The variation in pressure on various faces of a rectangular shaped tall building due to the presence of courtyard and open- ing is examined for a boundary layer flow condition corresponding to terrain category II of IS:875 (Part 3)- 2015. ANSYS CFX is used for the simulation. Two turbulence models, k- and shear stress transport (SST), are used in the validation of ANSYS CFX, and the results are compared with different international standards. In the presence of courtyard and opening, interesting and unusual pressure distributions on certain faces are observed due to a self-interference effect. Flow patterns around the building for different areas of opening are also studied to explain the phenomena occurring around the building. Furthermore, the polynomial expressions for calculating force coefficients and mean pressure coefficients of each face for different angles of attack and areas of opening are proposed using least-squares regression method. Accuracy of the fitted polynomials is measured by R value. Keywords Computational fluid dynamics · Courtyard · Opening · Mean pressure coefficients · Least-squares regression polynomial Introduction for providing good ventilation. In a housing complex, it can be used as a shared park-like space, parking garage or swim- With the continuous improvement of modern analysis and ming pool. Wind effects of conventional plan shape build - design technology and in the context of huge urban growth, ing are given in relevant wind standards such as Australian/ the number of tall buildings and skyscrapers is increasing NewZealand AS/NZS 1170.2: 2011, British BS 6399-2: day by day. Wind engineering is also getting much more 1997, American code ASCE 7-16 and Indian IS: 875 (Part- attention, as the need for study of the possible inconven- 3), 2015. ience, damage or benefits from wind on these tall build - However, these international standards are silent about ings arises. Such tall buildings may be of a conventional or the wind effects on the building when there is an inner court - uncommon shape in plan. Building with inner courtyard is yard. Windward face generally experiences critical pressure not very uncommon as courtyard is an integral component distribution for conventional plan shape model, but uncon- of constructed dwellings from old human civilizations such ventional or irregular plan shaped buildings sometimes as Indus Valley, Chinese, Egyptian or Mesopotamian. experience critical pressure distribution on other faces also. Courtyard is an unroofed area which is partially or com- Responses of unconventional plan shaped buildings to the pletely enclosed by walls or buildings in a large house or wind are estimated by employing CFD or wind tunnel tech- housing complex. Courtyard is generally used in buildings niques. Some researchers in the field of wind engineering conducted works on unconventional plan shape high rise buildings. Gomes et al. (2005) experimentally and analyti- * Prasenjit Sanyal cally calculated wind pressure on different faces of ‘U’ and prasenjit.sanyal14@gmail.com ‘L’ plan shaped tall buildings. Wind pressure distribution Sujit Kumar Dalui on various faces was observed to be different from that of sujit_dalui@rediffmail.com a square model. Amin and Ahuja (2011) presented experi- Department of Civil Engineering, Indian Institute mental results of pressure distribution on various faces of ‘T’ of Engineering Science and Technology, Shibpur, Howrah, and ‘L’ plan shape tall buildings for various wind incidence India Vol.:(0123456789) 1 3 170 International Journal of Advanced Structural Engineering (2018) 10:169–188 angles. It was observed that pressure distribution around layer wind profile is governed by the power law equation: these tall buildings largely depends on the plan shape. Fu U(z) = U Z∕Z 0 0 et al. (2008) presented field measurement data of bound- Where U(z) is velocity at some particular height Z, U ary layer wind characteristics over typical open country and is boundary layer velocity, Z is the boundary layer depth urban terrain for two super tall buildings. Results of full- and is power law exponent and its value is taken as 0.133 scale measurement were compared with wind tunnel data. which satisfies terrain category II, mentioned in IS 875-part Ramponi and Blocken (2012) calculated outdoor and indoor 3 (2015). air flows of a building under natural cross ventilation strat- egies. Montazeri and Blocken (2013) compared the wind Details of model effects on buildings with and without balconies. Experimen- tal investigation on aerodynamic characteristics of various The buildings are modelled in 1:300 scale and the wind triangular shaped tall buildings was done by Kumar et al. velocity scale is taken as 1:5. So as per the recommenda- (2013). Raj and Ahuja (2013) compared the base shear, base tion of IS 875-part 3 (2015), the scaled down velocity of moment and twisting moment of three rigid building mod- Kolkata zone is taken as 10 m/s. k- turbulence model is els having the same floor area, but different cross-sectional used for the numerical simulation. The k- models use the shapes by changing the wind incidence angle. Muehleisen gradient diffusion hypothesis to relate Reynolds stresses to and Patrizi (2013) compared a huge set of data and derived mean velocity gradients and turbulent viscosity. Turbulent a parametric equation of C . Bhattacharyya et al. (2014) viscosity is modelled as the product of turbulent length scale presented analytical and experimental results of pressure and turbulent velocity. k is the turbulent kinetic energy and distribution on various faces of ‘E’ plan shape tall build- is defined as the variance of fluctuations in velocity. It has 2 −2 ings for various wind incidence angles. Experimental and dimensions of L T . is the turbulence eddy dissipation analytical results of pressure distribution on various faces of which is actually the rate at which the velocity fluctuation ‘Y’ shape tall buildings were presented by Mukherjee et al. dissipates and has dimensions of per unit time. (2014). Peculiar pressure distribution has been observed The continuity and momentum equations are on certain face due to self-interference effect. Chakraborty et al. (2014) presented numerical and experimental study + = 0 (1) of ‘+’ shaped tall building for 0° and 45° angles of wind t x attack. The inter-building and intra-building aerodynamic behaviours of linked buildings were investigated by Song et al. (2016). Paul and Dalui (2016) calculated the Wind U U � U U U i j P j i i + =− + + + S , eﬀ M effects on ‘Z’ plan shaped tall building by changing the wind t x x x x x j i j j i incidence angle from 0° to 150° at an interval of 30°. The (2) flow and dispersion in cross-ventilated isolated buildings by where S is the sum of body forces, is the effective vis- M eﬀ changing the opening positions were analysed by Tominaga cosity accounting for turbulence and P is the modified pres- and Blocken (2016). sure. Density and velocity are denoted by and U. i and j are Very little research has been done on wind effects of two mutually perpendicular directions. opening on tall buildings till now. Furthermore, the Wind The k- model is based on the concept of eddy viscosity, Codes do not provide any guidelines for inner courtyard, so that which necessitates research on this area. The current work = + , eﬀ t (3) mainly focuses on wind effects of courtyard and opening on where is turbulent viscosity rectangular plan shaped tall building with inner courtyard for 0°–180° wind incidence angle at an interval of 30°. = C . (4) The values of k and come from the differential transport Numerical analysis of the tall building equations of turbulence kinetic energy and turbulence dis- by ANSYS CFX sipation rate kU (k) j t k In the present study, the rectangular plan shaped building + = + + P + P − − Y + S k b M k t x x x j j k j with opening and inner courtyard is analysed by the CFD (5) package, namely ANSYS CFX (version 16.0). The boundary 1 3 100 mm International Journal of Advanced Structural Engineering (2018) 10:169–188 171 � � �� � � () j (6) + = + + C S − C + C C P + S , 1 2 1 3 b t x x x k j j j k + on the leeward side and avoids backflow of wind. Moreover, where P represents the generation of turbulence kinetic no blockage correction is required. Meshing the domain is energy due to the mean velocity gradients, P represents done by tetrahedral elements (Fig. 2). The mesh near the the generation due to buoyancy, Y represents the contribu- building is made more fine compared to other location for tion of fluctuating dilatation in compressible turbulence to accurately checking the wind parameters. The mesh inflation overall dissipation rate and C and C are constants. and 1 2 k is provided near the boundaries to provide a smooth flow. are the turbulent Prandtl numbers for k (turbulence kinetic The velocity of wind at inlet is taken as 10 m/s. No slip energy) and (dissipation rate). The values considered for wall is considered at building faces and the bottom, and C , and are taken as 1.44, 1 and 1.3, respectively, as 1 k free slip wall is considered for the top and side faces of the per the recommendation of Jones and Launder (1972). domain. The relative pressure at outlet is taken as 0 Pa. The operating pressure in the domain is 1 atm, i.e. 101,325 Pa. Domain and meshing Validation A domain has 5H, 15H, 5H and 5H inlet, outlet, two side face and top clearances from edges of the buildings, where H Before starting the numerical wind analysis of the build- is the height of the model as shown in Fig. 1. This domain is ing with inner courtyard and opening, the results from the constructed as per recommendation of Franke et al. (2004). ANSYS CFX package are to be validated. For this rea- Such a large domain is good enough for vortex generation son, a square plan shaped building (Fig. 3) of dimension 100 mm × 150 mm and height 700 mm is analysed in the afore-mentioned domain by k-ɛ and SST turbulence model for 0 wind incidence angle using ANSYS CFX. The free 150 mm A C Fig. 1 Domain used for CFD simulation Fig. 3 Different faces of model with the direction of wind Fig. 2 a Typical mesh pattern in the computational domain. b Zoom-in view around the building mode 1 3 172 International Journal of Advanced Structural Engineering (2018) 10:169–188 stream velocity 10 m/s is considered at the inlet. The domain observed that the horizontal centrelines obtained from k- is constructed as per recommendation of Franke et al. (2004) model have a better agreement with the experimental results as mentioned earlier. The face average values of coefficient compared to those from SST model. So, further analysis has of pressures are determined by ANSYS CFX package and been done based on k- turbulence model. compared with different international wind codes. The external pressure coefficient ‘C ’ is calculated using the formula C = P∕(0.6V ) , where P is the wind pressure Parametric study and V is the design wind speed. The external surface pres- sure coefficients, C (face average value), for different faces The building is modelled in 1:300 scale. The scaled down of the model are listed and compared with different interna- dimension of the building is 600 mm × 500 mm × 500 mm. tional standards as shown in Fig. 4. The isometric views of different cases are shown in Fig. 6. To correlate the results obtained from the two models The numerical simulation of each building is also carried ◦ ◦ with those from experimental studies in the literature, a com- out by changing the wind incidence angle from 0 to 180 parison is made between present and Sarath et al. (2015) at an interval of 30 . Height of opening of Model C varies results. Eventually, dimensions and all other parameters from 0 to 500 mm. related to the wind flow are matched with the numerical At 500 mm opening, it simply becomes a U plan shaped studies. For better understanding between two turbulence tall building. models and experimental results, the pressure coefficients The top view and bottom view with wind incidence along the horizontal centrelines around the building periph- angles of Model C are shown in Fig. 7. The faces shown in ery for 0° wind incidence angle are compared. these plan views are sufficient enough for explaining differ - From Fig. 4, it can be seen that results found by the both ent faces of all the models. turbulence models are approximately the same with the values mentioned in different IS codes. From Fig. 5, it is Fig. 4 Comparison of mean k-e SST ASCE 7-16 AS/NZS-1170.2 (2011) IS:875 (Part-3) pressure coefficient between numerical results and different international standards 1.5 k-e SST 0.5 Wind tunnel results by 00 .0 50 .1 0.15 0. 20 .2 5 Sarath et al.(2015) -0.5 -1 -1.5 Peripheraldistance in m Fig. 5 Comparison of pressure coefficients around the building at mid depth for k- model, SST model and experimental results by Sarath et al. (2015) for 0° wind incidence angle 1 3 CP CP 0.77 0.77 0.80 0.80 0.90 -0.75 -0.79 -0.70 -0.65 -0.80 -0.49 -0.56 -0.40 -0.40 -0.85 -0.75 -0.77 -0.70 -0.65 -0.80 International Journal of Advanced Structural Engineering (2018) 10:169–188 173 (a) MODEL A : Building without courtyard (a) Top view (b) MODEL B: Building with courtyard (No opening) (b) Bottom View Fig. 7 Wind incidence angle ( ) with respect to plan [Model C]; 0 ≤ ≤ 180° the flowlines are symmetrical till the generation of vorti - ces. Wind flow separates after colliding with the windward Face A. So, it mainly experiences positive pressure with slight negative pressure near the edges due to flow separa- tion. Faces B and D experience negative pressure due to side (c) MODEL C: Building with courtyard wash. Two almost symmetrical vortices are formed in the (Opening DepthX :0 < X ≤500) wake region behind Face C. Unlike Model B, wind directly enters inside the courtyard from the opening for Model C, which causes change in pressure of the inner faces. For dif- Fig. 6 Isometric view of different cases (all dimensions are in mm ferent angles of attack, Models A and B follow almost the same type of flow pattern. With the increase in angle of attack, different faces change their position with respect to Results and discussion the windward direction and cause a huge change in pressure effects of these faces. For some cases, vortex is also formed Numerically predicted wind flow inside the courtyard of Model C. Flow patterns of each building for different wind incidence angles are shown in Fig. 8. For 0 wind incidence angle, 1 3 174 International Journal of Advanced Structural Engineering (2018) 10:169–188 (a) Flow around model A ( =0°) (b) Flow around model B( =0°) (c) Flow around model C ; x=0.25m ( =0°) (e) Flow around model A ( = (f) Flow around model B( = 30°) (d) Flow around model C ;x=0.5m ( =0°) 30°) (g) Flow around model C ; (h) Flow around model C ;x=0.5m (i) Flow around model A( = 60°) x=0.25m ( = 30°) ( = 30°) (j) Flow around model B( = 60°) (l) Flow around model C; x=0.5m (k) Flow around model C; x=0.25m ( = 60°) ( = 60°) (n) Flow around model B( = 90°) (o) Flow around model C;x=0.25m (m) Flow around model A( = ( = 90°) 90°) Fig. 8 Bottom view of 3D flow pattern around different models for different wind incidence angles 1 3 International Journal of Advanced Structural Engineering (2018) 10:169–188 175 (p) Flow around model C;x=0.5m (q) Flow around modelA ( =120°) (r) Flow around modelB ( =120°) ( = 90°) (s) Flow around model C;x=0.25m (t) Flow around model C;x=0.5m (u) Flow around model A( = ( = 120°) ( = 120°) 150°) (v) Flow around model B( = (w) Flow around model C; x=0.25m (x) Flow around model C; x=0.5m 150°) ( = 150°) ( = 150°) Fig. 8 (continued) (a)(b) (c) Fig. 9 Pressure contour of different faces of Model A [ = 0 ]. a Face A. b Faces B and D. c Face C Pressure distribution are sufficient for understanding the behaviour of every model under wind action for = 0 . Pressure contours of every For 0 wind incidence angle, each model experiences sym- plane for some particular cases at 0 wind angle are shown in Figs. 9, 10, 11 and 12. metrical flow pattern till the vortices are formed. Thus, sym- metrical faces will experience identical or almost similar The key features of the pressure contours on various sur- faces of different models are described as follows: Models pressure distribution; so only six Faces A, B, C, E, F and G 1 3 176 International Journal of Advanced Structural Engineering (2018) 10:169–188 (a)(b) (c) (d) (e)(f) Fig. 10 Pressure contour of different faces of Model B [ = 0 ]. a Face A. b Faces B and D. c Face C. d Face E. e Faces F and H. f Face G (a)(b) (c) (d) (e)(f) Fig. 11 Pressure contour of different faces of Model C (X = 0.25 m) [ = 0 ]. a Face A. b Faces B and D. c Face C. d Face E. e Faces F and H. f Face G 1 3 International Journal of Advanced Structural Engineering (2018) 10:169–188 177 (a)(b) (c) (d)(e) Fig. 12 Pressure contour of different faces of Model C (X = 0.5 m) [ = 0 ]. a Face A. b Faces B and D. c Face C. d Faces F and H. e Face G A and B experience similar type of pressure distribution A of Model A when the wind incidence angle is 0 , and for windward and leeward face. Only side faces observed maximum negative mean pressure coefficient of − 0.848 some discrepancy due to the difference in the formation of occurs on Face E of Model C(x = 0.25 m) at angle of ◦ ◦ vortices. Face A experiences mainly positive pressure except attack 60 . For 0 , wind angle symmetrical faces experi- near the edges. Pressure distribution is parabolic in nature ence almost the same pressure distribution. At the same due to boundary layer flow and symmetrical about vertical wind angle, the variation of C for different heights of centreline. Faces B and D have throughout negative pres- opening is not very significant for Faces A, B, C, D and sure with less negative value towards the leeward side due E. But for Faces F, G and H the variation is very high ◦ ◦ ◦ to some reattachment of wind. for wind angle 0 , 30 and60 . So, for these wind angles Face C has slightly positive pressure near the bottom and more cases of opening are considered. With the increase negative elsewhere. The negative pressure is due to the for- in opening, the C value for Faces F, G and H increases mation of vortex, and slight positive pressure at the bottom invariably. The variation of C value for different wind is because the reattachment wind pressure is higher than angles is more for the outer faces than the inner faces. the suction pressure. Inner courtyard Faces E, F and H have throughout negative pressure. Face G has lower negative In the context of detail study on wind pressure coeffi- pressure at bottom and higher negative pressure towards top. cients of each of the faces, the variation of C with wind For = 0 , Faces A, B, C and E do not experience much incidence angles and openings are required to plot. Also, it variation in pressure for different models. Faces F, G and H is important to quantify the mean pressure coefficients for a have negative value at top and positive value at bottom. With particular face of different models without rigorous calcu- the increase in area of opening these faces experience high lation. For that reason, it is of utter importance to propose increase in pressure at bottom of its surface. analytical expression of C for all the faces. C of different faces for Models A and B are Pressure and force coefficient plotted in Fig. 13 as scattered points. These data are then fitted as a fifth degree polynomial, 2 3 4 5 The mean pressure coefficient for all surfaces of Mod- C = + + + + + by least- p 0 1 2 3 4 5 els A, B and C is tabulated in Table 1. Maximum posi- squares regression method using the method as discussed tive mean pressure coefficient of 0.813 occurs on Face in Appendix. Where is the angle of attack and varies from 1 3 178 International Journal of Advanced Structural Engineering (2018) 10:169–188 Table 1 Mean pressure coefficients for each faces of different building models for various wind angles Model Face A Face B Face C Face D Face E Face F Face G Face H 0 Model A 0.813 − 0.624 − 0.391 − 0.624 Model B 0.800 − 0.461 − 0.204 − 0.461 − 0.456 − 0.459 − 0.456 − 0.459 Model C (X = 0.1 m) 0.564 − 0.578 − 0.364 − 0.438 − 0.450 − 0.344 − 0.126 − 0.344 Model C (X = 0.2 m) 0.619 − 0.528 − 0.383 − 0.528 − 0.488 − 0.049 0.139 − 0.049 Model C (X = 0.25 m) 0.651 − 0.493 − 0.376 − 0.563 − 0.591 0.008 0.217 0.008 Model C (X = 0.3 m) 0.658 − 0.468 − 0.369 − 0.598 − 0.534 0.186 0.388 0.186 Model C (X = 0.4 m) 0.661 − 0.657 − 0.434 − 0.675 − 0.432 0.425 0.714 0.425 Model C (X = 0.5 m) 0.664 − 0.691 − 0.473 − 0.691 – 0.539 0.715 0.539 30 Model A 0.646 − 0.146 − 0.748 − 0.398 Model B 0.641 0.015 − 0.655 − 0.322 − 0.659 − 0.650 − 0.639 − 0.643 Model C (X = 0.1 m) 0.397 0.031 − 0.553 − 0.388 − 0.288 − 0.185 − 0.047 − 0.073 Model C (X = 0.2 m) 0.407 0.050 − 0.543 − 0.372 − 0.345 0.019 0.187 0.156 Model C (X = 0.25 m) 0.422 0.069 − 0.515 − 0.450 − 0.445 0.190 0.260 0.250 Model C (X = 0.3 m) 0.432 0.089 − 0.500 − 0.478 − 0.373 0.420 0.411 0.437 Model C (X = 0.4 m) 0.509 0.129 − 0.461 − 0.538 − 0.308 0.515 0.548 0.483 Model C (X = 0.5 m) 0.567 0.133 − 0.455 − 0.525 – 0.311 0.628 0.559 60 Model A − 0.014 0.684 − 0.484 − 0.419 – – – – Model B 0.094 0.621 − 0.514 − 0.366 − 0.529 − 0.598 − 0.578 − 0.538 Model C (X = 0.1 m) − 0.185 0.560 − 0.735 − 0.473 − 0.650 − 0.531 − 0.487 − 0.195 Model C (X = 0.2 m) − 0.128 0.602 − 0.684 − 0.434 − 0.794 − 0.433 − 0.362 − 0.094 Model C (X = 0.25 m) − 0.111 0.604 − 0.753 − 0.443 − 0.848 − 0.328 − 0.343 − 0.098 Model C (X = 0.3 m) − 0.076 0.598 − 0.755 − 0.446 − 0.779 − 0.176 − 0.214 0.049 Model C (X = 0.4 m) − 0.051 0.604 − 0.663 − 0.409 − 0.628 − 0.020 − 0.062 0.188 Model C (X = 0.5 m) 0.017 0.542 − 0.632 − 0.385 – − 0.108 0.167 0.122 90 Model A − 0.654 0.783 − 0.654 − 0.545 – – – – Model B − 0.536 0.776 − 0.536 − 0.412 − 0.493 − 0.486 − 0.493 − 0.491 Model C (X = 0.25 m) − 0.517 0.779 − 0.539 − 0.412 − 0.714 − 0.478 − 0.487 − 0.383 Model C (X = 0.5 m) − 0.514 0.756 − 0.352 − 0.363 – − 0.389 − 0.313 − 0.278 120 Model A − 0.484 0.684 − 0.014 − 0.419 – – – – Model B − 0.514 0.621 0.074 − 0.366 − 0.578 − 0.598 − 0.592 − 0.538 Model C (X = 0.25 m) − 0.664 0.568 0.178 − 0.518 − 0.635 − 0.592 − 0.600 − 0.442 Model C (X = 0.5 m) − 0.669 0.560 0.039 − 0.492 – − 0.424 − 0.364 − 0.351 150 Model A − 0.748 − 0.146 0.646 − 0.398 – – – – Model B − 0.655 0.015 0.641 − 0.322 − 0.639 − 0.650 − 0.659 − 0.643 Model C (X = 0.25 m) − 0.548 0.070 0.638 − 0.507 − 0.629 − 0.495 − 0.552 − 0.517 Model C (X = 0.5 m) − 0.658 0.040 0.583 − 0.588 – − 0.511 − 0.487 − 0.491 180 Model A − 0.391 − 0.624 0.813 − 0.624 – – – – Model B − 0.204 − 0.461 0.800 − 0.461 − 0.456 − 0.459 − 0.456 − 0.459 Model C (X = 0.25 m) − 0.487 − 0.674 0.735 − 0.644 − 0.589 − 0.487 − 0.485 − 0.442 Model C (X = 0.5 m) − 0.447 − 0.619 0.711 − 0.689 – − 0.376 − 0.365 − 0.417 ◦ ◦ ◦ 0 to 180 . The polynomial coefficients along with along the the maximum positive pressure occurs at Face A for ≈ 11 regression coefficients (R ) for different faces are shown in and maximum negative pressure occurs at the same face for Table 2. It is found that most of the polynomials are fitted ≈ 155 . For Models A and B, significant pressure varia- well with fifth degree least-squares polynomial. All R val- tion occurs only on outside Faces A, B and C. For different ues are greater than 0.9 which is very much acceptable to wind angles, change in pressure on the inner faces of Model construct a model with least-squares regression polynomial. B is very small. The fitted polynomials are then plotted alongside of C data The external surface pressure coefficients, C (face aver- p p points in Fig. 13. From fitted polynomials, it is found that age value), of different faces for Model C are fitted as a 1 3 International Journal of Advanced Structural Engineering (2018) 10:169–188 179 1.2 Face A ; Model A Face A; Model B 0.8 Face B ; Model A 0.6 Face B ; Model B 0.4 Face C ; Model A 0.2 Face C ; Model B Face D ; Model A 020406080 100 120 140 160 180 -0.2 Face D ; Model B -0.4 Face E ; Model B -0.6 Face F ; Model B -0.8 Face G ; Model B -1 Face H ; Model B Angle of a ack (θ) Fig. 13 Plot of numerical data points and derived equations of mean pressure coefficient for Models A and B Table 2 Least-squares polynomials of pressure coefficient for each face of Models A and B Model 0 1 2 3 4 5 R Face A −5 −7 −10 Model A 0.806389 0.035764 − 0.00203 2.81 × 10 − 1.60 × 10 3.30 × 10 0.9771 −2 −3 −5 −8 −10 Model B 0.79448 2.34 × 10 − 1.36 × 10 1.77 × 10 − 9.61 × 10 1.95 × 10 0.9863 Face B −3 −4 −6 −8 −22 Model A − 0.62981 4.21 × 10 6.38 × 10 − 7.35 × 10 2.04 × 10 − 6.87 × 10 0.9866 −3 −4 −6 −8 −22 Model B − 0.46317 8.58 × 10 3.95 × 10 − 4.92 × 10 1.37 × 10 − 4.48 × 10 0.9973 Face C −5 −8 −10 Model A − 0.37595 − 0.02281 0.000787 − 1.27 × 10 9.47 × 10 − 2.41 × 10 0.9747 −5 −8 −10 Model B − 0.20919 − 0.03276 0.000946 − 1.29 × 10 8.74 × 10 − 2.13 × 10 0.9879 Face D −6 −8 −22 Model A − 0.62601 0.018239 − 0.00045 3.84 × 10 − 1.07 × 10 3.11 × 10 0.9433 −6 −9 −22 Model B − 0.46122 0.011159 − 0.00028 2.46 × 10 − 6.84 × 10 2.00 × 10 0.9979 Face E −6 −8 −12 Model B − 0.45512 − 0.01711 0.000445 − 3.90 × 10 1.12 × 10 − 1.71 × 10 0.9834 Face F −6 −8 −23 Model B − 0.45755 − 0.01651 0.00043 − 3.76 × 10 1.04 × 10 − 7.36 × 10 0.9569 Face G −6 −9 −12 Model B − 0.45512 − 0.01566 0.000411 − 3.58 × 10 9.62 × 10 1.71 × 10 0.9834 Face H −6 −8 −23 Model B − 0.45952 − 0.01565 0.000424 − 3.75 × 10 1.04 × 10 3.24 × 10 0.9933 second-order polynomial using least-squares regression through the opening is significant, we can use the equations method as discussed in Appendix. of Table 3. The polynomials are in the form of The variation of wind effects for different heights of the 2 2 C = + + x + + x + x . W her e is frontal opening is low for higher wind incidence angles. p 0 1 2 11 22 12 ◦ ◦ the angle of attack, which varies from 0 to 180 and x is the So, for obtaining more accurate curve fitting polynomials, height of opening varies from 0 to 500 mm. But for x = 0, we have separated the range of wind incidence angle from ◦ ◦ ◦ ◦ the building becomes Model B and so we can use the equa- 0 to 60 and from 6 0 to 180 . The polynomial coefficients tions of Table 2. For x > 0 , i.e. when the inflow of wind along with the regression coefficients ( R ) for different faces are shown in Table 3. It is found that most of the 1 3 Cp 180 International Journal of Advanced Structural Engineering (2018) 10:169–188 Table 3 Least-square polynomials of pressure coefficient for each face of Model C 2 2 C = + + x + + x + x , where 0 mm < x ≤ 500 mm p 0 1 2 11 22 12 Face Angle of attack 0 1 2 11 22 12 −7 −7 −7 ◦ ◦ Face A 0 ≤ ≤ 60 0.59627 − 0.00231 9.24 × 10 − 0.00019 3.65 × 10 7.26 × 10 0.9952 ◦ ◦ −2 −4 −4 −6 −6 60 <𝜃 ≤ 180 1.57160 − 3.41 × 10 − 2.43 × 10 1.33 × 10 1.05 × 10 − 3.58 × 10 0.9145 −4 −5 −6 −6 ◦ ◦ Face B 0 ≤ ≤ 60 − 0.61844 0.022658 6.97 × 10 − 8.56 × 10 − 1.53 × 10 6.04 × 10 0.9920 ◦ ◦ −2 −4 −4 −7 −6 60 <𝜃 ≤ 180 − 0.49380 2.84 × 10 − 1.92 × 10 − 1.59 × 10 4.11 × 10 − 1.42 × 10 0.9924 −3 −4 −5 −7 −6 ◦ ◦ Face C 0 ≤ ≤ 60 − 0.30069 − 5.60 × 10 − 5.27 × 10 − 2.28 × 10 6.09 × 10 6.89 × 10 0.9042 ◦ ◦ −2 −4 −5 −7 −7 60 <𝜃 ≤ 180 − 1.662 1.66 × 10 − 3.44 × 10 − 1.38 × 10 7.94 × 10 − 9.60 × 10 0.9485 −5 −7 −5 ◦ ◦ Face D 0 ≤ ≤ 60 − 0.33627 0.00158 − 0.00101 − 5.35 × 10 4.76 × 10 1.42 × 10 0.9430 ◦ ◦ −3 −4 −5 −7 −6 60 <𝜃 ≤ 180 − 0.67667 4.16 × 10 3.91 × 10 − 1.67 × 10 4.70 × 10 − 6.15 × 10 0.9031 ◦ ◦ −6 −6 Face E 0 ≤ ≤ 60 − 0.42726 0.01359 − 0.00108 − 0.00028 2.66 × 10 − 2.97 × 10 0.9014 ◦ ◦ −3 −3 −6 −6 −7 60 <𝜃 ≤ 180 − 0.76319 2.20 × 10 − 1.55 × 10 − 3.32 × 10 3.70 × 10 9.12 × 10 0.9244 ◦ ◦ −2 −3 −4 −6 −5 Face F 0 ≤ ≤ 60 − 0.61709 1.29 × 10 3.48 × 10 − 2.48 × 10 − 2.38 × 10 − 1.57 × 10 0.9263 −5 −7 −6 ◦ ◦ 60 <𝜃 ≤ 180 0.02360 − 0.01074 0.000674 4.51 × 10 4.50 × 10 − 4.61 × 10 0.9235 ◦ ◦ −4 −7 −5 Face G 0 ≤ ≤ 60 − 0.37080 0.01173 0.002781 − 2.99 × 10 − 9.71 × 10 − 1.06 × 10 0.9800 −5 −6 −6 ◦ ◦ 60 <𝜃 ≤ 180 0.01673 − 0.01185 0.001048 5.25 × 10 1.27 × 10 − 9.31 × 10 0.9017 ◦ ◦ −4 −6 −5 Face H 0 ≤ ≤ 60 − 0.69793 0.020195 0.003624 − 2.67 × 10 − 2.27 × 10 − 2.18 × 10 0.9757 −2 −3 −5 −7 −6 ◦ ◦ 60 <𝜃 ≤ 180 0.19899 − 1.26 × 10 1.49 × 10 5.03 × 10 − 2.57 × 10 − 7.72 × 10 0.9388 Max / Data Max / Equaon Min / Data Min / Equaon Fig. 14 Comparison of maximum and minimum mean pressure coefficients of different faces from numerical data and derived equations polynomials are fitted well. Least accuracy in terms of from ANSYS CFX in the desired direction, ‘P’ is the wind 2 ◦ ◦ R value is found for Face E (0 ≤ ≤ 60 ) because of its pressure and ‘A’ is the projected surface area to the wind. varying surface area and separation of inflow wind inside C along two perpendicular directions X (perpendicular the courtyard. However, all R values are greater than 0.9 to Face A) and Y (parallel to Face A) are tabulated in which is very much acceptable to construct a model with Table 4. least-squares regression polynomial. The force coefficients along the X and Y direc- The comparison of the maximum and minimum values tions are fitted as the second-order polynomial of form 2 2 of mean pressure coefficients obtained from numerical C = + + x + + x + x . To obtain f 0 1 2 11 22 12 data and derived equations is shown in Fig. 14, and has more accurate results, two different sets of equations are ◦ ◦ ◦ ◦ found that the deviation is within the allowable limit. formed for 0 ≤ ≤ 60 and 60 <𝜃 ≤ 180 and shown in Force coefficient (C ) is determined by the formula Table 5. The R values are found to be greater than 0.9. So, C = ,where ‘F’ is the value of total force exported P×A 1 3 0.81 0.99 -0.75 -0.74 0.78 0.90 -0.69 -0.65 0.81 0.98 -0.83 -0.77 -0.23 -0.32 -0.69 -0.72 -0.26 -0.17 -0.85 -0.79 0.54 0.55 -0.65 -0.73 0.72 0.81 -0.66 -0.74 0.56 0.63 -0.64 -0.69 International Journal of Advanced Structural Engineering (2018) 10:169–188 181 Table 4 Force coefficients for Model θ C C θ C C θ C C f,x f,y f,x f,y f,x f,y each faces of different building ◦ ◦ ◦ models for various wind angles Model A 0 1.195 − 0.023 30 1.134 0.145 60 0.425 0.841 Model B 0.975 − 0.005 0.999 0.173 0.516 0.860 Model C (X = 0.1 m) 1.308 − 0.010 1.117 0.203 0.615 0.850 Model C (X = 0.2 m) 1.537 − 0.007 1.189 0.325 0.717 0.898 Model C (X = 0.25 m) 1.650 − 0.000 1.131 0.469 0.824 0.925 Model C (X = 0.3 m) 1.720 − 0.010 0.986 0.643 0.866 0.952 Model C (X = 0.4 m) 2.043 − 0.005 1.073 0.711 0.785 0.959 Model C (X = 0.5 m) 2.266 − 0.017 1.091 0.833 0.942 0.977 ◦ ◦ ◦ Model A 90 0 1.188 120 − 0.425 0.841 150 − 1.134 0.145 Model B − 0.006 0.974 − 0.516 0.860 − 0.999 0.213 Model C (X = 0.25 m) 0.124 1.070 − 0.640 0.754 − 0.891 0.313 Model C (X = 0.5 m) 0.109 0.999 − 0.241 0.961 − 1.003 0.345 Model A 180° − 1.195 − 0.023 Model B − 0.975 − 0.015 Model C (X = 0.25 m) − 1.214 − 0.018 Model C (X = 0.5 m) − 1.071 − 0.004 Table 5 Least-squares polynomials of force coefficients for Model C (and Model B: X = 0 mm) 2 2 Angle of attack C = + + x + + x + x , where 0 mm ≤ x ≤ 500 mm f 0 1 2 11 22 12 0 1 2 11 22 12 R f,x ◦ ◦ −4 −7 −5 0 ≤ ≤ 60 1.116248 − 0.01521 0.002388 1.26 × 10 − 8.05 × 10 − 2.88 × 10 0.9134 −5 −7 −6 ◦ ◦ 60 <𝜃 ≤ 180 2.432911 − 0.03609 0.000938 9.27 × 10 5.59 × 10 − 7.76 × 10 0.9823 f,y −5 −7 −6 ◦ ◦ 0 ≤ ≤ 60 − 0.11434 0.015678 0.000412 − 2.26 × 10 1.46 × 10 3.78 × 10 0.9336 ◦ ◦ −5 −4 −7 −6 60 <𝜃 ≤ 180 0.286216 0.01674 − 5.96 × 10 − 1.06 × 10 − 2.04 × 10 1.97 × 10 0.9299 we can easily construct a model with least-squares regres- 2.50 sion polynomial. The comparison of the maximum and minimum values 2.00 of C and C obtained from numerical data and derived f,x f,y 1.50 equations is shown in Fig. 15 and has found that the devia- tion is within the allowable limit. 1.00 Figure 16 illustrates the graphical output provided 0.50 by postreg command of MATLAB. This output provides C C f,x f,y how the polynomials are fitted with the given data. 0.00 Here, due to scarcity of space only output vs target -0.50 graphs for force coefficients is provided. The data points -1.00 are plotted as some open circles. The best linear fit is indi- cated by a dashed line. The perfect fit (when output equal -1.50 to targets) is indicated by the red solid line. From these four figures of output vs target graph, we have found that Max / Data Max / Equaon it is very difficult to distinguish the best linear fit line from Min / Data Min / Equaon the perfect fit line, because these fits are very good. The combined graphs from these fitted polynomials along Fig. 15 Comparison of maximum and minimum force coefficients the X and Y directions are plotted in Fig. 17. C decreases from numerical data and derived equations f,x 1 3 2.27 2.11 -1.21 -1.15 1.07 1.10 -0.04 -0.13 182 International Journal of Advanced Structural Engineering (2018) 10:169–188 ° ° ° ° (a) (0 ≤ ≤60 ) (b) (60 ≤ ≤180 ) , , ° ° ° ° (c) (0 ≤ ≤60 ) , (d) (60 ≤ ≤180 ) Fig. 16 Output vs target graph for force coefficients ◦ ◦ with the increase in angle of attack. But for 0 wind inci- has a maximum value of 2.11 for Model C (x = 0.5 m) at 0 dence angle, it increases with the increase in opening and wind angle and the same along the Y direction is extreme obtains the maximum value of 2.27 at X = 0.5 m. The value for Model C (x = 0.5 m) at 60 wind incidence angle with of C is almost zero at θ = 0 wind incidence angle. Then a value of 1.1. f,y it increases up to θ = 90 and decreases again and becomes Graphical plots representing effect of change of wind almost 0 at θ = 180 . From numerical data, it is found that incidence angle and area of opening on different faces of the force coefficient (C ) along the X direction has a maximum rectangular plan shaped tall building are shown in Figs. 18 value of 2.267 for Model C (x = 0.5 m) at 0 wind angle and and 19. Pressure on each face has been compared along the the same along the Y direction is extreme for Model A at vertical centreline for different cases. The comparison along 90 wind incidence angle with a value of 1.188. But from the perimeter has also been carried out at 0.125, 0.25 and fitted polynomials, it is found that C along the X direction 0.375 m height from the base of the building model. Only 1 3 International Journal of Advanced Structural Engineering (2018) 10:169–188 183 Fig. 17 Variation of force coef- ficients with wind incidence angle and height of opening (a) Force coefficient along x direction (C ) f,x (b) Force coefficient along y direction (C ) f,y ◦ ◦ ◦ be analysed thoroughly as the variation of pressure at differ - some cases of 0 , 30 and 60 are used for the comparison as the effect of variation is low for higher wind angles. ent positions of these faces is very high. From comparison along horizontal lines, it is also found that pressure variation With the change in angle of attack, different faces change their position and the variation of pressure coefficients along on the outside faces is similar; only magnitudes of pressure coefficient increase with the increase in height. horizontal and vertical centrelines also changes accordingly. For the same wind incidence angle, the nature of pressure on Face A does not experience much variation for different models. For Faces B, C and D, the variation is also very Conclusion low. Face E of Model C experiences more suction due to the separation of incoming flow and formation of vortices inside This paper described the pressure variation on all the sur- faces of rectangular plan shaped tall building in the pres- the courtyard. Faces F, G and H experience negative pres- sure for zero opening. But with the increase in opening, the ence of courtyard and opening. CFD Simulation has been done by ANSYS CFX software. k- and SST model have pressure gradually increases on all these faces. From vertical and horizontal pressure lines, it is found that the pressure in been used to validate the data with different international standards. As k- model gives more accurate result, it is different positions of Face F is highly irregular in nature and its unevenness is higher than other inner faces such as G and used for the further numerical simulations. The significant outcomes of the current study are: H. For some cases, the average C value of Faces F, G and H can be very small, but for design purposes these faces should 1 3 184 International Journal of Advanced Structural Engineering (2018) 10:169–188 0.5 0.5 0.5 0.45 0.45 0.45 0.4 0.4 0.4 0.35 0.35 0.35 0.3 0.3 0.3 0.25 0.25 0.25 0.2 0.2 0.2 0.15 0.15 0.15 0.1 0.1 0.1 0.05 0.05 0.05 -0.3 0.20.7 1.2 -1.2 -0.2 0.8 -1.5 -1 -0.5 00.5 Cp Cp Cp (a) Face A (b) Face B (c) Face C 0.5 0.5 0.5 0.45 0.45 0.45 0.4 0.4 0.4 0.35 0.35 0.35 0.3 0.3 0.3 0.25 0.25 0.25 0.2 0.2 0.2 0.15 0.15 0.15 0.1 0.1 0.1 0.05 0.05 0.05 0 0 -1 -0.5 0 -1.2 -0.2 0.8 -1.5 -1 -0.5 0 Cp Cp Cp (d) Face D (e) Face E (f) Face F 0.5 0.5 MODEL A (θ=0°) 0.45 0.45 MODEL B (θ=0°) 0.4 0.4 MODEL C ( X= 0.25m) (θ=0°) 0.35 0.35 MODEL C ( X=0.5m) (θ=0°) 0.3 0.3 MODEL A (θ=30°) 0.25 0.25 0.2 0.2 MODEL B (θ=30°) 0.15 0.15 MODEL C ( X=0.25m) (θ=30°) 0.1 0.1 MODEL C ( X=0.5m) (θ = 30°) 0.05 0.05 MODEL A (θ=60°) 0 0 MODEL B (θ=60°) -1.8 -1.3 -0.8 -0.3 0.20.7 1.2 -1.5 -1 -0.5 00.5 1 MODEL C ( X=0.25m) (θ = 60°) Cp Cp MODEL C ( X=0.5m) (θ = 60°) (g) Face G (h) Face H Fig. 18 Comparison of pressure coefficients along vertical centreline on different surfaces of various models for different angles of attack 1 3 Height (h) m Height (h) m Height (h) m Height (h) m Height (h) m Height (h) m Height (h) m Height (h) m International Journal of Advanced Structural Engineering (2018) 10:169–188 185 0.375m 0.25m 0.125m (a) Horizontal lines of different models along which pressure coefficients are compared 1.5 0.5 00.2 0.40.6 0.81 1.21.4 1.61.8 22.2 -0.5 -1 A B C D -1.5 Length (m) (b) Variation of pressure coefficients along perimeter at 0.375 m above base of MODEL A, MODEL B and MODEL C(X=0.25m) 1.5 0.5 00.2 0.40.6 0.81 1.21.4 1.61.8 22.2 -0.5 -1 A D -1.5 B C Length (m) (c) Variation of pressure coefficients along perimeter at 0.250 mm above base of MODEL A and MODEL B 1.5 0.5 00.2 0.40.6 0.81 1.21.4 1.61.8 22.2 -0.5 -1 A B C D -1.5 Length (m) (d) Variation of pressure coefficients along perimeter at 0.125m above base of MODEL A and MODEL B Fig. 19 Variation of pressure coefficients along perimeter of different models 1 3 Pressure Coeﬃcient (Cp) Pressure Coeﬃcient (Cp) Pressure coeﬃcient (Cp) 186 International Journal of Advanced Structural Engineering (2018) 10:169–188 1.5 0.5 00.2 0.40.6 0.81 1.21.4 1.61.8 22.2 2.42.6 2.83 -0.5 AR H G F AL B C D -1 Length (m) -1.5 (e) Variation of pressure coefficients along perimeter at 0.125 m above base of MODEL C(X=0.25m) and MODEL C (X=0.5m) Fig. 19 (continued) • From numerical data, it is found that maximum posi- tions of Faces A, B, C and D do not experience a large tive mean pressure coefficient of 0.81 occurs on Face variation of pressure for different areas of opening. But A of Model A when the wind incidence angle is 0 , and the lower portion of Faces F, G and H experience maxi- maximum negative mean pressure coefficient of − 0.85 mum increase in pressure with the increase in area of occurs on Face E of Model C (x = 0.25 m) at angle of opening. = • attack 60 . Face E experiences more negative pressure in Model C • From numerical data, it is found that force coefficient due to flow separation and formation of vortex inside the (C ) along the X direction has a maximum value of courtyard. 2.267 for Model C (x = 0.5 m) at 0 wind angle and the • Furthermore, some analytical expression has been pro- same along the Y direction is extreme for Model A at posed for each of the face of different building models 90 wind incidence angle with a value of 1.188. using least-squares regression polynomial. The force The windward faces experience positive pressure coef- coefficients along the X and Y directions are also fitted ficients since undeviating wind force is coming there. as least-squares regression polynomial. Accuracy of Due of frictional flow separation and formation of vor - the regression models is measured by R value. These tices, the leeward and side faces are exposed to suction expressions are very suitable in predicting mean wind pressure. pressure coefficient, and force coefficient at any wind • Formation of the vortices in the wake region happens in incidence angle varies between 0° and 180° for the build- the presence of windward side pressure force and leeward ing models. side suction force. It causes the deflection of the body. • From curve fitting polynomials, it is found that maximum Formation of vortices inside the inner courtyard also positive mean pressure coefficient of 0.99 occurs on Face ◦ ◦ ◦ occurs due to the inward flow for 30 and 60 wind inci- A of Model A when the wind incidence angle is 11 and dence angle. maximum negative mean pressure coefficient of − 0.79 • The maximum variation of pressure occurs on outside occurs on Face E of Model C (x = 0.20 m) at angle of Faces A, B and C and inside Faces F, G and H. attack 60 . Force coefficient (C ) along the X direction • Not only the opening Face A, but also the other outer has a maximum value of 2.11 for Model C (x = 0.5 m) Faces B, C and D also change their C value due to the at 0 wind angle and the same along the Y direction is change in opening. extreme for Model C (x = 0.5 m) at 60 wind incidence Variations of pressure coefficient along horizontal and angle with a value of 1.1 vertical centerline have also been studied. Different por - 1 3 Pressure Coeﬃcient (Cp) International Journal of Advanced Structural Engineering (2018) 10:169–188 187 Open Access This article is distributed under the terms of the Crea- The sum of squares of residuals: tive Commons Attribution 4.0 International License (http://creat iveco mmons.or g/licenses/b y/4.0/), which permits unrestricted use, distribu- n tion, and reproduction in any medium, provided you give appropriate SS = (y − y ̂ ) . res i i credit to the original author(s) and the source, provide a link to the i=1 Creative Commons license, and indicate if changes were made. The total sum of squares: Appendix SS = (y − y ̃) . tot i i=1 The mean pressure coefficients for Models A and B vary The most general definition of the coefficient of deter - with angle of attack only. So, we can form a single variable 2 k mination is, kth degree polynomial, y = + + x +⋯ + x for 0 1 2 k finding the values of C for different wind angles. SS res R = 1 − . The variation of mean pressure coefficients and force SS tot coefficients for Model C is dependent on two variables, wind MATLAB software is used for all these curve fitting angle and height of opening. As there is an interaction operations. between these two variables, so a second-order polynomial ∑ ∑ ∑ ∑ k k k of form y = 𝛼 + 𝛼 x + 𝛼 x + 𝛼 x x is 0 j j jj ij i j j=1 j=1 j i<j j=2 References required to predict the equations. To evaluate the approximation functions, is incorpo- Amin JA, Ahuja AK (2011) Experimental study of wind-induced pres- rated to counter the approximation error. sures on buildings of various geometries. Int J Eng Sci Technol 3(5):1–19 So, by including , both the equations can be expressed ANSYS, Inc. (2015) Tutorial for ANSYS CFX 16.0, 2015. http://www. in a matrix form y = x + ansys .com. Accessed 15 Apr 2017 Now, to find the coefficients of approximated equations, AS, NZS: 1170.2 (2011) Structural design actions, part 2: wind actions. we have to use least-squares method. Standards Australia/Standards New Zealand, Sydney ASCE: 7–16 (2016) Minimum design loads for buildings and other struc- By this approach, sum of the square of error of all tures. Structural Engineering Institute of the American Society of simultaneous equation needs to be minimised. Civil Engineering, Reston We wish to find the vector of least-squares estimators, Bhattacharyya B, Dalui SK, Ahuja AK (2014) Wind induced pres- S, that minimises sure on „E‟ plan shaped tall buildings. Jordon J Civil Eng 8(2):120–134 Chakraborty S, Dalui SK, Ahuja AK (2014) Wind load on irregular plan 2 T T shaped tall building—a case study. Wind Struct Int J 19(1):59–73 S = = =( − x) ( − x). Franke J, Hirsch C, Jensen A, Krus H, Schatzmann M, Westbury P, Miles i=1 S, Wisse J, Wright NG (2004) Recommendations on the use of CFD in wind engineering. In: COST action C14: impact of wind and For minimum error, partial differentiation of S with storm on city life and built environment. von Karman Institute for respect to , must be zero. Fluid Dynamics After differentiation and simplification, the predicted Fu JY, Li QS, Wu JR, Xiao YQ, Song LL (2008) Journal of Wind Engi- least-squares estimator of is found as, neering field measurements of boundary layer wind characteristics and wind-induced responses of super-tall buildings. J Wind Eng Ind T −1 T =( ) . Aerodyn 96:1332–1358 Gomes Ã, Rodrigues AM, Mendes P (2005) Experimental and numerical And the predicted response values, study of wind pressures on irregular-plan shapes. J Wind Eng Ind Aerodyn 93:741–756 y ̂ = x. IS: 875 (2015) Indian standard code of practice for design loads (other The accuracy of the fitted polynomial can be obtained than earthquake) for buildings and structures, part 3 (wind loads). Bureau of Indian Standards, New Delhi from the R value. It provides a measure of how well the Jones WP, Launder BE (1972) The prediction of laminarization with observed outcomes are reflected by the model, based on a two-equation model of turbulence. Int J Heat Mass Transf the proportion of total variation of the outcomes. 15(1972):301–314 If a dataset has n values marked y ….y , each associated Kumar EK, Tamura Y, Yoshida A, Kim YC, Yang Q (2013) Journal of 1 n wind engineering experimental investigation on aerodynamic char- with a predicted (or modelled) value y ̂ …y ̂ 1 n acteristics of various triangular-section high-rise buildings. 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J Wind Eng Ind Aerodyn 149:1–16 J 19(5):523–540 Tominaga Y, Blocken B (2016) Wind tunnel analysis of flow and disper - Paul R, Dalui SK (2016) Wind effects on “Z” plan-shaped tall building: sion in cross-ventilated isolated buildings: impact of opening posi- a case study. Int J Adv Struct Eng. https ://doi.org/10.1007/s4009 tions. J Wind Eng Ind Aerodyn 155:74–88 1-016-0134-9https ://en.wikip edia.org/wiki/Coe fficien t_of_deter minat ion Raj R, Ahuja AK (2013) Wind loads on cross shape tall buildings. J Acad Ind Res 2(2):111–113 Publisher’s Note Springer Nature remains neutral with regard to Ramponi R, Blocken B (2012) CFD simulation of cross-ventilation for jurisdictional claims in published maps and institutional affiliations. a generic isolated building: impact of computational parameters. Build Environ 53:34–48 Sarath KH, Selvi RS, Joseph AA, Ramesh BG, Srinivasa RN, Guru JJ (2015) Aerodynamic coefficients for a rectangular tall building 1 3
International Journal of Advanced Structural Engineering – Springer Journals
Published: Jun 4, 2018
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