3D Engineering Model of Downburst Evolution in Thunderstorm

Transcription

1 Available online at Pocedia Engineeing 17 ( The nd Intenational Symposium on Aicaft Aiwothiness (ISAA 11 3D Engineeing Model of Downbust Evolution in Thundestom TANG Chu a *, HONG Guanxin a a School of Aeonautics Science and Engineeing, Beihang Univesity, Beijing, P.R.Chia Abstact Downbust in thundestom mainly efes to the outflow on fontie and the stong wind shea caused by the downbust. In this pape, the thundestom evolution is divided into thee stages as gowing, matue and dissipating stages accoding to its development. Based on meteoological data, tends of elevant paametes ae pesented. Then with the 3D ing votices method, the classical fluid mechanics theoy is applied though adding linea souce model to simulate the distibution of velocity in the wind shea field and its evolution ove time. This modeling method could effectively simulate the evolution of downbust, and is suitable fo engineeing application. 11 Published by Elsevie Ltd. Selection and/o pee-eview unde esponsibility of Aiwothiness Technologies Reseach Cente NLAA, and Beijing Key Laboatoy on Safety of Integated Aicaft and Populsion Systems, China Open access unde CC BY-NC-ND license. Keywod: Thundestom, Downbust, Evolution, Votex ings model, Linea souce model 1. Intoduction A vaiety of meteoological phenomena can cause downbust. Geneally, stong convection cuent in cetain conditions will cause downbust. Downbust is easy to fom, detemined by the chaacteistics of thundestom. Downbust affects flight safety, and fo an aicaft flying though downbust, the wind changes fom head wind into tail wind in shot time, which will cause deviations of the aicaft fom the * Coesponding autho. Tel.: addess: tangchu@ase.buaa.edu.cn Published by Elsevie Ltd. doi:1.116/j.poeng Open access unde CC BY-NC-ND license.

2 14 TANG Chu and HONG Guanxin / Pocedia Engineeing 17 ( oiginal flight path and difficulty fo to pilot to contol it, especially in take-off and landing opeations. Sevee downbust even causes flight accidents. In ode to exploe the dynamics of aicaft in the downbust wind field, it is necessay to build up a model to eflect the eal fluid chaacteistics of downbust. Thee kinds of methods have gained favo in past to simulate downbust. The fist one is to simulate the fluid field chaacteistics by disposing fundamental solutions of potential flow theoy and selecting its positions and numbes. The second method is to deive atmospheic dynamic equations with basic fluid dynamics equations and themodynamic laws and then solve fo the velocity distibutions of the wind field and its change with time. The thid one is to establish a database with data fom eal measuements, such as JAWS and Dopple adas. The fist method is simple and easy to use, and models with this method include the doublet sheet model [1], the votex section model [], and the votex ing model [3,4], etc., all of which ae 3D models that can simulate downbust field chaacteistics at a cetain time. Howeve, the assumption of fozen field is geneally used, which means velocity is only the function of position, so it cannot continuously descibe the evolution stage of the downbust field. The second method is based on atmospheic dynamics, descibing wind field chaacteistic completely, such as wind speed, ainfall, tempeatue, pessue and ada eflectivity facto. It shows the evolution of downbust clealy, but is not suitable fo engineeing eseach because of its complexity and huge amount of calculation. The thid models, though close to eality, ae esticted by measuing methods and costs, with limited usable data. Theefoe, it is necessay to develop a simple method to descibe the evolution of downbust fom beginning to end that facilitates engineeing applications. With cuent engineeing simulation methods and simulation esults of atmospheic dynamics equations, this pape pesents a 3D evolution model of downbust by intoducing time vaying ing votices and linea souce models.. Modeling Method.1. The Basic chaacte and Evolution Downbust in Thundestom In diffeent zones, two kinds of wind shea can be fomed by downbust in thundestom as the downdaft unde thundestom and the outflow afte it eaches gound [5]. Thundestom evolution can be divided into thee stages as gowing, matue and dissipating phase. Fo diffeent scales, evolution times also diffe, fom a few to dozens of minutes. Figue 1 shows the life cycle of a typical downbust. Fom (T-5 to T is the gowing phase. In this phase, the main fom is downdaft, and then the outflow appeas gadually as time passes. Fom T to (T+1 is the matue phase. Duing this phase, outflow velocity value eaches the maximum and the hoizontal velocity becomes the lagest at (T+1. Afte (T+1 is the dissipating phase. The ada detects hoizontal wind shea at (T- and gives the alam till the end of the life cycle. Fig. 1. the life cycle of downbust [6]

3 TANG Chu and HONG Guanxin / Pocedia Engineeing 17 ( Mak R. Hjelmfelt genealized the ule of downbust evolution afte studying the Dopple ada data of 6 cases in JAWS. In the beginning, the descending downbust showed no obsevable wind shea. When downdaft eached the suface, the Dopple ada fist found hoizontal wind shea and only a shot time befoe suface-level divegence was seen. As the downdaft eached the gound suface, the outflow began to take fom. The wind shea inceased to intensity and began to gow. The hoizontal votex ciculation developed and began to move away fom the thundestom coe. Afte eaching maximum intensity, about half of the downdaft continued to expand. The est weakened without futhe gowth. Finally, some outflows gew beyond downdaft scale and became lage-scale outflows befoe dissipating [6]. The biggest theat fo flight though a downbust is the stong hoizontal wind shea fom seveal dozens to a hunded metes above gound. Data shows that the hoizontal shea value of 1 - s -1 is the dange limit fo commecial aicaft [7]. The dange will incease when the maximum vetical velocity height is lowe... Downbust Calculation Model As mentioned above, this pape uses ing votex and linea souce models with time vaying positions and intensities to simulate the chaacteistics of downbust wind field. It is assumed that, the gound bounday laye can be ignoed due to its small thickness; the wind field is filled with incompessible and inviscid ideal gas; the effects of ain and tempeatue changes can be ignoed. Both ing votex and linea souce models ae axisymmetic, theefoe when studying the induced speed field, only the field on one side of the symmetic axis need to be consideed. Select cylindical coodinate system to descibe the model, whee is the adial coodinate, and h is the axial coodinate. The wind field dimension is R H (R is the maximum adius, H is the maximum height, and P(, h is an abitay point inside the wind field. Zeo height means the gound. The ing votex has stength of Γ, with its cente at ( v, h v and a adius of v. The unit linea souce model has a stength of Q with its two ends at (, and (, h v...1. The Ring Votex Model In ode to find the speed components at a point caused by the ing votex, it is equied to calculate the Stokes steam function, Ψ. The Stokes steam function due to a ing votex ciculation Γ is given by (see Fig [8], Γ ψ ( R1+ R F1( λ E1( λ π (1 Whee, λ R 1 and R ae the fathest and the neaest distance fom P to the ing votex. R max + h h, + + h h 1 ( ( v ( v ( v ( v ( ( v ( v ( v ( v R min + h h, + + h h 1 ( F λ and E 1 (λ ae elliptic integals. In the calculation of F 1 (λ E 1 (λ, the appoximation method employed by Ivan [3] was used, quoted as Equation (. Fo λ 1.

4 144 TANG Chu and HONG Guanxin / Pocedia Engineeing 17 ( λ [ F1( λ E1( λ] λ The adial and vetical speeds (v and v h espectively ae calculated with, v v h 1 ψ h 1 ψ ( (3 Thee ae aeas within the velocity field whee Equation (1 and Equation (3 cannot be used. The esulting division by zeo can be avoided by setting v along the vetical axis. The coesponding vetical velocity is then calculated fom the equation fo the velocity induced along the axis of a ing votex. v Γ h vh 1 + v v 3 The velocity field is calculated by Equation (3 and (4. (4 The Ring Votex Model (- v, h v ( v, h v (, h v h R 1 R dh α R P(,h h s The Linea Souce Model Fig.. The ing votex and linea souce model diagam... The Linea Souce Model The linea souce model is the continuous distibutions of point souce between the cente of the ing votex and the gound. The model is used to simulate outflow of the downbust. dh is an element of the linea souce (see Fig, and the induced velocity at P by the element dh is

5 TANG Chu and HONG Guanxin / Pocedia Engineeing 17 ( Qdh dv 4π R Whee, ( R + h h s The induced velocity components ae Qdh dvs R 4π R ( h hs Qdh dvhs R 4π R Integating above equations leads to the induced velocity components of the linea souce model at P(,h as in Equation (5, vs vhs hv hv Qdh R 4π R h hs Qdh R 4π ( (5 As shown in Figue, a vaiable α is intoduce to help solve Equation (5, and α has such elations with, R, h, h s as sinα R h hs cosα R (6 Velocity components fom Equation (5 and (6 ae Q vs 4π Q vhs 4π Whee, ( cosα cosα 1 ( sinα sinα 1 h hs sin α1, cosα1 + h + h h h sin α, cosα s + ( h hv + ( h hv..3. Gound Bounday Conditions The velocity field to be simulated is that of the model close to the gound. This implies zeo vetical

6 146 TANG Chu and HONG Guanxin / Pocedia Engineeing 17 ( velocity (v h along the gound suface plane. In ode to poduce pope flow bounday conditions, mio models eflected in the gound plane is intoduced. The ciculation stength of the eal ing votex is Γ, so that of its image must be -Γ. Also, the cente of the image ing votex is ( v, -h v, and the stength of the image linea souce is Q. As above, the two ends of the image linea souce model is at (, and (, -h v, and the velocity components in the image models ae v and v h...4. Supeposed model To simulate the field of downbust, the ing votex model will be supeposed on linea souce model. And, the velocity field is the supeposition of speeds of the eal and the image models. Futhemoe, the thundestom is moving with a tanslation speed of V, so the total vecto is the summation of the tanslation speed and the wind speed geneated by the model, as showed in Equation (7, V V + V + V + V + V (7 s s Whee, V and V s ae the velocity vectos of ing votex and linea souce espectively in the eal models and V and V s in the image models...5. Downbust evolution Evolution is the time histoy of velocity field. Though analysis, the esults of atmospheic dynamics showed that the paametes include stength, adius, height of the ing votex, and stength of the linea souce. The evolution model is divided into thee stages. See Table 1. Table 1. Phases and main fom of downbust evolution Phase Time Main fom Gowing -t1 Downdaft Matue t1-t Outflow appeas and eaches the maximum speed Dissipating t-t3 Velocity decays till the cycle ends In the two-dimensional ectilinea votex model, Swolinshky poposed the ule that the induced velocity and the adius follow the exponential ule along with the time change [9]. Theefoe, intoduce time-vaying paametes (Γ, v, h v, Q, such as in Equation (8, bt Γ Γ t ae v ( ( Γ bt t ae bt h ae ( < t t1 h hv ( t Ht ( ( 1 t > t bq t ae Q ( < t t Qt ( Q( t ( t > t Whee, a Г, a, a h, b Г, b, b h ae coesponding paametes detemined by the field. (8 3. Simulation Results and Analysis 3.1. Compaison of Simulation esults As an example, the downbust on June 3, 198 in Denve is simulated with this method. Measued values and the simulation esults of the matue phase ae compaed. See Table. In this pape, the whole evolution pocess of this downbust is simulated. Table lists the simulation

7 TANG Chu and HONG Guanxin / Pocedia Engineeing 17 ( esults, atmospheic dynamics simulation esults and the measued esults of the matue phase. The esults show that, the simulation esults with this method ae close to those obtained with atmospheic dynamics. Yet the diamete and velocity vectos ae smalle than measued values. Table. Simulation values and measued values Simulation value of this pape Simulation value in liteatue [1] Measued value [11] u max (m/s Δu v min (m/s ~-15 Diamete of u max (m Height of v min (m Analysis of Simulation Results As the hoizontal scale of an isolated thundestom is usually a dozen kilometes, define the simulation egion as 16km 4km, and the hoizontal and vetical gid spacing is.km. The coefficients of timevaying paametes (Γ, v, h v, Q ae shown in Table 3. Fom the gowing to the matue phase, tends with time of the votex ing stength, adius, height and the linea souce stength ae calculated and the esults ae shown in fig 3. In the dissipating phase, diamete of the ing votex is beyond the hoizontal scale of thundestom and when v >1km, the evolution ends. This model simulates velocity field of downbust fom the gowing to the dissipating stage. At 7.5min, downdaft eached the gound. Befoe 7.5min was the gowing phase, fom 7.5min to 13min was the matue phase, and afte 13min was the dissipating phase. The vetical velocity was 9.8m/s at 7.5min, and then the outflow appeaed, and the hoizontal velocity eached its maximum value. Afte 13min, velocity was gadually deceasing. At 1min, the adius of the outflow cente was moe than km, and the outflow egion was expanding. Table 3. Time-vaying paametes Γ v hv Q a b /π 1/π -1/3 4/5π Fig 4 shows gaphics of the maximum hoizontal velocities and the maximum vetical velocities fom 4min to min in the field. The hoizontal velocity is waning to 7.7m/s, u alam [1]. T is the time the alam lasted. In the gowing phase, both hoizontal and vetical velocities inceased ove time, howeve, the two values ae not significant. At the matue phase, downdaft eached the gound and fomed the outflow, indicating that the hoizontal velocity inceased apidly. Finally, in the dissipating phase, hoizontal and vetical velocities wee both decaying. Accoding to the esults, the maximum hoizontal velocities fom 7.5min to1min ae lage than the dange limit of the hoizontal shea; the isk peak is even s -1 at 9min. Afte 7.5min, the vetical velocity eached a peak value, moe than 9m/s, and the height was less than 1km, which will incease the isk of flight.

8 148 TANG Chu and HONG Guanxin / Pocedia Engineeing 17 ( x x1 5 1 Γ 1 1.x1 5 5.x1 4 h v / km (a t / min t / min (b 1.6x x1 5 v / km Q 8.x x1 4 (c t / min t / min (d Fig. 3. (a Γ as a function of time; (b time histoy of hv; (c time histoy of v; (d time histoy of Q u max 15 v max u alam V max / m s T t / min Fig. 4. time histoy of the maximum hoizon/ vetical velocity Wind field simulation of each phase is shown in fig 5. Velocity values fom the smallest to the lagest ae epesented with changing colos with blue fo the smallest to ed fo the lagest. It can be seen fom the figue that, in the gowing phase, the altitude of downbust was highe (moe than km, the outflow did not appea nea the gound, and the downdaft was the main facto affecting flight. In the matue phase, outflow appeaed nea the gound. Flying though a downbust egion, an aicaft encountes outflow and downdaft (at altitude less than 1km, and they all affect flight safety. It is extemely dangeous to fly though the wind field duing this phase. That is the eason why most models only

9 TANG Chu and HONG Guanxin / Pocedia Engineeing 17 ( simulate the wind field of this phase. In the dissipating phase, outflow became lage. The velocity change of outflow font will also affect flight safety y / m h / m a Gowing phase y / m h / m b Matue phase y / m h / m c Dissipating phase -5 5 Fig. 5. Flow lines of hoizontal section and velocity of longitudinal pofile of each phase

10 15 TANG Chu and HONG Guanxin / Pocedia Engineeing 17 ( Conclusions This pape pesents an engineeing model to simulate downbust evolution though intoducing timevaying paametes of ing votex and linea souce models, and the esults ae compaed with measued values. Following conclusions ae obtained: 1 Based on the ing votex model of downbust, though supeposing the linea souce model, the new model can descibe downbust evolution well. The method is simple and easy fo calculation. By intoducing the linea souce model, the new model could descibe outflow when the downdaft eaches the gound. 3 Paametes affecting the downbust evolution include the stength, adius and altitude of the ing votex and the stength of the linea souce. These paametes follow the exponential ule with time. 4 Duing matue and dissipating phases, the hoizontal shea value is lage and it can even exceed the dange limit, thus theaten flight safety. 5 The model is able to simulate the whole evolution pocess of downbust thus can be used in the eseach of flight chaacteistics though downbust. This pape simulated the downbust unde an isolated axisymmetic thundestom without tanslation speed. The model descibes the stuctue of downbust flow with some meteoological paametes neglected. In addition, thunde clouds often accompany sevee isolated thundestom, so the inteactions between them need futhe study. Refeences [1] Zhu Shangxiang, Etkin B. Model of the Wind Field in a downbust. Jounal of Aicaft, 1985;(7: [] Liu Gang, Wang Xingen, Jia Rongzhen. Engineeing Simulation of Vaiable Wind Field in Synthetic Natual Envionment. Jounal of System Simulation, 6,18(:97-3 [3] Ivan M. A Ring-Votex Downbust Model fo Flight Simulatos. Jounal of Aicaft, 1986;3 (3: 3-36 [4] Gao Zhenxing, Gu Hongbin, Liu Hui. Real-time Simulation of Lage Aicaft Flying Though Micobust. Chinese Jounal of Aeonautics, 9(: [5] Zhu Shangxiang. Hydokinetics Model of Micobust. Flight Dynamics, 1985;59-7 [6] Mak R. Hjelmfelt. Stuctue and Life Cycle of Micobust Outflows Obseved in Coloado. Jounal of applied meteoology, 1987;(7: 9-97 [7] Fed H. Pocto. Numeical Simulation of an Isolated Micobust. Pat I: Dynamics and Stuctue. Jounal of the atmospheic sciences,1988;45 (1: [8] Paul Aaon Robinson. The Modeling of Tubulence and Downbusts fo Flight Simulatos. Toonto: Univesity of Toonto, 1991 [9] Xiao Yelun, Jin Changjiang. Flight Pinciple in Atmospheic Distubance. Beijing: National Defence Industy Pess, 1993 [1] Kong Fanyou, Huang Meiyuan, Xu Huanying. Numeical Simulations of the Micobust. Sciatica Atmospheic Sinica, 1994;18 (1:11-1 [11] Sun Qingmin, Jin Changjiang. Numeical Simulation of Micobust Case. Flight Dynamics,1995;13 (4:9-3 [1] Chen Huizhi. Aviation Flight and Safety unde Dangeous Weathe Condition. Southwest Jiaotong Univesity. 3