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If you need an account, please register here Email [ ] Password [ ] Forgot password? Keep me logged in [ ] [LOGIN] Journal logo Nuclear explosion impact on humans indoors * PDF * Tools + Download Citation + Add to favorites + Reprints and Permissions * Share E-mail Facebook Linkedin Twitter Reddit Mendeley Recommend to Librarians * Home > * Physics of Fluids > * Volume 35, Issue 1 > * 10.1063/5.0132565 Check for updates on crossmark Prev Next related articles Energy indoors more... Sakharov, Gorbachev, and nuclear reductions Frank von Hippel more... Alert status of nuclear weapons Hans M. Kristensen more... The Nuclear Non-Proliferation Treaty and the Comprehensive Nuclear-Test-Ban Treaty, the relationship Thomas Graham Jr. more... Nuclear weapons modernizations Hans M. Kristensen more... The future of U.S.-Russia nuclear arms control Steven Pifer more... Nuclear terrorism - Threat or not? Miles A. Pomper and Gabrielle Tarini more... 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Free Submitted: 29 October 2022 Accepted: 05 December 2022 Published Online: 17 January 2023 * Nuclear explosion impact on humans indoors * featured Physics of Fluids 35, 016114 (2023); https://doi.org/10.1063/ 5.0132565 [orcid] Ioannis W. Kokkinakis^a) and [orcid] Dimitris Drikakis^b) more...View Affiliations * University of Nicosia, Nicosia CY-2417, Cyprus * ^a)Electronic mail: [email protected] ^b)Author to whom correspondence should be addressed: [email protected] View Contributors * Ioannis W. Kokkinakis: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing - original draft (equal); Writing - review & editing (equal). * Dimitris Drikakis: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing - original draft (equal); Writing - review & editing (equal). * PDF * CHORUS * Abstract * Full Text * Figures * Tools + Download Citation + Add to Favorites + Reprints and Permissions * E-mail Facebook Linkedin Twitter Reddit Mendeley Recommend to Librarian * Share E-mail Facebook Linkedin Twitter Reddit Mendeley Recommend to Librarian metrics 0 Views * Topics + Collections o Featured o Press Release + Topics o Fluid dynamics o Computational fluid dynamics o Nuclear weapons o Nuclear explosions o Gravitational force o Finite volume methods o Aerodynamics o Fluid drag o Shock waves o Ideal gas ABSTRACT This study investigates the nuclear blast effects on humans inside a building within a moderate damage zone. These effects depend on many parameters that must be better understood. In addition, the nuclear blast effects will spread further away than the devastating destruction zone, where most people are killed instantly. However, these injuries will vary depending on a person's position in the building and the air velocities attained when the blast wave enters indoors. The blast wave effects are examined for an indicative, easily reproducible indoor arrangement. The airspeed behind the blast wave accelerates to even higher velocities in the interior. The supersonic shock waves arising from the blast undergo expansion as they enter a room through an opening leading to channeling effects. The results show that most of the air is directed toward the corridor rather than through the opposite room's door, leading to high airspeed developed in rooms further down the aisle. The airspeed attained in the interior is calculated for two blast wave overpressures, 3 and 5 pounds per square inch, for which most concrete buildings do not collapse. The data reveal that the force applied to a standing person from the speed of the gusts formed at several locations in the interior is equivalent to several g-forces of body mass acceleration capable of lifting and throwing any person off the ground. It is then the impact onto solid surfaces that can lead to severe injury or death. Finally, the results reveal preferential areas in the rooms where a human can avoid the risk of exposure to the highest wind forces. I. INTRODUCTION Section: [Choose ] Previous sectionNext section The detonation of a nuclear bomb will have devastating effects on humans and assets. The shock waves and thermal and ionizing radiation will cause destruction. Moreover, radioactive fallout will impact for years. The shock waves will cause most of the damage through fast changes in air pressure that will destroy people, trees, and manufactured structures. The destruction will depend on the magnitude of the explosion, and the greater the distance one wants to achieve, the greater the burst height should be. Air bursts will result in higher overpressures at longer distances. In contrast, surface explosions will lead to higher overpressures at closer distances. Although estimating the various effects at different distances is complicated, a general assessment based on past nuclear tests and engineering projections suggests that overpressures at and above 20 pounds per square inch (psi) will partially or entirely demolish heavy concrete buildings.^1-31. S. Glasstone and P. J. Dolan, The Effects of Nuclear Weapons, 3rd ed. ( US Department of Defense, US Department of Energy, Washington, DC, 1977).2. G. F. Kinney and K. J. Graham, Explosive Shocks in Air ( Springer, Berlin, Heidelberg, 1985).3. Federal Emergence Management Agency (FEMA), Planning Guidance for Response to a Nuclear Detonation, 3rd ed. ( U.S. Department of Homeland Security, 2022). At 10 psi, most people will die, and severe damage will occur. At 5 psi, severe injuries and fatalities to humans will be widespread and significant damage to heavy structures will occur. Finally, at longer distances featuring 3 psi, overpressure will result in severe human injuries, and the destruction of smaller built-in structures.^33. Federal Emergence Management Agency (FEMA), Planning Guidance for Response to a Nuclear Detonation, 3rd ed. ( U.S. Department of Homeland Security, 2022). For the range of overpressures below 5 psi, humans outdoors will be exposed to the absolute risk of severe injury or death. The blast waves, debris from structures, radiation, and nuclear fallout will cause the above. Several studies in the past have simulated the dispersion and deposition of radioactive fallout from nuclear tests^4,54. B. E. Moroz, H. L. Beck, A. Bouville, and S. L. Simon, " Predictions of dispersion and deposition of fallout from nuclear testing using the NOAA-HYSPLIT meteorological model," Health Phys. 99, 252-269 (2010). https://doi.org/10.1097/HP.0b013e3181b436975. J. C. Schofield, " Mapping nuclear fallout using the weather research & forecasting (WRF) model," Ph.D. thesis [ Air Force Institute of Technology (AFIT) , 2012]. or terrorist nuclear detonations^6-86. R. E. Marrs, " Radioactive fallout from terrorist nuclear detonations," Technical Report No. UCRL-TR-230908 ( Lawrence Livermore National Laboratory, 2007).7. Assessing Medical Preparedness to Respond to a Terrorist Nuclear Event: Workshop Report, edited by G. C. Benjamin , M. McGeary , and S. R. McCutchen ( Institute of Medicine Committee on Medical Preparedness for a Terrorist Nuclear Event, National Academies Press, Washington, DC, 2009).8. M. Levi, On Nuclear Terrorism ( Harvard University Press, Cambridge, MA/London, England, 2021). and modeled the radioactive fallout from stabilized nuclear clouds^99. G. Rolph, F. Ngan, and R. Draxler, " Modeling the fallout from stabilized nuclear clouds using the HYSPLIT atmospheric dispersion model," J. Environ. Radioact. 136, 41-55 (2014). https://doi.org/10.1016/ j.jenvrad.2014.05.006 and atomic weapon tests.^1010. E. W. Bierly and A. W. Klement, " Radioactive fallout from nuclear weapons tests," Science 147, 1057-1060 (1965). https://doi.org/10.1126/ science.147.3661.1057 Obviously, near the nuclear bomb detonation, the devastation would be widespread, and the fatality rate would be practically 100%. However, outside of the severe damage zone (SDZ), the effect of the blast reduces and survivability increases. Severe injuries can be reduced at distances corresponding to overpressures below 5 psi, particularly for people inside concrete buildings within the moderate damage zone (MDZ). In this case, the primary danger to human survivability in indoor spaces becomes the extreme high-speed winds that enter through the various openings in the building, e.g., windows. In addition, the propagation of shock waves indoors will interact with walls and deflect around corners, doors, and obstacles. These interactions may induce higher pressures due to channeling effects, thus increasing the injury risk. The problem is multiparametric, as indoor spaces vary depending on obstacles and architectural layout. Thus, the details of the phenomena will be dependent on indoor arrangement. Despite that, significant conclusions can be drawn from the induced forces, which can help minimize the effect of blast impact. This study shows that in the range of nuclear explosion far-field overpressures below 5 psi, the injury for people indoors can vary and be reduced depending on the position of humans in the building. Tactical nuclear weapons range between 5 and 15 kilotons (kT). In the present study, however, we have chosen a 750 kT atomic warhead as this corresponds to an extreme scenario of an upper range value of a multiple independently targetable reentry vehicle (MIRV), for example, the RS-28 Sarmat (Satan II).^1111. A. Genys, http:// www.military-today.com/missiles/rs28_sarmat.htm " RS-28 Sarmat," (last accessed October 18, 2022). Of course, this scenario is unthinkable, but it represents a catastrophic scenario due to the existence of such a warhead and the increasing geopolitical tensions. Therefore, we aim to alert the world through rigorous scientific simulations of the impact of such a scenario, particularly in MDZ. To the best of our knowledge, no previous studies have examined the risk to humans caused by high-speed winds from nuclear blasts entering buildings within the MDZ. Section II provides a brief description of the computational methodology. Section III describes (i) the computational setup used to simulate the nuclear blast in Sec. III A, (ii) the equations for modeling the blast wave at the building windows, Sec. III B, (iii) the layout and dimensions of a (simplified) model room layout, Sec. III C, and (iv) the calculation of the force on a human, Sec. III D. In Sec. IV, we present the simulation results obtained for the considered nuclear blast scenario of a 750 kT atomic warhead, Sec. IV A and establish the hazard imposed to humans indoors within the MDZ, Sec. IV B. Finally, in Sec. V, we summarize the main findings drawn from this study. II. COMPUTATIONAL METHODOLOGY Section: [Choose ] Previous sectionNext section We solve the compressible Euler equations for ideal gas using the finite volume method (FVM). In integral form, the equations are formulated as follows: [?][?]t[?]Vr dV=-[?]Aru*n dA, (1) [?][?]t[?]Vru dV=-[?]A(ruu+pI)*n dA+[?]Vrfb dV, (2) [?][?]t[?]Vret dV=-[?]A(ret+p)u*n dA+[?]Vrfb*u dV, (3) where r is the density; u is the velocity vector; p is the static pressure; n is the outward pointing unit normal of a surface element dA of the closed finite control volume dV; fb is the external body force vector defined in Sec. III A; et=e+u*u/2 is the total energy per unit mass; e=cvT is the specific internal energy. Furthermore, T is the temperature, c[v] is the specific heat capacity at constant volume, and g is the heat capacity ratio (g=cp/cv), where c[p] is the specific heat capacity at constant pressure. The ideal gas equation of state is employed, p=rR*T, where R*=287.05 J/kg K is the specific gas constant of atmospheric air. We have employed the computational fluid dynamics (CFD) code CNS3D,^ 1212. I. Kokkinakis, D. Drikakis, K. Ritos, and S. M. Spottswood, " Direct numerical simulation of supersonic flow and acoustics over a compression ramp," Phys. Fluids 32, 066107 (2020). https://doi.org/ 10.1063/5.0010548 which has been extensively validated against theoretical and computational results for shock-physics flows.^13,14 13. M. Hahn, D. Drikakis, D. L. Youngs, and R. J. R. Williams, " Richtmyer-Meshkov turbulent mixing arising from an inclined material interface with realistic surface perturbations and reshocked flow," Phys. Fluids 23, 046101 (2011). https://doi.org/10.1063/1.357618714. A. Bagabir and D. Drikakis, " Numerical experiments using high-resolution schemes for unsteady, inviscid, compressible flows," Comput. Methods Appl. Mech. Eng. 193, 4675-4705 (2004). https:// doi.org/10.1016/j.cma.2004.03.012 A detailed description of the numerical methods used can be found in the study by Kokkinakis et al. ^1212. I. Kokkinakis, D. Drikakis, K. Ritos, and S. M. Spottswood, " Direct numerical simulation of supersonic flow and acoustics over a compression ramp," Phys. Fluids 32, 066107 (2020). https://doi.org/ 10.1063/5.0010548 In brief, CNS3D uses an upwind, Godunov-type method for the convective terms. We discretize the inter-cell numerical fluxes by solving the Riemann problem using the reconstructed values of the primitive variables at the cell interfaces. We use a one-dimensional swept unidirectional stencil for the reconstruction of the variables. The Riemann problem is solved using the so-called "Harten, Lax, van Leer, and (the missing) Contact" (HLLC) approximate Riemann solver.^1515. E. F. Toro, M. Spruce, and W. Speares, " Restoration of the contact surface in the HLL-Riemann solver," Shock Waves 4, 25-34 (1994). https://doi.org/10.1007/BF01414629 A one-dimensional swept unidirectional stencil is used for the reconstruction of the variables. High-resolution (11th-order) discretization is achieved in the framework of the Weighted-Essentially Non-Oscillatory (WENO) scheme^1616. D. S. Balsara and C.-W. Shu, " Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy," J. Comput. Phys. 160, 405-452 (2000). https://doi.org/10.1006/ jcph.2000.6443 with specific implementation details previously presented.^1212. I. Kokkinakis, D. Drikakis, K. Ritos, and S. M. Spottswood, " Direct numerical simulation of supersonic flow and acoustics over a compression ramp," Phys. Fluids 32, 066107 (2020). https://doi.org/10.1063/5.0010548 We briefly mention below the WENO characteristics in the framework of CNS3D. The left and right reconstruction stencils are normalized, per variable, according to a transformation function.^1212. I. Kokkinakis, D. Drikakis, K. Ritos, and S. M. Spottswood, " Direct numerical simulation of supersonic flow and acoustics over a compression ramp," Phys. Fluids 32, 066107 (2020). https://doi.org/10.1063/5.0010548 The transformation normalizes the candidate stencils so that the entire stencil's maximum value equals one. The minimum value takes a positive and nonzero value, and the value range scales relative to the maximum. Normalizing the total stencil values per variable prevents negative WENO smoothness indicator values, reduces the numerical dissipation, and simplifies applying the proceeding step. Furthermore, the WENO implementation^1212. I. Kokkinakis, D. Drikakis, K. Ritos, and S. M. Spottswood, " Direct numerical simulation of supersonic flow and acoustics over a compression ramp," Phys. Fluids 32, 066107 (2020). https://doi.org/10.1063/5.0010548 uses a total variation (TV) limiting procedure for each candidate stencil and obtains the maximum TV ratio between the candidate stencils. If all stencils contain significant discontinuities, the maximum TV ratio can be incorrectly small. Thus, an additional criterion is introduced through the linear WENO weights, i.e., the standard WENO weights are also modified according to the mapped WENO (WENO-M) approach.^1717. A. K. Henrick, T. D. Aslam, and J. M. Powers, " Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points," J. Comput. Phys. 207, 542-567 (2005). https://doi.org/10.1016/j.jcp.2005.01.023 Extensive past research has shown that the order of accuracy and the numerical design of the method used for the discretization of the convective (non-linear) terms significantly influence the accuracy of the simulations.^18,1918. Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics, edited by F. Grinstein , L. Margolin , and W. Rider ( Cambridge University Press, 2007).19. K. Ritos, I. W. Kokkinakis, D. Drikakis, and S. M. Spottswood, " Implicit large eddy simulation of acoustic loading in supersonic turbulent boundary layers," Phys. Fluids 29, 046101 (2017). https://doi.org/10.1063/ 1.4979965 The above is due to the non-linearity of these terms responsible for capturing shock waves and contact discontinuities. The solution is advanced in time using a five-stage (fourth-order accurate) optimal strong-stability-preserving Runge-Kutta method.^20 20. R. Spiteri and S. Ruuth, " A new class of optimal high-order strong-stability-preserving time discretization methods," SIAM J. Numer. Anal. 40, 469-491 (2002). https://doi.org/10.1137/ S0036142901389025 III. COMPUTATIONAL PROBLEM DESCRIPTION Section: [Choose ] Previous sectionNext section The computational domain is discretized using a uniform Cartesian mesh for the fireball and the indoor simulations. We performed simulations using half of the mesh resolution and found that this reduces the accuracy of the calculated forces by up to 5%. We concluded that the employed mesh resolutions provide an optimal approach regarding the accuracy and computational cost. A. Nuclear blast simulation The 3D fireball test case represents a 750 kT air burst detonated in the planar center and at the height of he=2840 m in a domain of size 6 x 6 x 13 km^3 (Fig. 1). The computational domain is discretized using a cell size of 40 m. A symmetry boundary condition is used to model the ground and a (non-reflective) buffer layer is used for all other boundary surfaces. figure FIG. 1. Three-dimensional illustration of the air blast and the generated blast wave 10 s following the detonation of a 750 kT nuclear warhead above a typical metropolitan city; the radius of the shock bubble at ground level is 4.6 km, with a peak overpressure of slightly over 7 psi. * PPT| * High resolution The test problem is based on the superposition of heated gas representing a fireball with a standard lapse atmosphere. The only external body force is gravity, with the initial atmosphere setup to be in static equilibrium under this force. It is assumed that the ideal gas equation of state holds and that the specific heat capacities are constant for all temperatures and densities and are, therefore, calorically perfect. The lapse atmosphere is used to model the atmospheric air properties as a function of the altitude:^2121. E. Houghton, P. Carpenter, S. H. Collicott, and D. T. Valentine, Aerodynamics for Engineering Students, 6th ed. ( Butterworth-Heinemann, Boston, 2013). T(h)=T0-Lp h,p(h)=p0(T(h)T0)ex,r(h)=r0(T(h)T0)ex-1, (4) where h is the altitude, ex=g/(LpR*) is the exponential term, the gravity is g = 9.81 m/s^2, standard atmospheric conditions are considered at sea level, i.e., T0=288.15 K, p0=101 325 Pa, r0=1.225 kg/m^3, specific gas constant R*=287 J/kg K, and finally, the lapse rate Lp=6.5x10-3 K/m. The above values are (strictly) valid up to an altitude of ~ 13 km. Moreover, the body force term in Eqs. (2) and (3) is zero in all directions except the vertical (y-direction), which is obtained according to fby(h)=-dp(h)/dh to ensure hydrostatic equilibrium. An initial explosion fireball radius of R[e] = 80 m is used, within which the internal energy of the air corresponds to the strength of the explosion considered. B. Blast wave properties We calculated the flow conditions behind the blast wave for the two overpressures, p[op], of 3 and 5 psi considered, using the below procedure. The static pressure after the blast shock wave is ps=p0+pop, where p0 =101 325 Pa is the standard atmospheric ambient pressure at ground level. The Mach number of the shock wave is obtained by Ms=g-12g+g+12gpsp0. (5) The velocity of the propagating shock wave and the density of the air at the shock wave are given by us=Msgp0/r0 (6) and rs=(g+1)Ms2+(g-1)Ms. (7) The velocity of the shocked air, i.e., wind speed at the shock wave, is given by usa=us(1-1/rs). (8) The pressure after the passage of the blast will gradually decay over time until it eventually drops below the atmospheric ambient pressure. The time interval from the initial pressure peak to the first recovery (ambient value) is called the positive shock duration (td+). Various empirical relations have been developed to provide an estimate for the duration of the positive pressure of the blast pressure wave.^2222. A. Ullah, F. Ahmad, H.-W. Jang, S.-W. Kim, and J.-W. Hong, " Review of analytical and empirical estimations for incident blast pressure," KSCE J. Civ. Eng. 21, 2211-2225 (2017). https://doi.org/10.1007/s12205-016-1386-4 Here, we employed the following form:^2323. M. Sadovskiy, " Mechanical effects of air shockwaves from explosions according to experiments," in Selected Works: Geophysics and Physics of Explosion ( Nauka Press, Moscow, 2004). td+=0.0012W6R, (9) where R is the distance from the center of a spherical charge in meters (m), and W is the charge mass expressed in kilograms (kg) of trinitrotoluene. The resulting value of td+, Eq. (9), is in units of seconds. The radius (meters) of the blast wave is calculated to give the target overpressure p[op]:^2424. M. Held, " Blast waves in free air," Propellants, Explos., Pyrotech. 8, 1-7 (1983). https://doi.org/ 10.1002/prep.19830080102 R=10002W2/3/pop. (10) Based on various empirical relations in the literature, Eqs. (9) and (10) were found to have the best agreement for the simulation results of the nuclear bomb air blast scenario considered in this study. The exponential decay phase of the blast wave pressure front can be calculated using the modified Friedlander's equation:^25,2625. J. Henrych, The Dynamics of Explosion and Its Use ( Elsevier Scientific Publishing Company, Amsterdam and New York, 1979), p. 562.26. W. Baker, P. Cox, J. Kulesz, R. Strehlow, and P. Westine, Explosion Hazards and Evaluation ( Elsevier Science, 1983), p. 840. p(t)=(1-ttd+)exp (-a ttb+)pop+p0, (11) where the time, t, is measured from when the overpressure peak occurs, and a is a constant controlling the decay rate. The density behind the blast wave at ground level is obtained using the following isentropic relations: r(t)=p(t)r0p0. (12) Finally, the velocity of the air behind the shock is calculated as:^ 2727. J. M. Dewey, " The air velocity in blast waves from TNT explosions," Proc. R. Soc. London, Ser. A 279, 366-385 (1964). https: //doi.org/10.1098/rspa.1964.0110 u(t)=usa(1-bt) exp (-at)+a ln (1+bt), (13) where a and b are constants obtained from Dewey.^2727. J. M. Dewey, " The air velocity in blast waves from TNT explosions," Proc. R. Soc. London, Ser. A 279, 366-385 (1964). https://doi.org/10.1098/ rspa.1964.0110 C. Rooms layout Figure 2 shows the indoors arrangement considered in this study. The floor plan is symmetric, with the centerline going through the middle of the lower room, which permits the simulation of just half of the interior domain, thus, reducing the overall computational cost. figure FIG. 2. Three-dimensional Illustration of the considered interior floor plan; mirror symmetry is set in the lateral direction. * PPT| * High resolution The dimensions of the rooms, corridor, windows, and doors are given in Fig. 3. They are typical among residential buildings. For example, interior doors have 36 x 80 in.^2 in width and height. The windows and doors have the same width and finish at the same height of 60 in. ^2828. B. Mahajan, see https://civiconcepts.com/blog/ standard-window-size for " What is Standard Window Size" (2019-2022) (last accessed 21 October, 2022). This gives a surface area of ~ 900 square inches, which is close to the minimum net-clear opening area of 821 square inches (or 5.7 square feet) set by the 2012 International Residential Code (IRC)^2929. International Code Council, 2012 International Residential Code (ICC, 2019); https:// codes.iccsafe.org/content/IRC2012P13/ for an egress window in residential properties. figure FIG. 3. Detailed schematic of the considered room layout; all dimensions in meters; top: isometric view, middle: door dimensions, bottom: window dimensions. * PPT| * High resolution A symmetry boundary condition is used to model the walls (slip wall), whereas all windows are set as outflow except from which the blast wave enters (inflow). The computational domain is discretized using a cell size of 3 inches. The shock wave enters the interior through the window of the front room (Fig. 2). According to Sec. III B, at the time of the peak overpressure, at the window inlet (t = 0), the values of density and velocity are r[?]1.4 kg/m^3 and usa[?]45.78 m/s for an overpressure of 3 psi, and r[?]1.51 kg/m^3 and usa[?]72.77 m/s for an overpressure of 5 psi. The pressure, density, and inlet velocity gradually decrease over time for Eqs. (11)-(13). D. Wind force on human The dynamic pressure is related to the mass airflow (gust) generated by the passing pressure wave. For example, a very high wind velocity can occur even at a slight overpressure. Dynamic pressure is highly destructive and is one of the leading causes of destruction caused by a nuclear explosion. Aside from the damage caused to buildings, the dynamic pressure can also lead to severe human injuries and fatalities. Given the known area (A) and coefficient of drag (C[d]) of some objects, it is possible to calculate the resulting force from the airflow. Here, we assume an average built person standing upright with a drag coefficient of Cd[?]1.3 and a height and frontal area of 1.76 m and ~Ah=0.65 m^2, respectively, giving CdAh[?]0.84; these values are typical for an average human adult.^3030. J. F. R. McIlveen, " The everyday effects of wind drag on people," Weather 57, 410-413 (2002). https://doi.org/10.1256/wea.29.02 The force exerted by the wind is then given by Fair=12ru2CdAh. (14) It is possible to estimate the force of the airspeed acting on a standing person at each location in the interior (xz-plane) using the computational results: Fs=Cd2[?]y=0Ly[?]s=s1s2rus|us|) ds dy, (15) where s is a direction on the xz-plane. We considered the directions defined by the unit vectors (1, 0), (0, 1), (1/2,1/2), and (1/2,-1/2) , e.g., the normal and diagonal directions (Fig. 4); us is the velocity in the s-direction, and ds is the computational cell's projected area on the plane normal to the said direction. Finally, Ly =1.76 m is the average person's height and Ls=Ah/Ly=|s1-s2| is the average width. The values of s1,2 are adjusted at each location such that Ls=Ah/Ly always holds. figure FIG. 4. Illustration of the aerodynamic drag force as per Eq. (15). * PPT| * High resolution IV. DISCUSSION Section: [Choose ] Previous sectionNext section A. Nuclear explosion scenario We simulated a nuclear blast explosion of a 750 kT atomic warhead. This detonation is a typical upper range value of a multiple independently targetable reentry vehicle (MIRV), for example, the RS-28 Sarmat (Satan II).^1111. A. Genys, http:// www.military-today.com/missiles/rs28_sarmat.htm " RS-28 Sarmat," (last accessed October 18, 2022). The nuclear warhead detonation is set to occur at an altitude of 2.84 km above ground to maximize the distance over which the pressure behind the blast wave has an overpressure above 5 psi,^3131. A. Wellerstein, https:// nuclearsecrecy.com/nukemap/?&kt=750&lat=51.499167&lng=-0.124722& hob_psi=5&hob_ft=9308&psi=5,1,3&rem=&zm=11 " Nukemap" (last accessed October 18, 2022). i.e., to maximize the moderate to severe damage zone (MDZ-SDZ) to buildings in a city.^33. Federal Emergence Management Agency (FEMA), Planning Guidance for Response to a Nuclear Detonation, 3rd ed. ( U.S. Department of Homeland Security, 2022). An illustration of the obtained explosion and resulting blast wave about 10 s after detonation is given in Fig. 1. The radius of the blast wave at ground level is about 4.6 km, while its peak overpressure is slightly over 7 psi. According to Glasstone and Dolan,^11. S. Glasstone and P. J. Dolan, The Effects of Nuclear Weapons, 3rd ed. ( US Department of Defense, US Department of Energy, Washington, DC, 1977). the fireball size at the late stages of the explosion will be approximately twice that of the fireball's luminosity profile breakaway with time. The relationship between the maximum fireball radius and the bomb yield is, thus, given by R (2x@breakaway)[?]220 W0.4, where R is the fireball radius in feet, and W is the explosion yield in kilotons TNT equivalent. For the nuclear explosion yield considered here, W = 750 kT, R[?]3108 feet or ~1.02 km. This value matches the maximum fireball radius computationally obtained when measured based on the atmospheric air heated to temperatures at and above 5000 K. The evolution of the blast wave is shown in Fig. 5. The upper value limit (red color) corresponds to a maximum pressure value of 138 kPa, resulting in an overpressure of slightly over 5.3 psi. The results show the four stages of development of the spherical blast wave. In the first stage, the shock front forms as it separates from the rapid expansion of the air burst itself. In the second stage, the fully formed shock front ("incident" shock wave) travels toward the ground. Finally, a reflected wave is produced in the third stage as the incident shock wave reflects from the ground. For a smooth surface, the total reflected overpressure in the region near ground zero will be more than twice the value of the peak overpressure of the incident blast wave. Note that the reflected wave travels through atmospheric air, heated and compressed by the incident wave. As a result, the reflected wavefront moves faster than the incident wave and, under certain conditions, overtakes it so that the two wavefronts eventually merge to produce a single wavefront, called the "Mach stem." In Fig. 5, the Mach stem remains relatively small due to the explosion parameters considered. The above results and analysis also agree with the observations of Glasstone and Dolan.^11. S. Glasstone and P. J. Dolan, The Effects of Nuclear Weapons, 3rd ed. ( US Department of Defense, US Department of Energy, Washington, DC, 1977). figure FIG. 5. Two-dimensional contour plots of the shock wave evolution following the 750 kT detonation of a nuclear warhead; x and y axes are the ground distance and altitude in units of km; seconds after initial blast from left-to-right and top-to-bottom: 0.6, 2.8, 6.7, 12.0, 14.4, and 21.1. * PPT| * High resolution During the earlier time instants shown in Fig. 5, the pressure behind the blast wave is significantly higher, as evidenced by the saturation of the corresponding color (red). However, even 5 km from the explosion epicenter, the overpressure remains slightly above 5 psi (36.7 kPa). The thermal radiation emitted from such a nuclear explosion would be sufficient to cause third-degree burns (severe scarring or disablement, amputation) up to 10.7 km away.^3131. A. Wellerstein, https://nuclearsecrecy.com/nukemap/?&kt=750&lat= 51.499167&lng=-0.124722&hob_psi=5&hob_ft=9308&psi=5,1,3&rem=&zm=11 " Nukemap" (last accessed October 18, 2022). Moreover, since thermal radiation travels at the speed of light, its effect would be felt instantly and before the blast wave. Thus, the intense wind speeds behind the blast wave would also intensify and spread fires. Typically, overpressures of 5 psi cause moderate blast damage, e.g., most residential (timber) buildings collapse, injuries are universal, and fatalities are widespread. On the contrary, overpressures of 3 psi are estimated to lead to light and moderate damages in cities.^ 33. Federal Emergence Management Agency (FEMA), Planning Guidance for Response to a Nuclear Detonation, 3rd ed. ( U.S. Department of Homeland Security, 2022). Buildings are damaged between 2 and 5 psi, primarily due to the abrupt rise in the air velocity following the blast shock wave impact (Fig. 6). Though such overpressures are not sufficiently high to harm humans directly, despite the abrupt pressure rise, high-speed winds behind the blast wave can injure humans and cause fatalities. At an overpressure of 1 psi, glass windows may be partially damaged. At the overpressures of 3 and 5 psi considered here, most residential building windows will shutter instantly,^33. Federal Emergence Management Agency (FEMA), Planning Guidance for Response to a Nuclear Detonation, 3rd ed. ( U.S. Department of Homeland Security, 2022). and the blast wave is assumed to travel through the window unobstructed. Most residential buildings will not structurally withstand the wind speeds associated with higher overpressures and, thus, are not within the scope of the present study. figure FIG. 6. Two-dimensional contour plots of the pressure and airspeed generated behind the shock wave ~12 s after the detonation of a 750 kT nuclear warhead; x- and y- axis are the ground distance and altitude in units of km; skyscrapers depicted for reference are from right-to-left the Chrysler Building, the One World Trade Center, and the Burj Khalifa. * PPT| * High resolution B. Indoor hazard We examined the effect of the airspeed entering through a single window of an indicative indoor arrangement to establish the severity of danger to humans. Within the MDZ, the high-wind speeds behind the blast wave are one of the principal destruction mechanisms. The effects of wind at different velocities are described below: * 50 mph (22.35 m/s): raindrops begin to hurt; bending or leaning forward is required to stay balanced; large trees can be blown down. * 70 mph (31.3 m/s): maximum wind speed most humans can withstand without getting blown away; can blow down some street signs and power lines; cars start rocking and potentially flip. * 100 mph (44.7 m/s): The force exerted by the wind on a human is almost equivalent to the gravitational pull of the earth, e.g., the equivalent of walking up a vertical wall; likely to be blown away unless grabbing onto a firm object or hiding behind it; capable of moving most cars. * 120+ mph (53.65 m/s): staying upright is no longer possible. For indoor skydiving, wind tunnels are used to create artificial winds of 100-130 mph (~ 44.7-58.1 m/s) to keep a person facing head-on (face down in this case) "afloat" in the air against the pull of gravity. Figure 7 shows the 3D contours of the maximum airspeed attained. The highest speed is at the window and door of the front room (room 1), where the blast wave enters the space (Fig. 2). At an overpressure of 3 psi, the maximum internal airspeed is slightly over 140 m/s, whereas at 5 psi, it is slightly over 184 m/s. The short time over which the high-speed winds occur does not allow sufficient time to take a protective stance, e.g., lean forward, bend, lie flat on the floor, etc. Sustaining wind speeds of 140 m/s for about 1 s would lift and throw most humans off the ground. figure FIG. 7. Contours of the maximum airspeed attained during the first 10 s after the blast wave enters the window; overpressure of (top) 3 psi, and (bottom) 5 psi. * PPT| * High resolution The results show that the maximum indoor air velocities are much higher compared to the airspeed entering through the window, i.e., the blast wave peak wind velocities (outdoors) are 46 and 73 m/s at 3 and 5 psi overpressures, respectively, while the indoor peak velocities are 140 and 184 m/s, respectively. The physical mechanism responsible for the increased interior wind speed is the sudden expansion of the shock through the front room window. The density of the shocked air behind the blast wave is higher than the local ambient value. Therefore, despite the shock's expansion process, the shock air density is around the ambient value. As a result, the effect of the dynamic pressure at such wind speeds indoors is comparable to the impact of the naturally occurring high-speed winds outdoors. An essential difference is a duration over which the high-speed wind will last. Nonetheless, despite the shorter time of the high-speed wind behind the blast wave, the imparted force still remains substantial. Moreover, high airspeed would accelerate flying debris picked up by the blast wave outdoors and pieces from the shuttered window. Therefore, numerous high-speed projectiles will impact the room as the blast wave develops after entering the room. In black powder muskets, firearm muzzle velocities range from approximately 120 to 370 m/s. Therefore, any solid debris traveling anywhere near such wind speeds has the potential to cause severe injury or fatalities. By applying the methodology of Sec. III D in conjunction with the computational results, we can estimate the maximum (aerodynamic) force exerted on an average weight person, approximately 80 kg,^32,33 32. S. C. Walpole, D. Prieto-Merino, P. Edwards, J. Cleland, G. Stevens, and I. Roberts, " The weight of nations: An estimation of adult human biomass," BMC Public Health 12, 439 (2012). https:// doi.org/10.1186/1471-2458-12-43933. Wikipedia Contributors, see https://en.wikipedia.org/w/index.php?title=Human_body_weight&oldid= 1096037841 for " Human Body Weight: Wikipedia, the Free Encyclopedia" (last accessed October 21, 2022). during the first 10 s after the blast wave enters. This allows the creation of a simple map indicating which indoor areas are hazardous. We use the gravitational force to normalize the wind force and plot the contour surface of the normalized force in Fig. 4. Areas at which the force exerted equals that of the gravitational force, F[g] = mg, are in yellow, indicating the potential hazard of losing balance and falling over (Fig. 8). Forces around F/Fg[?]0.5, green-colored areas, would remain hazardous, particularly for people weighing less than the average weight. Values of 5 and above, red-colored areas, would be extremely hazardous, with values above 10 reflecting stronger than hurricane forces being exerted. Such regions practically guarantee that humans would be violently pushed and thrown over. Most of the force is applied in less than half a second (Fig. 9). Using the data of Fig. 9, it is estimated that in the worst-case scenario and for the overpressure of 3 psi, an average-weight person standing in the corridor could be pushed about 10 m within less than a second, excluding surface friction and any change in the person's stand within that time. In the front room (room 1), the same person would be thrown about 9.5 m; in room 2, over 2.2 m; in room 3, around (approximately) 1.7 m. For an overpressure of 5 psi, and in the worst-case scenario, the average weight person could be thrown at a distance of 21 m in room 1, 8.5 m in room 2, 3.3 m in room 3, and 20 m in the corridor. figure FIG. 8. Contours of the maximum air force (as a multiple of the gravitational body force) applied to an average person during the first 10 s after the blast wave enters the window; results for overpressures of 3 and 5 psi are shown in the left and right plots, respectively. * PPT| * High resolution figure FIG. 9. Plot of the maximum air force (as a multiple of the gravitational body force) vs time applied to an average person during the first 10 s after the blast wave enters through the window; overpressure of (top) 3 psi, and (bottom) 5 psi. * PPT| * High resolution Due to the rooms' dimensions, humans will not be ejected such a large distance. Instead, they will be thrown with great force to the walls. In rooms 2 and 3, however, the force generated at 5 psi is sufficient to throw a person standing near the door out of the window. Otherwise, the impact on a solid surface will cause severe injury or death. Regarding critical indoor regions, the most dangerous locations are the corridor, near the doors, and particularly the front room area. At 5 psi, the critical region extends into room 2. The acceleration is also significant. For example, at an overpressure of 3 psi, the acceleration is 50 g in room 1 and 80 g in the corridor. At 5 psi, the acceleration exceeds 140 g. People can survive accelerations over 18 g momentarily and even withstand up to 35 g and still survive, as was demonstrated in the mid-1950s.^34,35 34. J. P. Stapp, " Effects of mechanical force on living tissues. I. Abrupt deceleration and windblast," J. Aviat. Med. 26, 268-288 (1955); see https://pubmed.ncbi.nlm.nih.gov/13242509/35. C. D. Hughes and J. P. Stapp, " Effects of mechanical force on living tissues. II. Supersonic deceleration and windblast," J. Aviat. Med. 27, 407-413 (1956); available at https://pubmed.ncbi.nlm.nih.gov/13366880/ In the same experiments, a (trained) test subject withstood 46.2 g over 1.1 s and was (surprisingly) still able to walk away unscathed. In another experiment, a person endured a whopping 40 g (albeit for 0.04 s) with a peak value of 83 g during a nearly instantaneous stop. ^3636. N. R. Council, Impact Acceleration Stress: A Symposium ( The National Academies Press, Washington, DC, 1962). The person walked away from the experiment without any side effects. Thus, despite the violent accelerations involved, the experiments show that the human body can handle massive g-loads, but only when subjected to them for a very short time. V. CONCLUSIONS Section: [Choose ] Previous section We studied the impact of a nuclear blast corresponding to a 750 kT atomic warhead on humans indoors in a nuclear explosion's moderate damage zone (MDZ). MDZ is the area where concrete buildings may not collapse. At distances featuring overpressures of 5 psi, severe injuries and fatalities will be widespread, and damage to heavy structures will occur. At longer distances featuring an overpressure of 3 psi, severe human injuries and the destruction of smaller built-in structures will occur. The study revealed that the airspeed behind the blast wave induces significant forces on humans indoors. The most potent forces are experienced for a short period of up to half a second. The airspeed behind the blast wave accelerates indoors to even higher velocities. This stems from the expansion of the shock waves entering the space through an opening such as a window. Furthermore, channeling effects can further accelerate the air in the corridors. The force hitting a standing person indoors is equivalent to several g-forces of body mass acceleration and could lift a person off the ground and throw them to the walls. At an overpressure of 3 psi, the acceleration can reach 80 g, while at 5 psi, the acceleration exceeds 140 g. However, there are areas inside the rooms where the airspeed and the associated forces are reduced. The simulations provide colored maps of the indoor areas where the risk of human injury is reduced. Given the findings, the relevant authorities could issue instructions to prevent the nuclear blast from affecting humans situated indoors from the exposure to high-speed winds behind the incoming blast waves. Moreover, the results could guide the future design of concrete structures. AUTHOR DECLARATIONS Conflict of Interest The authors have no conflicts to disclose. Author Contributions Ioannis William Kokkinakis: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing - original draft (equal); Writing - review & editing (equal). Dimitris Drikakis: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing - original draft (equal); Writing - review & editing (equal). DATA AVAILABILITY The data that support the findings of this study are available from the corresponding author upon reasonable request. REFERENCES 1. 1. S. Glasstone and P. J. Dolan, The Effects of Nuclear Weapons, 3rd ed. ( US Department of Defense, US Department of Energy, Washington, DC, 1977). Google ScholarCrossref 2. 2. G. F. Kinney and K. J. Graham, Explosive Shocks in Air ( Springer, Berlin, Heidelberg, 1985). Google ScholarCrossref 3. 3. Federal Emergence Management Agency (FEMA), Planning Guidance for Response to a Nuclear Detonation, 3rd ed. ( U.S. Department of Homeland Security, 2022). Google Scholar 4. 4. B. E. Moroz, H. L. Beck, A. Bouville, and S. L. 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Council, Impact Acceleration Stress: A Symposium ( The National Academies Press, Washington, DC, 1962). Google Scholar 1. (c) 2023 Author(s). Published under an exclusive license by AIP Publishing. Article Metrics Views 0 Citations Crossref 0 Web of Science ISI 0 Altmetric Please Note: The number of views represents the full text views from December 2016 to date. Article views prior to December 2016 are not included. [noscript-2] Resources * AUTHOR * LIBRARIAN * ADVERTISER General Information * ABOUT * CONTACT * HELP * PRIVACY POLICY * TERMS OF USE * FOLLOW AIP PUBLISHING: Website (c) AIP Publishing LLC. Article copyright remains as specified within the article. Scitation logo