum sinkage of 0.89% of the ship length for the depth-to-draft ratio h/T = 4.0. This corresponds to a midship sinkage of 1.88 meters for a 200 meter ship. Exper

20、iments on maximum squat were also performed by Du & Millward (1991) using NPL round bilge series hulls. They obtained a maximum midship sinkage of 1.4% of the ship length for model 150B with h/T =2.3. This</p>

21、<p>　　It is important to note that only ships that are capable of traveling at transcritical Froude numbers will ever reach this maximum sinkage. Therefore, maximum sinkage predictions will be less relevant for slo

22、wer ships such as tankers or bulk carriers. Since the ships or catamarans that frequently travel at transcritical Froude numbers are usually comparatively slender, we expect that slender-body theory will provide good res

23、ults for the maximum sinkage of these ships.</p><p>　　For ships traveling in channels, the width of the channel becomes increasingly important around when the flow is unsteady and solitons are emitted forwar

24、d of the ship (see e.g.,Wu & Wu 1982). Hence experiments performed in channels cannot be used to accurately predict maximum sinkage for ships in open water. The experiments of Graff et al were done in a wide tank, ap

25、proximately 36 times the model beam, and are the best results available with which to compare an open-water theory. However, even w</p><p>　　Transcritical shallow-water theory (TSWT)</p><p>　　It

26、 is not possible simply to set ? in (1) in order to gain useful information about the flow near . As with transonic aerodynamics, it is necessary to include other terms that have been neglected in the linearized derivat

27、ion of SWT (1).</p><p>　　An approach suggested by Mei (1976) (see also Mei & Choi,1987) is to derive an evolution equation of Korteweg-de Varies (KdV) type for the flow near. The usual one-dimensional fo

28、rms of such equations contain both nonlinear and dispersive terms. It is not difficult to incorporate the second space dimension y into the derivation, resulting in a two-dimensional KdV equation, which generalizes (1) b

29、y adding two terms to give</p><p><b>　　(6)</b></p><p>　　The nonlinear term in but not the dispersive term in was included by Lea & Feldman (1972). Further solutions of this nonl

30、inear but nondispersive equation were obtained by Ang (1993) for a ship in a channel. Chen & Sharma (1995) considered the unsteady problem of soliton generation by a ship in a channel, using the Kadomtsev-Petviashvil

31、i equation, which is essentially an unsteady version of equation (6). Although they concentrated on finite-width domains, their method is also applicable to open </p><p>　　Mei (1976) considered the full equa

32、tion (6) in open water and provided an analytic solution for the linear case where the term is omitted. He showed that for sufficiently slender ships the nonlinear term in equation (6) is of less importance than the disp

33、ersive term and can be neglected; also that the reverse is true for full-form ships where the nonlinear term is dominant. This is also discussed in Gourlay (2000).</p><p>　　As stated earlier, most ships that

34、 are capable of traveling at transcritical speeds are comparatively slender. For these ships it is dispersion, not nonlinearity, that limits the sinkage in open water. Nonlinearity is usually included in one-dimensional

35、KdV equations by necessity, as a steepening agent to provide a balance to the broadening effect of the dispersive term in .In open water, however, there is already an adequate balance with the two-dimensional term in .

36、This is in contrast to fin</p><p>　　Therefore, for slender ships in shallow water of large or in finite width, we can solve for maximum squat using the simple transcritical shallow-water (TSWT) equation</

37、p><p><b>　　(7)</b></p><p>　　(Writing ), subject to the same boundary condition (2). The term in ? provides dispersion that was absent in the SWT,and limits the maximum sinkage.</p>

38、;<p>　　Conclusions</p><p>　　We have used two slender-body methods to solve for the sinkage and trim of a ship traveling at arbitrary Froude number, including the transcritical region.</p><p

39、>　　The transcritical shallow water theory (TSWT) developed by Mei (1976) has been extended and exploited numerically, using numerical Fourier transform methods to give sinkage and trim via a double numerical integrati

40、on. This theory has also been extended to the case of a ship moving in a channel of finite width; however, the numerical difficulty in computing the resulting force integral, and its limited validity, mean that the open-

41、water theory is more practically useful.</p><p>　　The finite-depth theory (FDT) developed by Tuck & Taylor (1970) has also been improved and used for general hull shapes. This theory gives a sinkage forc

42、e and trim moment that are slightly oscillatory in . Since the theory involves summing infinite-depth and finite-depth contributions, both of which vary with at high Froude numbers, any error will grow approximately qua

43、dratically with U. Therefore we cannot use this theory at large supercritical Froude numbers. Also, the difficulty in finding t</p><p>　　In practice, scenarios in which ships are at risk of grounding will no

44、rmally have h/L < 0.125. Since the TSWT is a shallow water theory and it works well at h/L = 0.125, we expect that it will give even better results at smaller, practically useful values of h=L. Also, since the TSWT an

45、d FDT give almost identical results for h/L <0.125, and the TSWT is a much simpler theory, we recommend it as a simple and accurate method for predicting transcritical squat in open water.</p><p>　　備注：T.P

46、.Gourlay and E.O.Tuck．The Maximum Sinkage of a ship[J]．Jourmal of Ship Research，2001．50~58</p><p>　　<文獻(xiàn)翻譯二：譯文></p><p><b>　　船舶最大下沉量&l

47、t;/b></p><p>　　T. P. Gourlay and E. O. Tuck</p><p>　　澳大利亞阿德萊德大學(xué)</p><p>　　一艘在等深為h的淺水中平穩(wěn)前行的船舶通常趨向于受到向下的合力并產(chǎn)生船體下沉, 這種下沉是一種潛在的下沉或吃水增加。下沉量隨船速增加而增加，直至臨界速率。此處我們同時(shí)利用”線性跨臨界淺水方程”和”完全分散限深理論

48、”研究典型船體在接近臨界速度時(shí)的水流和計(jì)算這些船體的最大下沉量、縱傾角和船尾位移。</p><p><b>　　引言</b></p><p>　　對(duì)于在水深為h且無寬度限制的淺水流中的一艘瘦長(zhǎng)型的從船底至頂均為垂直舷側(cè)的物體, Michell (1898) 證明了小擾動(dòng)速率的電位 (x,y)滿足淺水理論(SWT)線性方程 </p><p>　　

49、其中, 且 ，傅汝德數(shù)建立在 x-wise 流速 U 和水深h的基礎(chǔ)上。此方程與描述通過瘦長(zhǎng)型翼型的線性空氣動(dòng)力學(xué)的流體的方程 (見Newman 1977 p. 375)是大致相同的, 不同的是用 r代替了馬赫數(shù)。對(duì)于一艘常見橫截面形狀的瘦長(zhǎng)型船舶來說, Tuck (1966) 指出解決方程（1）受到如下形式的船體邊界條件的限制</p><p>　　其中 S(x) 是在x處水下橫截面區(qū)域.邊界條件(2) 指示船舶

50、在 (x ,y) 水平面處的表現(xiàn)如一個(gè)瘦長(zhǎng)形的對(duì)稱翼型，其厚度S(x)/h是通過對(duì)水深求全船橫截面厚度的平均數(shù)獲得。在無限寬水流中同樣也有邊界條件，主要是擾動(dòng)速率 在緩流 ()中消失了.</p><p>　　同空氣動(dòng)力學(xué)中一樣, 方程(1)的解答僅僅針對(duì)充分緩流(橢圓形)或充分緩流(雙曲線形). 對(duì)以上任何一種緩流, 方程的解答中都存在奇點(diǎn)如, 或 。特別地，亞臨界力(正向上)由Tuck (1966)給出<

51、;/p><p>　　B(x) 是x位置處的橫梁. 此處和之后的積分下限是在船舶浸濕長(zhǎng)度之內(nèi)，即 這里L(fēng)是船舶水線面的長(zhǎng)度。</p><p>　　這個(gè)F力通常是負(fù)的，即方向向下，并且對(duì)于一艘首尾對(duì)稱的船舶， 靜力學(xué)中給出最終的船中下沉量</p><p>　　其中 是船舶排水容量，且</p><p>　　其中 是船舶水線面區(qū)域。 由Tuck &

52、; Taylor(1970)給出的非色散系數(shù) 已被證明接近恒定不變，只是很微弱的受船殼形狀影響。</p><p>　　此處下沉量根據(jù)線性非色散理論將趨向于無窮大。然而，實(shí)際情況中，在 附近存在的色散效應(yīng)限制了下沉量并導(dǎo)致其在臨界速度處達(dá)到最大值。</p><p>　　精確的最大下沉量的全船實(shí)驗(yàn)數(shù)據(jù)也非常的有限。然而，根據(jù)線性無粘理論，最大下沉量對(duì)于給定的船型跟船長(zhǎng)成正比（見下文）。這意味著

53、最大下沉量的模擬實(shí)驗(yàn)，能夠給出全面的結(jié)果，提供的深吃水船舶也保持不變。</p><p>　　這個(gè)最大下沉量的幅度相當(dāng)大。例如，1964年Graff er al 研究的Taylor系列A3模型在水深吃水比為4時(shí)具有船長(zhǎng)的0.89%的下沉量。這相當(dāng)于一艘200米的船舶，船中部下沉1.88米。在1991年Du & Millward利用NPL系列船殼進(jìn)行了船舶坐底量實(shí)驗(yàn)。他們獲得了在水深吃水比為2.3時(shí)150B型

54、的船舶中部最大下沉量為船長(zhǎng)的1.4%。這相當(dāng)于200米長(zhǎng)的船舶船中下沉2.8米?？紤]到這個(gè)因素，當(dāng)最大下沉發(fā)生時(shí)通常會(huì)有一個(gè)顯著地船首縱向上揚(yáng)角度，船尾處的下沉更加大，對(duì)于一艘200米船舶來講可能更多。</p><p>　　值得注意的是只有的傅汝得數(shù)相應(yīng)的船舶才能達(dá)到這個(gè)最大下沉量。因此，對(duì)于油輪或者散貨船起最大下沉量的預(yù)測(cè)將會(huì)減少。由于航行的傅汝德系數(shù)內(nèi)的船舶大都比較瘦長(zhǎng)，我們希望細(xì)長(zhǎng)體理論能夠提供一個(gè)關(guān)于最大

55、下沉量的好結(jié)果。</p><p>　　對(duì)于航道中行駛的船舶，當(dāng)在附近且流布穩(wěn)定時(shí)航道的寬度變得更加重要（如見，Wu & Wu 1982）。Hence在航道中的實(shí)驗(yàn)不能很準(zhǔn)確的用來預(yù)測(cè)船舶在開敞水域的最大下沉量。Graff et al 在大水箱中的實(shí)驗(yàn)，相當(dāng)于實(shí)驗(yàn)寬度的36倍，跟開敞水域理論相比已經(jīng)是個(gè)不錯(cuò)的結(jié)果。然而，盡管有如此大的試驗(yàn)箱，當(dāng)時(shí)岸壁效應(yīng)依舊產(chǎn)生影響，因此仍需要討論。</p>

56、<p><b>　　淺水理論</b></p><p>　　這是不可能簡(jiǎn)單的在（1）中設(shè)置，為了增加在時(shí)的有用信息。根據(jù)空氣動(dòng)力學(xué)，還需要包括其他在SWT中忽略的方面。</p><p>　　在1976年Mei建議的方法是一個(gè)時(shí)KdV方程。通常的一維形式既包括此類方程非線性和色散條款。由于不難推到納入第二空間的維數(shù)，通過添加兩個(gè)方面給出二維KdV方程，從而給出了

57、</p><p>　　中的非線性項(xiàng)被 Lea & Feldman (1972)加入其中，但沒有包括中的色散項(xiàng)。這個(gè)非線性但非色散方程的對(duì)水道中的船舶的進(jìn)一步求解被 Ang (1993) 獲得。 Chen & Sharma (1995) 考慮到了水道中船舶產(chǎn)生的孤波的不穩(wěn)定問題， 利用 Kadomtsev-Petviashvili 方程, 即方程（6）一種不規(guī)則形式。 盡管主要針對(duì)的是寬度有限的水域

58、，他們的方法仍適用于開放水域，雖然這樣的計(jì)算量較龐大。非線性和色散方面的內(nèi)容進(jìn)一步被陳（1999）列入，從而允許有限寬度的結(jié)果計(jì)算覆蓋傅汝德數(shù)的較大范圍。</p><p>　　Mei (1976) 研究了方程（6）在開放水域中的完全形式并對(duì)忽略了項(xiàng)的線性情況提供了解析解法。他闡明了對(duì)于船體足夠細(xì)長(zhǎng)的船舶，方程（6）中的非線性項(xiàng)不如色散項(xiàng)重要并可以被忽略；同樣，反過來說對(duì)于船體肥大的船舶非線性項(xiàng)則是主要的。這在 G

59、ourlay (2000)中也有涉及。</p><p>　　如前所述，大多數(shù)可以跨臨界速度航行的船舶相對(duì)而言都是較為細(xì)長(zhǎng)的。 對(duì)于這些船舶，色散限制了其在開放水域中的下沉量，而不是非線性。非線性項(xiàng)因其必要性通常包含在一維KdV方程中，作為steepening中介以平衡中的色散項(xiàng)的寬化效應(yīng)。但是在開放水域，在中的二維項(xiàng)對(duì)該效應(yīng)已有足夠的平衡。 這是相對(duì)于寬度有限水域來說的，在限寬水域有擴(kuò)大跨臨界效應(yīng)的趨勢(shì)，并引起水

60、流更加接近于單一方向。 此時(shí)非線性特性在限寬水道變得如此重要，以至于在接近臨界速度的狹小速度范圍內(nèi)穩(wěn)定的水流可能性極小(見 Constantine 1961, Wu & Wu 1982).</p><p>　　因此，對(duì)大寬度或無限寬度的淺水域中的瘦長(zhǎng)型船舶來說， 我們可以利用簡(jiǎn)化跨臨界淺水域(TSWT) 方程解決最大下沉</p><p>　　(注：)，服從邊界條件(2). 公式中的

61、項(xiàng)提供了SWT中缺少的色散性并限制了最大下沉量。</p><p><b>　　結(jié)論</b></p><p>　　我們已經(jīng)用兩個(gè)細(xì)長(zhǎng)體理論來解決客船在任意傅汝德系數(shù)的下沉和縱傾，包括跨區(qū)域的。有Mei在1976年提出的TSWT理論利用數(shù)值模擬進(jìn)行了擴(kuò)展和利用，通過數(shù)值傅里葉變換給出一種雙重?cái)?shù)值積分方法來計(jì)算下沉和縱傾。這個(gè)理論同樣被用于寬度受限的航道中運(yùn)動(dòng)的船舶。然而，

62、其在數(shù)值計(jì)算上的困難意味著在開敞水域理論更加的實(shí)用。</p><p>　　由Tuck & Taylor (1970)開發(fā)的FDT技術(shù)同樣被發(fā)展和用于一般的船型。這個(gè)理論給出的下沉力和縱傾有略微的研究?jī)r(jià)值。由于涉及到受限和無限寬度的條件限制，在傅汝的系數(shù)較大時(shí)都發(fā)生變化。任何錯(cuò)誤都將增加二次。因此，在傅汝得數(shù)較大時(shí)不能用此理論。此外，在尋找無限寬度條件時(shí)也存在困難，以及需要額外的數(shù)值積分來計(jì)算力和力矩，使F